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In all early civilizations, the first expression of mathematical understanding appears in the form of counting systems. Numbers in very early societies were typically represented by groups of lines, though later different numbers came to be assigned specific numeral names and symbols (as in India) or were designated by alphabetic letters (such as in Rome). Although today, we take our decimal system for granted, not all ancient civilizations based their numbers on a ten-base system. In ancient Babylon, a sexagesimal (base 60) system was in use.
The Decimal System in Harappa
In India a decimal system was already in place during the Harappan period, as indicated by an analysis of Harappan weights and measures. Weights corresponding to ratios of 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50, 100, 200, and 500 have been identified, as have scales with decimal divisions. A particularly notable characteristic of Harappan weights and measures is their remarkable accuracy. A bronze rod marked in units of 0.367 inches points to the degree of precision demanded in those times. Such scales were particularly important in ensuring proper implementation of town planning rules that required roads of fixed widths to run at right angles to each other, for drains to be constructed of precise measurements, and for homes to be constructed according to specified guidelines. The existence of a gradated system of accurately marked weights points to the development of trade and commerce in Harappan society.
Mathematical Activity in the Vedic Period
In the Vedic period, records of mathematical activity are mostly to be found in Vedic texts associated with ritual activities. However, as in many other early agricultural civilizations, the study of arithmetic and geometry was also impelled by secular considerations. Thus, to some extent early mathematical developments in India mirrored the developments in Egypt, Babylon and China . The system of land grants and agricultural tax assessments required accurate measurement of cultivated areas. As land was redistributed or consolidated, problems of mensuration came up that required solutions. In order to ensure that all cultivators had equivalent amounts of irrigated and non-irrigated lands and tracts of equivalent fertility - individual farmers in a village often had their holdings broken up in several parcels to ensure fairness. Since plots could not all be of the same shape - local administrators were required to convert rectangular plots or triangular plots to squares of equivalent sizes and so on. Tax assessments were based on fixed proportions of annual or seasonal crop incomes, but could be adjusted upwards or downwards based on a variety of factors. This meant that an understanding of geometry and arithmetic was virtually essential for revenue administrators. Mathematics was thus brought into the service of both the secular and the ritual domains.
Arithmetic operations (Ganit) such as addition, subtraction, multiplication, fractions, squares, cubes and roots are enumerated in the Narad Vishnu Purana attributed to Ved Vyas (pre-1000 BC). Examples of geometric knowledge (rekha-ganit) are to be found in the Sulva-Sutras of Baudhayana (800 BC) and Apasthmaba (600 BC) which describe techniques for the construction of ritual altars in use during the Vedic era. It is likely that these texts tapped geometric knowledge that may have been acquired much earlier, possibly in the Harappan period. Baudhayana's Sutra displays an understanding of basic geometric shapes and techniques of converting one geometric shape (such as a rectangle) to another of equivalent (or multiple, or fractional) area (such as a square). While some of the formulations are approximations, others are accurate and reveal a certain degree of practical ingenuity as well as some theoretical understanding of basic geometric principles. Modern methods of multiplication and addition probably emerged from the techniques described in the Sulva-Sutras.
Pythagoras - the Greek mathematician and philosopher who lived in the 6th C B.C was familiar with the Upanishads and learnt his basic geometry from the Sulva Sutras. An early statement of what is commonly known as the Pythagoras theorem is to be found in Baudhayana's Sutra: The chord which is stretched across the diagonal of a square produces an area of double the size. A similar observation pertaining to oblongs is also noted. His Sutra also contains geometric solutions of a linear equation in a single unknown. Examples of quadratic equations also appear. Apasthamba's sutra (an expansion of Baudhayana's with several original contributions) provides a value for the square root of 2 that is accurate to the fifth decimal place. Apasthamba also looked at the problems of squaring a circle, dividing a segment into seven equal parts, and a solution to the general linear equation. Jain texts from the 6th C BC such as the Surya Pragyapti describe ellipses.
Modern-day commentators are divided on how some of the results were generated. Some believe that these results came about through hit and trial - as rules of thumb, or as generalizations of observed examples. Others believe that once the scientific method came to be formalized in the Nyaya-Sutras - proofs for such results must have been provided, but these have either been lost or destroyed, or else were transmitted orally through the Gurukul system, and only the final results were tabulated in the texts. In any case, the study of Ganit i.e mathematics was given considerable importance in the Vedic period. The Vedang Jyotish (1000 BC) includes the statement: "Just as the feathers of a peacock and the jewel-stone of a snake are placed at the highest point of the body (at the forehead), similarly, the position of Ganit is the highest amongst all branches of the Vedas and the Shastras."
(Many centuries later, Jain mathematician from Mysore, Mahaviracharya further emphasized the importance of mathematics: "Whatever object exists in this moving and non-moving world, cannot be understood without the base of Ganit (i.e. mathematics)".)
Panini and Formal Scientific Notation
A particularly important development in the history of Indian science that was to have a profound impact on all mathematical treatises that followed was the pioneering work by Panini (6th C BC) in the field of Sanskrit grammar and linguistics. Besides expounding a comprehensive and scientific theory of phonetics, phonology and morphology, Panini provided formal production rules and definitions describing Sanskrit grammar in his treatise called Asthadhyayi. Basic elements such as vowels and consonants, parts of speech such as nouns and verbs were placed in classes. The construction of compound words and sentences was elaborated through ordered rules operating on underlying structures in a manner similar to formal language theory.
Today, Panini's constructions can also be seen as comparable to modern definitions of a mathematical function. G G Joseph, in The crest of the peacock argues that the algebraic nature of Indian mathematics arises as a consequence of the structure of the Sanskrit language. Ingerman in his paper titled Panini-Backus form finds Panini's notation to be equivalent in its power to that of Backus - inventor of the Backus Normal Form used to describe the syntax of modern computer languages. Thus Panini's work provided an example of a scientific notational model that could have propelled later mathematicians to use abstract notations in characterizing algebraic equations and presenting algebraic theorems and results in a scientific format.
Philosophy and Mathematics
Philosophical doctrines also had a profound influence on the development of mathematical concepts and formulations. Like the Upanishadic world view, space and time were considered limitless in Jain cosmology. This led to a deep interest in very large numbers and definitions of infinite numbers. Infinite numbers were created through recursive formulae, as in the Anuyoga Dwara Sutra. Jain mathematicians recognized five different types of infinities: infinite in one direction, in two directions, in area, infinite everywhere and perpetually infinite. Permutations and combinations are listed in the Bhagvati Sutras (3rd C BC) and Sathananga Sutra (2nd C BC).
Jain set theory probably arose in parallel with the Syadvada system of Jain epistemology in which reality was described in terms of pairs of truth conditions and state changes. The Anuyoga Dwara Sutra demonstrates an understanding of the law of indeces and uses it to develop the notion of logarithms. Terms like Ardh Aached , Trik Aached, and Chatur Aached are used to denote log base 2, log base 3 and log base 4 respectively. In Satkhandagama various sets are operated upon by logarithmic functions to base two, by squaring and extracting square roots, and by raising to finite or infinite powers. The operations are repeated to produce new sets. In other works the relation of the number of combinations to the coefficients occurring in the binomial expansion is noted.
Since Jain epistemology allowed for a degree of indeterminacy in describing reality, it probably helped in grappling with indeterminate equations and finding numerical approximations to irrational numbers.
Buddhist literature also demonstrates an awareness of indeterminate and infinite numbers. Buddhist mathematics was classified either as Garna (Simple Mathematics) or Sankhyan (Higher Mathematics). Numbers were deemed to be of three types: Sankheya (countable), Asankheya (uncountable) and Anant (infinite).
Philosophical formulations concerning Shunya - i.e. emptiness or the void may have facilitated in the introduction of the concept of zero. While the zero (bindu) as an empty place holder in the place-value numeral system appears much earlier, algebraic definitions of the zero and it's relationship to mathematical functions appear in the mathematical treatises of Brahmagupta in the 7th C AD. Although scholars are divided about how early the symbol for zero came to be used in numeric notation in India, (Ifrah arguing that the use of zero is already implied in Aryabhatta) tangible evidence for the use of the zero begins to proliferate towards the end of the Gupta period. Between the 7th C and the 11th C, Indian numerals developed into their modern form, and along with the symbols denoting various mathematical functions (such as plus, minus, square root etc) eventually became the foundation stones of modern mathematical notation.
The Indian Numeral System
Although the Chinese were also using a decimal based counting system, the Chinese lacked a formal notational system that had the abstraction and elegance of the Indian notational system, and it was the Indian notational system that reached the Western world through the Arabs and has now been accepted as universal. Several factors contributed to this development whose significance is perhaps best stated by French mathematician, Laplace: "The ingenious method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value) emerged in India. The idea seems so simple nowadays that its significance and profound importance is no longer appreciated. It's simplicity lies in the way it facilitated calculation and placed arithmetic foremost amongst useful inventions."
Brilliant as it was, this invention was no accident. In the Western world, the cumbersome roman numeral system posed as a major obstacle, and in China the pictorial script posed as a hindrance. But in India, almost everything was in place to favor such a development. There was already a long and established history in the use of decimal numbers, and philosophical and cosmological constructs encouraged a creative and expansive approach to number theory. Panini's studies in linguistic theory and formal language and the powerful role of symbolism and representational abstraction in art and architecture may have also provided an impetus, as might have the rationalist doctrines and the exacting epistemology of the Nyaya Sutras, and the innovative abstractions of the Syadavada and Buddhist schools of learning.
Influence of Trade and Commerce, Importance of Astronomy
The growth of trade and commerce, particularly lending and borrowing demanded an understanding of both simple and compound interest which probably stimulated the interest in arithmetic and geometric series. Brahmagupta's description of negative numbers as debts and positive numbers as fortunes points to a link between trade and mathematical study. Knowledge of astronomy - particularly knowledge of the tides and the stars was of great import to trading communities who crossed oceans or deserts at night. This is borne out by numerous references in the Jataka tales and several other folk-tales. The young person who wished to embark on a commercial venture was inevitably required to first gain some grounding in astronomy. This led to a proliferation of teachers of astronomy, who in turn received training at universities such as at Kusumpura (Bihar) or Ujjain (Central India) or at smaller local colleges or Gurukuls. This also led to the exchange of texts on astronomy and mathematics amongst scholars and the transmission of knowledge from one part of India to another. Virtually every Indian state produced great mathematicians who wrote commentaries on the works of other mathematicians (who may have lived and worked in a different part of India many centuries earlier). Sanskrit served as the common medium of scientific communication.
The science of astronomy was also spurred by the need to have accurate calendars and a better understanding of climate and rainfall patterns for timely sowing and choice of crops. At the same time, religion and astrology also played a role in creating an interest in astronomy and a negative fallout of this irrational influence was the rejection of scientific theories that were far ahead of their time. One of the greatest scientists of the Gupta period - Aryabhatta (born in 476 AD, Kusumpura, Bihar) provided a systematic treatment of the position of the planets in space. He correctly posited the axial rotation of the earth, and inferred correctly that the orbits of the planets were ellipses. He also correctly deduced that the moon and the planets shined by reflected sunlight and provided a valid explanation for the solar and lunar eclipses rejecting the superstitions and mythical belief systems surrounding the phenomenon. Although Bhaskar I (born Saurashtra, 6th C, and follower of the Asmaka school of science, Nizamabad, Andhra ) recognized his genius and the tremendous value of his scientific contributions, some later astronomers continued to believe in a static earth and rejected his rational explanations of the eclipses. But in spite of such setbacks, Aryabhatta had a profound influence on the astronomers and mathematicians who followed him, particularly on those from the Asmaka school.
Mathematics played a vital role in Aryabhatta's revolutionary understanding of the solar system. His calculations on pi, the circumferance of the earth (62832 miles) and the length of the solar year (within about 13 minutes of the modern calculation) were remarkably close approximations. In making such calculations, Aryabhatta had to solve several mathematical problems that had not been addressed before including problems in algebra (beej-ganit) and trigonometry (trikonmiti).
Bhaskar I continued where Aryabhatta left off, and discussed in further detail topics such as the longitudes of the planets; conjunctions of the planets with each other and with bright stars; risings and settings of the planets; and the lunar crescent. Again, these studies required still more advanced mathematics and Bhaskar I expanded on the trigonometric equations provided by Aryabhatta, and like Aryabhatta correctly assessed pi to be an irrational number. Amongst his most important contributions was his formula for calculating the sine function which was 99% accurate. He also did pioneering work on indeterminate equations and considered for the first time quadrilaterals with all the four sides unequal and none of the opposite sides parallel.
Another important astronomer/mathematician was Varahamira (6th C, Ujjain) who compiled previously written texts on astronomy and made important additions to Aryabhatta's trigonometric formulas. His works on permutations and combinations complemented what had been previously achieved by Jain mathematicians and provided a method of calculation of nCr that closely resembles the much more recent Pascal's Triangle. In the 7th century, Brahmagupta did important work in enumerating the basic principles of algebra. In addition to listing the algebraic properties of zero, he also listed the algebraic properties of negative numbers. His work on solutions to quadratic indeterminate equations anticipated the work of Euler and Lagrange.
Emergence of Calculus
In the course of developing a precise mapping of the lunar eclipse, Aryabhatta was obliged to introduce the concept of infinitesimals - i.e. tatkalika gati to designate the infinitesimal, or near instantaneous motion of the moon, and express it in the form of a basic differential equation. Aryabhatta's equations were elaborated on by Manjula (10th C) and Bhaskaracharya (12th C) who derived the differential of the sine function. Later mathematicians used their intuitive understanding of integration in deriving the areas of curved surfaces and the volumes enclosed by them.
Applied Mathematics, Solutions to Practical Problems
Developments also took place in applied mathematics such as in creation of trigonometric tables and measurement units. Yativrsabha's work Tiloyapannatti (6th C) gives various units for measuring distances and time and also describes the system of infinite time measures.
In the 9th C, Mahaviracharya ( Mysore) wrote Ganit Saar Sangraha where he described the currently used method of calculating the Least Common Multiple (LCM) of given numbers. He also derived formulae to calculate the area of an ellipse and a quadrilateral inscribed within a circle (something that had also been looked at by Brahmagupta) The solution of indeterminate equations also drew considerable interest in the 9th century, and several mathematicians contributed approximations and solutions to different types of indeterminate equations.
In the late 9th C, Sridhara (probably Bengal) provided mathematical formulae for a variety of practical problems involving ratios, barter, simple interest, mixtures, purchase and sale, rates of travel, wages, and filling of cisterns. Some of these examples involved fairly complicated solutions and his Patiganita is considered an advanced mathematical work. Sections of the book were also devoted to arithmetic and geometric progressions, including progressions with fractional numbers or terms, and formulas for the sum of certain finite series are provided. Mathematical investigation continued into the 10th C. Vijayanandi (of Benares, whose Karanatilaka was translated by Al-Beruni into Arabic) and Sripati of Maharashtra are amongst the prominent mathematicians of the century.
The leading light of 12th C Indian mathematics was Bhaskaracharya who came from a long-line of mathematicians and was head of the astronomical observatory at Ujjain. He left several important mathematical texts including the Lilavati and Bijaganita and the SiddhantaShiromani, an astronomical text. He was the first to recognize that certain types of quadratic equations could have two solutions. His Chakrawaat method of solving indeterminate solutions preceded European solutions by several centuries, and in his Siddhanta Shiromani he postulated that the earth had a gravitational force, and broached the fields of infinitesimal calculation and integration. In the second part of this treatise, there are several chapters relating to the study of the sphere and it's properties and applications to geography, planetary mean motion, eccentric epicyclical model of the planets, first visibilities of the planets, the seasons, the lunar crescent etc. He also discussed astronomical instruments and spherical trigonometry. Of particular interest are his trigonometric equations: sin(a + b) = sin a cos b + cos a sin b; sin(a - b) = sin a cos b - cos a sin b;
The Spread of Indian Mathematics
The study of mathematics appears to slow down after the onslaught of the Islamic invasions and the conversion of colleges and universities to madrasahs. But this was also the time when Indian mathematical texts were increasingly being translated into Arabic and Persian. Although Arab scholars relied on a variety of sources including Babylonian, Syriac, Greek and some Chinese texts, Indian mathematical texts played a particularly important role. Scholars such as Ibn Tariq and Al-Fazari (8th C, Baghdad), Al-Kindi (9th C, Basra), Al-Khwarizmi (9th C. Khiva), Al-Qayarawani (9th C, Maghreb, author of Kitab fi al-hisab al-hindi), Al-Uqlidisi (10th C, Damascus, author of The book of Chapters in Indian Arithmetic), Ibn-Sina (Avicenna), Ibn al-Samh (Granada, 11th C, Spain), Al-Nasawi (Khurasan, 11th C, Persia), Al-Beruni (11th C, born Khiva, died Afghanistan), Al-Razi (Teheran), and Ibn-Al-Saffar (11th C, Cordoba) were amongst the many who based their own scientific texts on translations of Indian treatises. Records of the Indian origin of many proofs, concepts and formulations were obscured in the later centuries, but the enormous contributions of Indian mathematics was generously acknowledged by several important Arabic and Persian scholars, especially in Spain. Abbasid scholar Al-Gaheth wrote: " India is the source of knowledge, thought and insight". Al-Maoudi (956 AD) who travelled in Western India also wrote about the greatness of Indian science. Said Al-Andalusi, an 11th C Spanish scholar and court historian was amongst the most enthusiastic in his praise of Indian civilization, and specially remarked on Indian achievements in the sciences and in mathematics. Of course, eventually, Indian algebra and trigonometry reached Europe through a cycle of translations, traveling from the Arab world to Spain and Sicily, and eventually penetrating all of Europe. At the same time, Arabic and Persian translations of Greek and Egyptian scientific texts become more readily available in India.
The Kerala School
Although it appears that original work in mathematics ceased in much of Northern India after the Islamic conquests, Benaras survived as a center for mathematical study, and an important school of mathematics blossomed in Kerala. Madhava (14th C, Kochi) made important mathematical discoveries that would not be identified by European mathematicians till at least two centuries later. His series expansion of the cos and sine functions anticipated Newton by almost three centuries. Historians of mathematics, Rajagopal, Rangachari and Joseph considered his contributions instrumental in taking mathematics to the next stage, that of modern classical analysis. Nilkantha (15th C, Tirur, Kerala) extended and elaborated upon the results of Madhava while Jyesthadeva (16th C, Kerala) provided detailed proofs of the theorems and derivations of the rules contained in the works of Madhava and Nilkantha. It is also notable that Jyesthadeva's Yuktibhasa which contained commentaries on Nilkantha's Tantrasamgraha included elaborations on planetary theory later adopted by Tycho Brahe, and mathematics that anticipated work by later Europeans. Chitrabhanu (16th C, Kerala) gave integer solutions to twenty-one types of systems of two algebraic equations, using both algebraic and geometric methods in developing his results. Important discoveries by the Kerala mathematicians included the Newton-Gauss interpolation formula, the formula for the sum of an infinite series, and a series notation for pi. Charles Whish (1835, published in the Transactions of the Royal Asiatic Society of Great Britain and Ireland) was one of the first Westerners to recognize that the Kerala school had anticipated by almost 300 years many European developments in the field.
Yet, few modern compendiums on the history of mathematics have paid adequate attention to the often pioneering and revolutionary contributions of Indian mathematicians. But as this essay amply demonstrates, a significant body of mathematical works were produced in the Indian subcontinent. The science of mathematics played a pivotal role not only in the industrial revolution but in the scientific developments that have occurred since. No other branch of science is complete without mathematics. Not only did India provide the financial capital for the industrial revolution (see the essay on colonization) India also provided vital elements of the scientific foundation without which humanity could not have entered this modern age of science and high technology.
Mathematics and Music: Pingala (3rd C AD), author of Chandasutra explored the relationship between combinatorics and musical theory anticipating Mersenne (1588-1648) author of a classic on musical theory.
Mathematics and Architecture: Interest in arithmetic and geometric series may have also been stimulated by (and influenced) Indian architectural designs - (as in temple shikaras, gopurams and corbelled temple ceilings). Of course, the relationship between geometry and architectural decoration was developed to it's greatest heights by Central Asian, Persian, Turkish, Arab and Indian architects in a variety of monuments commissioned by the Islamic rulers.
Transmission of the Indian Numeral System: Evidence for the transmission of the Indian Numeral System to the West is provided by Joseph (Crest of the Peacock):-
Quotes Severus Sebokht (662) in a Syriac text describing the "subtle discoveries" of Indian astronomers as being "more ingenious than those of the Greeks and the Babylonians" and "their valuable methods of computation which surpass description" and then goes on to mention the use of nine numerals.
Quotes from Liber abaci (Book of the Abacus) by Fibonacci (1170-1250): The nine Indian numerals are ...with these nine and with the sign 0 which in Arabic is sifr, any desired number can be written. (Fibonaci learnt about Indian numerals from his Arab teachers in North Africa)
Influence of the Kerala School: Joseph (Crest of the Peacock) suggests that Indian mathematical manuscripts may have been brought to Europe by Jesuit priests such as Matteo Ricci who spent two years in Kochi (Cochin) after being ordained in Goa in 1580. Kochi is only 70km from Thrissur (Trichur) which was then the largest repository of astronomical documents. Whish and Hyne - two European mathematicians obtained their copies of works by the Kerala mathematicians from Thrissur, and it is not inconceivable that Jesuit monks may have also taken copies to Pisa (where Galileo, Cavalieri and Wallis spent time), or Padau (where James Gregory studied) or Paris (where Mersenne who was in touch with Fermat and Pascal, acted as an agent for the transmission of mathematical ideas).
1.Studies in the History of Science in India (Anthology edited by Debiprasad Chattopadhyaya)
2.A P Juskevic, S S Demidov, F A Medvedev and E I Slavutin: Studies in the history of mathematics, "Nauka" (Moscow, 1974), 220-222; 302.
3. B Datta: The science of the Sulba (Calcutta, 1932).
4.G G Joseph: The crest of the peacock (Princeton University Press, 2000).
5. R P Kulkarni: The value of pi known to Sulbasutrakaras, Indian Journal Hist. Sci. 13 (1) (1978), 32-41.
6. G Kumari: Some significant results of algebra of pre-Aryabhata era, Math. Ed. (Siwan) 14 (1) (1980), B5-B13.
7. G Ifrah: A universal history of numbers: From prehistory to the invention of the computer (London, 1998).
8. P Z Ingerman: 'Panini-Backus form', Communications of the ACM 10 (3)(1967), 137.
9.P Jha, Contributions of the Jainas to astronomy and mathematics, Math. Ed. (Siwan) 18 (3) (1984), 98-107.
9b. R C Gupta: The first unenumerable number in Jaina mathematics, Ganita Bharati 14 (1-4) (1992), 11-24.
10. L C Jain: System theory in Jaina school of mathematics, Indian J. Hist. Sci. 14 (1) (1979), 31-65.
11. L C Jain and Km Meena Jain: System theory in Jaina school of mathematics. II, Indian J. Hist. Sci. 24 (3) (1989), 163-180
12. K Shankar Shukla: Bhaskara I, Bhaskara I and his works II. Maha-Bhaskariya (Sanskrit) (Lucknow, 1960).
13. K Shankar Shukla: Bhaskara I, Bhaskara I and his works III. Laghu-Bhaskariya (Sanskrit) (Lucknow, 1963).
14. K S Shukla: Hindu mathematics in the seventh century as found in Bhaskara I's commentary on the Aryabhatiya, Ganita 22 (1) (1971), 115-130.
15. R C Gupta: Varahamihira's calculation of nCr and the discovery of Pascal's triangle, Ganita Bharati 14 (1-4) (1992), 45-49.
16. B Datta: On Mahavira's solution of rational triangles and quadrilaterals, Bull. Calcutta Math. Soc. 20 (1932), 267-294.
17. B S Jain: On the Ganita-Sara-Samgraha of Mahavira (c. 850 A.D.), Indian J. Hist. Sci. 12 (1) (1977), 17-32.
18. K Shankar Shukla: The Patiganita of Sridharacarya (Lucknow, 1959).
19. H. Suter: Mathematiker
20. Suter: Die Mathematiker und Astronomen der Araber
21. Die philosophischen Abhandlungen des al-Kindi, Munster, 1897
22. K V Sarma: A History of the Kerala School of Hindu Astronomy (Hoshiarpur, 1972).
23. R C Gupta: The Madhava-Gregory series, Math. Education 7 (1973), B67-B70
24. S Parameswaran: Madhavan, the father of analysis, Ganita-Bharati 18 (1-4) (1996), 67-70.
25. K V Sarma, and S Hariharan: Yuktibhasa of Jyesthadeva : a book of rationales in Indian mathematics and astronomy - an analytical appraisal, Indian J. Hist. Sci. 26 (2) (1991), 185-207
26. C T Rajagopal and M S Rangachari: On an untapped source of medieval Keralese mathematics, Arch. History Exact Sci. 18 (1978), 89-102.
27. C T Rajagopal and M S Rangachari: On medieval Keralese mathematics, Arch. History Exact Sci. 35 (1986), 91-99.
28. A.K. Bag: Mathematics in Ancient and Medieval India (1979, Varanasi)
29. Bose, Sen, Subarayappa: Concise History of Science in India, (Indian National Science Academy)
30. T.A. Saraswati: Geometry in Ancient and Medieval India (1979, Delhi)
31.N. Singh: Foundations of Logic in Ancient India, Linguistics and Mathematics ( Science and technology in Indian Culture, ed. A Rahman, 1984, New Delhi, National Instt. of Science, Technology and Development Studies, NISTAD)
32. P. Singh: "The so-called Fibonacci numbers in ancient and medieval India, (Historia Mathematica, 12, 229-44, 1985)
33. Chin Keh-Mu: India and China: Scientific Exchange (History of Science in India Vol 2.)
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Curtain Call: On Your Feet!
The new show 'On Your Feet!' depicts the life of Gloria Estefan and unsurprisingly, the costumes are perfectly over-the-top. We caught up with the designer behind the costuming, Emilio Sosa, to find out his inspiration for the designs.
By Aaron Lyle Leth
Matthew Murphy
Cuba is having a moment, not just politically, but in the fashion world as well. So it's a perfect time to hoist a musical centered on the life of one of the country's biggest stars, Gloria Estefan. On Your Feet! is a bio-musical showcasing the rise of Gloria (played by newcomer Ana Villafane) and her husband Emilio's (Josh Segarra) breakthrough into the American music market. Unsurprisingly, the costumes are over-the-top and sartorially seductive.
The task of recreating each sequin and sash worn by Estefan was charged to Emilio Sosa, who knows a thing or two about costuming thanks to his work for Motown: The Musical and Project Runway. We asked Sosa about his process and his work for On Your Feet!
Harper's BAZAAR: What brought you from Project Runway into the theater world?
Emilio Sosa: I always say 'theater chose me,' not the other way around. I was a second year design student at New York's Pratt Institute, when the opportunity to work part time at one of the leading costume shops, Grace Costumes, opened up and I needed a job. I had never seen a Broadway show or had any intentions of becoming a costume designer, but I've been hooked ever since!
HB: You designed the costumes for Motown: The Musical. What was different for On Your Feet! after the great success of your Tony nomination and Project Runway? Were you more confident?
ES: Every show is different, so I approach them accordingly. After my Tony nomination, I became more focused and inspired. Both Motown and On Your Feet! celebrate the American dream of "hard work pays off." Having experienced a large scale musical like Motown prepared me to tackle this show with a burst of confidence.
HB: What was your inspiration for On Your Feet?
ES: I grew up on Gloria and Emilio's music, so it was already in my DNA. But what makes the difference was having access to the Estefans' extensive archives of personal family photos and tour costumes. They keep everything, which made it a treat for me to re-live part of my life through them.
HB: What are some of your favorite cultural references for the designs, besides the influence of Gloria and her music?
ES: I was in high school and college in the 1980s so I wore a lot of the things you see on the stage. It was all about big hair, bright colors and shoulder pads!
HB: What colors are important in the show and did any current trends make it into your thought process?
ES: Miami plays an important role in the show and nothing says "Miami" more than bright colors and pastels. Acid wash denim was huge at the time, and I was happy to see it in the runways and stores, making New York shopping a lot easier. So much of that period is out there now. It was perfect timing for this show!
On Your Feet! is playing at the Marquis Theater.
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There didn't appear to be many people talking about Corsair CMSO4GX3M1A1333C9 4GB PC-10600 and it's compatibility with 2011 MacBook Pros, so I thought I'd write a quick post about it. I bought 4 of these sticks, 2 for my 13″ 2.7GHz i7 MacBook Pro (8,1), and 2 for another 15″ 2.2GHz i7 Macbook Pro. We put them in and our MacBooks booted perfectly, neither machines have had any issues, so I'm confident to say that these modules work great in 2011 MacBook Pros. Despite the fact I never actually reached 4GB usage on the standard RAM, my MacBook feels snappier and quicker to boot. It's probably just a placebo though. Either way, at $45 AUD a pop (so, $90 AUD to upgrade to 8GB), these modules are great value and well worth the upgrade.


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Sushant Singh Rajput's family lawyer Vikas Singh claims the family was 'forced' to sign statements in Marathi by Mumbai Police
Sushant Singh Rajput's family lawyer Vikas Singh claims the family was 'forced' to sign statements in Marathi by Mumbai Police
Sushant Singh Rajput's f ...
Sushant Singh Rajput passed away on June 14. Since then the actor's family has been fighting for justice as they do not believe that he committed suicide. During the investigation, questions were raised on Mumbai Police's way of handling the case. Now, Vikas Singh, the advocate who is representing Sushant's father said that the family were forced to sign statements in Marathi by Mumbai Police.
In a press conference on Wednesday, Vikas Singh said, "The family has never given any statement of Sushant dying by suicide. These statements were recorded by the Mumbai Police in Marathi. The family also objected, 'Please don't write in Marathi if you want us to sign.' They were forced to sign a statement written in Marathi. They had no clue of what was being written."
He further added, "We have not been supplied that statement. We don't know what was recorded by the Mumbai Police, we know what we said."
https://www.instagram.com/p/CDrbPCeFs45/?utm_source=ig_web_copy_link
He also said that a translation was not read out to the family as well. "The statement was just written in Marathi, that's it. There was nothing read out to anybody. Even if you read out in Marathi… If I write something in a language you don't know and I then read out whatever I want you to hear… If I don't know Marathi, how will I check if what you are telling me is what is written? It's simple logic!." the senior lawyer said.
However, according to a report by NDTV, Sushant's father KK Singh in a statement to Mumbai Police had said, "I am not aware as to why my son Sushant has committed suicide. He never discussed with me regarding any type of depression or tension. I do not have any suspicion of or any complaint against Sushant. I feel that Sushant might have done suicide out of dejection. My statement was written in Marathi and explained to me in Hindi and it is correct as I told."
Stay tuned to this space to know what Mumbai Police has to say about these allegations made by Vikas Singh.
Also Read: Sushant Singh Rajput's ex-manager Shruti Modi's lawyer claims she had offered to quit after learning about his drug consumption
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Ek Villain Returns song Galliyan Returns: John, Arjun, Disha, Tara deliver the essence of the…
Darlings: Alia Bhatt announces teaser release date of 'thoda dark, thoda comedy' movie
Bengali filmmaker Padma Shri Tarun Majumdar passes away at 91
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package com.google.errorprone.bugpatterns.checkreturnvalue;

import static com.google.errorprone.BugPattern.SeverityLevel.WARNING;
import static com.google.errorprone.util.ASTHelpers.getType;
import static com.google.errorprone.util.ASTHelpers.isSameType;

import com.google.errorprone.BugPattern;
import com.google.errorprone.VisitorState;
import com.google.errorprone.bugpatterns.BugChecker;
import com.google.errorprone.bugpatterns.BugChecker.ImportTreeMatcher;
import com.google.errorprone.fixes.SuggestedFix;
import com.google.errorprone.matchers.Description;
import com.google.errorprone.suppliers.Supplier;
import com.sun.source.tree.ImportTree;
import com.sun.tools.javac.code.Type;

/**
 * Checker that recommends using ErrorProne's version of {@code @CheckReturnValue} over the version
 * in JSR305 (which is defunct).
 */
@BugPattern(
    summary = "Prefer ErrorProne's @CheckReturnValue over JSR305's version.",
    severity = WARNING)
public final class UsingJsr305CheckReturnValue extends BugChecker implements ImportTreeMatcher {
  private static final String EP_CRV = "com.google.errorprone.annotations.CheckReturnValue";
  private static final String JSR305_CRV = "javax.annotation.CheckReturnValue";

  private static final Supplier<Type> JSR305_TYPE =
      VisitorState.memoize(state -> state.getTypeFromString(JSR305_CRV));

  @Override
  public Description matchImport(ImportTree tree, VisitorState state) {
    Type jsr305Type = JSR305_TYPE.get(state);
    if (isSameType(getType(tree.getQualifiedIdentifier()), jsr305Type, state)) {
      // TODO(kak): the JSR305 version of @CheckReturnValue has an element named `when` and the
      // ErrorProne version does not. Technically, this means the import swap is not 100% safe,
      // but we have never actually seen `when` get used in practice.
      SuggestedFix fix = SuggestedFix.builder().removeImport(JSR305_CRV).addImport(EP_CRV).build();
      return describeMatch(tree, fix);
    }
    return Description.NO_MATCH;
  }

  // TODO(kak): we also may want to match on fully qualified JSR305 CRV annotations, for example:
  //   @javax.annotation.CheckReturnValue public String frobber() { ... }
  // To do so, we'd need to look for IdentifierTrees and MemberSelectTrees.
  // However, that style is very very uncommon.
}

redpajama_set_name: RedPajamaGithub


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Keep It Or Trade It?: Super Mario 3D Land (3DS)
December 3, 2011 January 7, 2012 Shaan Joshi
I'll be honest. A few hours into Super Mario 3D Land, I wasn't impressed, and I was almost ready to write the game off. It has some control issues, the levels can be all too easy, and the game relies on some power-ups too often. But as I pressed on, the game began to grow on me. Sure it isn't perfect, but it's still a good game, and stands out as one of the better titles on the 3DS.
So, surprise surprise, Bowser has kidnapped Peach again, and it's up to the portly plumber to save the day. This is the main motivation to trek through the 8 worlds on your way to Bowser, but have we ever really needed any other reason to jump, flip and stomp our way to victory? The story won't win any awards, but the level design stands out as a high mark for the series. Although you are given full analog control of Mario, most of the levels are akin to the 2D side-scroller Mario titles with a little bit of Z-axis control thrown in for good measure. The worlds run the gamut of environments, with mountain, ice, fire levels being some of the level themes. While this might sound stale, Nintendo has thrown in some cool levels which pay homage to other games. In one level, the camera switches to a top-down perspective à la Legend of Zelda, with torch puzzles and sound effects to boot.
The graphics complement the level design perfectly. The game is not a powerhouse by any means, but the art assets and textures are very clean and simple, and the animations are very fluid, making it the best looking game on the system to date. The 3D in the game is some of the best on the system. The game plays around with camera angles and perspectives to create some interesting puzzles, where stepping on a switch will reveal hidden Star Coins (more on those later). However, the 3D shines when you are moving Mario into/out of the screen, where the 3D effect is used to create a realistic sense of depth. The tunes aren't as memorable as those featured in Super Mario Galaxy or New Super Mario Bros. Wii, but the main theme stands out from other Mario songs, and don't be surprised if you find yourself whistling some of the music throughout your day.
In terms of gameplay, this is the same tried-and-true running and jumping that you've been playing for years. If you're new to the series, here's a quick recap. You'll control Mario throughout 8 worlds, dodging obstacles, defeating enemies and reaching the end-of-the-level flagpole. Power-ups are back, with the fire flower and mushroom returning as standbys. The game does include some new items; a boomerang suit allows Mario to toss boomerangs to defeat enemies and pick up items. My favorite item is the Tanooki Suit, which makes its first appearance (in more than 20 years) since Super Mario Bros. 3. While you can use these power-ups to take care of pesky enemies, you'll have to use them to nab Star Coins. Each level in Super Mario 3D Land features 3 Star Coins, which are hidden in secret areas and behind environmental obstacles. While Star Coins were optional in other games, you will need to collect them in order to unlock levels throughout the game. To unlock some of these star coins, Mario will take control of binoculars, which you control with the 3DS gyroscope controls, which work well and add some variety to the game. While I have always preferred the "secret exit" mechanic in Super Mario World, the Star Coins serve their purpose well. If you're not a completionist, backtracking through old levels to mop up remaining Star Coins might be a burden, but you'll want to collect them all to unlock later levels.
Speaking of later levels, while the "main game" has 8 worlds, there is a set of 8 special worlds that unlock after rescuing Peach. These 8 special worlds offer a significant increase in difficulty, and will test the most experienced Mario veterans. While this may sound like players of all skill levels will have something to enjoy, it serves to highlight some of the core problems with the game. Unfortunately, the game is not very well balanced, with the first 8 worlds being way too easy, with a sudden spike in difficulty with the 8 special worlds. This makes the first half of the game quite boring, and if you have played your fair share of Mario games, don't be surprised if you rarely feel challenged for the first couple of hours. The balancing issues extend to the power-ups and the controls as well. The power-ups aren't over or underpowered in any way, but the game relies on the Tanooki Suit too often in order to snag an illusive Star Coin or reach the top of the flagpole. This relegates these challenges to simply storing a Tanooki Suit in your "backup" power-up slot. While the controls for the game aren't broken (as a matter of fact, the controls are tight and responsive), this is the first Mario game that features both a run and crouch button. This creates some issues when trying to pull off special moves. For example, in previous Mario games, running and crouching would pull of a long-jump. However, in Super Mario 3D Land, you cannot run unless you hold the run button, so executing a long-jump requires you to hold the run button while tapping the crouch and jump buttons. The game would have benefited from removing the run button, and having Mario run by using the slide pad/analog stick (like in every other 3D Mario game).
Everyone seems to ask whether Super Mario 3D Land makes owning a 3DS worthwhile. I don't know whether I would call it a killer app, as the first few hours offer very little challenge and don't prepare you for the trials and tribulations of the special worlds, but if you own a 3DS, or you are looking for another reason to pick one up, definitely pick up Super Mario 3D Land.
Intangibles:
ForTransfer, Games3DS, Games, Review, Super Mario 3D Land
2011 Game of the Year List - Shaan Joshi | G.A.M.E.S.
[…] #9 Super Mario 3D Land (3DS) […]


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Catherine Cortez Masto
Katie McGinty
FOX 13 11:00 News : WTVT : March 14, 2016 11:00pm-11:30pm EDT
expressway. time. the deputy's funeral will be hell this friday. visitation begins at 11:00 a.m. the funeral starts at 1:00. massachusetts{ where his family lives. his father is a member of the massachusetts state police. >> the maryland police officer was shot during an ambush yesterday died of his injuries today. three brothers of hand arrested for the death of officer jacai colson. investigator says michael ford wanted to die so he opened fire outside the police station, and during the guckfight it was actually friendly fire that struck and killed officer colson. investigators say it have been prestretches ford's brothers hadn't just sat and watch from the car. >> that image is of one of the ford brothers standing by, take nothing action, on a video recording device, attaching this, his brother, shooting at police officers. they knew in advance, they had every opportunity to call 9-1-1. they had every opportunity to seek medical help. >> ford and his brothers face more than 20 charges. colson was a four-year veteran on the department. >> new at 11:00, the st. pete city counci
expressway. time. the deputy's funeral will be hell this friday. visitation begins at 11:00 a.m. the funeral starts at 1:00. massachusetts{ where his family lives. his father is a member of the massachusetts state police. >> the maryland police officer was shot during an ambush yesterday died of his injuries today. three brothers of hand arrested for the death of officer jacai colson. investigator says michael ford wanted to die so he opened fire outside the police station, and during...
WNBC (NBC)
The Tonight Show Starring Jimmy Fallon : WNBC : February 4, 2016 11:34pm-12:37am EST
by WNBC
. [ laughter ] and i don't know what the hell i was thinking. and i just -- i give j.j. abrams a giant titty-twister. [ laughter and applause ] >> jimmy: why? why? no. >> because i'm a stupid person. [ laughter ] >> jimmy: in the middle of adele singing "hello." >> she's like -- hello >> jimmy: he doesn't know you. >> jimmy: yeah yeah yeah. >> and then he's also with his kids by the way. [ laughter ] i twisted this man's nipples in front of his children. [ laughter ] like you know, and bradley and him are oh, good to see you, we're good friends. i just go like. and i go j.j., how's it going? [ laughter ] and he looks at me like -- i'm literally the most disgusting person he's ever seen in his life. >> jimmy: he doesn't know what you were doing. >> and this is the nicest. >> jimmy: oh he's one of the best. >> he's notoriously like a nice man >> jimmy: one of the coolest human beings ever. >> and also now the world's biggest filmmaker. >> jimmy: in the history of film, yeah. >> jimmy: what happened? >> and so --. he looks at me like this and i am like it's loud and she's singing li
. [ laughter ] and i don't know what the hell i was thinking. and i just -- i give j.j. abrams a giant titty-twister. [ laughter and applause ] >> jimmy: why? why? no. >> because i'm a stupid person. [ laughter ] >> jimmy: in the middle of adele singing "hello." >> she's like -- hello >> jimmy: he doesn't know you. >> jimmy: yeah yeah yeah. >> and then he's also with his kids by the way. [ laughter ] i twisted this man's nipples in front of...
FOX 29 News at 6PM : WTXF : March 26, 2016 6:00pm-7:01pm EDT
go to hell? well you might want to check it out. we're head to do a town, it's a real town named hell. meet the man who wants you to buy it from him. ♪ >>> military doctors have been trying out a new and unusual way to help our troops suffering from the psychological and physical traumas of war. they're getting our wounded warriors involved in art therapy. we took a look at the emotional journey from the art of war to the art of healing and the local researchers who just made may decide that program's future. ♪ they look like art critics but they're not judging the artistic skill of these unique masks. >> we are coding for visual elements. >> one is an art therapist at direct system university. she and research coordinator adele gonzaga have been assigned a special government mission. engaged. >> to carefully analyze and categorize -- >> scroll down. >> the hundreds and hundreds of torn and tortured souls. >> passion for battles. >> behind these masks. >> struggling with issues of death and injury. >> active duty military service members who suffer traumatic brain injuries, physic
go to hell? well you might want to check it out. we're head to do a town, it's a real town named hell. meet the man who wants you to buy it from him. ♪ >>> military doctors have been trying out a new and unusual way to help our troops suffering from the psychological and physical traumas of war. they're getting our wounded warriors involved in art therapy. we took a look at the emotional journey from the art of war to the art of healing and the local researchers who just made may...
KUSA (NBC)
Late Night With Seth Meyers : KUSA : February 4, 2016 11:37pm-12:37am MST
by KUSA
truth. at my bake sale yeah we can't wait to bake hell yeah hell yeah lovin havin sex hell yeah all day hell yeah we be countin cake hell yeah puffin on this dank hell yeah we can't wait to bake hell yeah i've been on the phone yeah gettin calls from home yeah so i started up a bake sale yeah yeah yeah they know i got all the cake yeah yeah yeah cookies and og come to my crib we blow by the os kush you already know we wakin and bakin and puffin this j and lurkin -- song we wakin and bakin and puffin this j she told me that i'm her new favorite how much do we blaze a hundred a day say they got the good but what the pack smell like felt like it's a dream but now we back to real life it's incredible i got flowers wax and it's all at my bake sale roll another one help me think well i stay with the plane i'm slangin them things you know we ain't new to this let's turn on the stove and call up some girls let's roll up and do this thing at my bake sale yeah we can't wait to bake hell yeah laughin off this drink hell yeah lovin havin sex hell yeah all day hell yeah we be countin cake hell yeah
truth. at my bake sale yeah we can't wait to bake hell yeah hell yeah lovin havin sex hell yeah all day hell yeah we be countin cake hell yeah puffin on this dank hell yeah we can't wait to bake hell yeah i've been on the phone yeah gettin calls from home yeah so i started up a bake sale yeah yeah yeah they know i got all the cake yeah yeah yeah cookies and og come to my crib we blow by the os kush you already know we wakin and bakin and puffin this j and lurkin -- song we wakin and bakin and...
WRAL News Saturday : WRAL : November 26, 2016 6:00pm-6:30pm EST
[music playing] -show me yours. -come on kattrain, quit loloing and get back to work. -go to hell, man. -argh! ah! my leg! ah! -get back to work. -ah! oh, my leg! thanks, man. thanks for the diversion. -argh! why you. break! [moans] -hey, what are you doing? -get out. -no! -get out of the car. [screamingng freeze, kattrain. -help me. [screaming] narrator: he was a cop, and good at his job. but he committed the ultimate sin and testified against other cops gone bad. cops that tried to kill him, but got the woman he loved instead. framed for murder, now he prowls the badlands, an outlaw hunting outlaws, a bounty hunter, a renegade. -oh, oh. nice to meet you too. -kattrtrn! -chicago? that's over 2,000 miles away. we don't have a case in chicago. whatatre you going to do there? -it's just, it's something i got to handle on my own, bobby. -ah, secret mission in the windy city, need to know basis. you could tell me more, then i'd know too much, and then you're forced to kill me. -it's just something i got to t te care of on my own of days. give m mregards to chey. -ok, you just be safe,
[music playing] -show me yours. -come on kattrain, quit loloing and get back to work. -go to hell, man. -argh! ah! my leg! ah! -get back to work. -ah! oh, my leg! thanks, man. thanks for the diversion. -argh! why you. break! [moans] -hey, what are you doing? -get out. -no! -get out of the car. [screamingng freeze, kattrain. -help me. [screaming] narrator: he was a cop, and good at his job. but he committed the ultimate sin and testified against other cops gone bad. cops that tried to kill him,...
KPNX (NBC)
Today : KPNX : September 3, 2016 2:07am-3:00am MST
by KPNX
up for her hell no tour this fall. she's out with her seventh studio album. this one's called "it doesn't have to make sense." >> so true. i love your title. >> tha y >> by the way, hell no is such a great anthem song. >> thank you. >> how do these songs come to you? >> we were writing in nashville, two writers and i, and that was the first lyric that came out. it was just hell no. what are we saying it to? what makes sense? i think a breakup pretty much makes sense with the words. so we kind of built the whole me. >> it reveals itself, doesn't it? >> exactly. >> and there's also a lot of depth in this cd. a lot of heart ache i think it's fair to say. >> yeah. i lost my mom. i went through a divorce. i had a lot to mourn. and i was trying to figure out how to do that. and when i realized that when i try to stop making sense of everything, i was able to breathe, i was able to have joy. defining everything and controlling everything. because i'm very controlling. and it ended up being the best decision i could make. that's why i named the record that. >> if you lost someone and list
up for her hell no tour this fall. she's out with her seventh studio album. this one's called "it doesn't have to make sense." >> so true. i love your title. >> tha y >> by the way, hell no is such a great anthem song. >> thank you. >> how do these songs come to you? >> we were writing in nashville, two writers and i, and that was the first lyric that came out. it was just hell no. what are we saying it to? what makes sense? i think a breakup...
Bad News Bears : COM : April 2, 2016 2:32pm-5:15pm PDT
by COM
held up, sorry about that. are you drinking? oh, hell, no. that's, uh... nonalcoholic. i'm drivin', you know. ( laughs ): oh. i'm so sorry. you hear that, toby? drinking and driving don't mix. that's right. stay away from crack too. one hit of that stuff, and you wake up in prison married to some guy named big blue, and he's branding his initials in your ass with a hot coat hanger. i knew a guy. uh-- uh-- uh, yes, crack...is bad too. yeah, i know, mom. but we are really excited to have you do this, and toby's really excited to play. aren't ya, honey? uh-huh. between his trumpet lessons, photo club, boy scouts and swimming, this is his favorite, isn't it, honey? can you believe they tried to keep these kids out of the league? all kids should be able to play baseball, no matter what their skills. well, i think they heard me loud and clear. all that aside, forget i filed the injunction. just go out there and have fun. don't let the legalese crimp your enthusiasm in any way. yeah, i got enthusiasm flying out my ass. got the check? it's a shame none of the fathers could be here. is that thin
held up, sorry about that. are you drinking? oh, hell, no. that's, uh... nonalcoholic. i'm drivin', you know. ( laughs ): oh. i'm so sorry. you hear that, toby? drinking and driving don't mix. that's right. stay away from crack too. one hit of that stuff, and you wake up in prison married to some guy named big blue, and he's branding his initials in your ass with a hot coat hanger. i knew a guy. uh-- uh-- uh, yes, crack...is bad too. yeah, i know, mom. but we are really excited to have you do...
The Nightly Show With Larry Wilmore : COM : February 10, 2016 9:00am-9:38am PST
for you. just remember there's a special place in hell for women who don't help each other. >> larry: so, if a woman feels the bern, it's actually the fires of hell? [applause] if there's a special place in hell for women who don't help each other, why did no one come to the aid of a certain 22-year-old intern back in 1998? what's interesting is albright has used this hell line before, but while in the past she's used it as a rallying cry, now she's using it to divide. well, to find out if there really is a special place in hell, we're going live to hell itself. please welcome hell-based tour guide, rebecca harris. [crowd cheering] >> great to be here, larry. >> larry: so, is there really a special place in hell for women who don't help each other? >> oh yeah, larry. there are going to be a ton of bernie supporters down here soon. >> larry: wait, it's real? it's not a metaphor? >> yep. but this special place isn't just for women who don't support hillary. it's for all the evil women who defy society's very clearly defined rules. >> larry: oh come on, come on. that's crazy. when was t
for you. just remember there's a special place in hell for women who don't help each other. >> larry: so, if a woman feels the bern, it's actually the fires of hell? [applause] if there's a special place in hell for women who don't help each other, why did no one come to the aid of a certain 22-year-old intern back in 1998? what's interesting is albright has used this hell line before, but while in the past she's used it as a rallying cry, now she's using it to divide. well, to find out...
Talk to Al Jazeera : ALJAZAM : January 2, 2016 7:30am-8:01am EST
by ALJAZAM
jokes, illustrated by carl titolo. reflections from hell is richard lewis's guide on how not to live. it focuses a lot on his parents. > i had a-- not a great upbringing. was an alcoholic and a drug addict for a long time. i was with a lot-- i was in horrible relationships by my own doing. i wasn't-- wasn't always their fault, i own up to a lotta that. >> as an actor, lewis starred in larry david's curb your enthusiasim. the first met when they were 12. >> in-- a-- a summer camp, sports camp. hated each other, never saw each other till we were comedians. became inseparable best friends. that ran over a course of almost a decade. larry came over my house, you had asked me. and he said, "would you mind playing yourself?" >> and now he's staring in another television series called blunt talk. >> playing a psychiatrist is really a trip for me, 'cause i been in-- in and outta therapy and psychiatry for f-- almost my whole life. >> i spoke to richard lewis in new york. >> you been sober for 21 years- >> almost 21. >> --almost 21 years sober. >> yes. >> you're married. >> married, ten years, yo
jokes, illustrated by carl titolo. reflections from hell is richard lewis's guide on how not to live. it focuses a lot on his parents. > i had a-- not a great upbringing. was an alcoholic and a drug addict for a long time. i was with a lot-- i was in horrible relationships by my own doing. i wasn't-- wasn't always their fault, i own up to a lotta that. >> as an actor, lewis starred in larry david's curb your enthusiasim. the first met when they were 12. >> in-- a-- a summer...
Nightline : KTNV : November 26, 2016 12:37am-1:07am PST
in his beliefs. >> do you know there's a heaven or a hell? >> no. >> to others a ruthless dictator that brought the west to the brink of nuclear war. now his legion of faithful followers mourning. but his detractors celebrating in the streets. his death galvanizing the cuban/american diplomacy resumes. >> this special edition of "nightline" will be right back. ?? ?? nobody likes a dog with bad breath. that's why there's oravet dental hygiene chews. oravet's dual action approach cleans teeth and gets to the underlying cause of bad breath by blocking bacteria to help prevent plaque and tartar. serious oral care made simple >>> good evening. thank you for joining us. we begin tonight with breaking news out of havana, the death of fidel castro. the activist who became a rebel, facto dictator of cuba, dead tonight at the age of 90. the announcement made this even big cuba's president, castro's younger brother raul. no word yet on the cause of death. barely a whisper on the streets of cuba. since the announcement was made on state television. but a very different scene here in the u.s. t
in his beliefs. >> do you know there's a heaven or a hell? >> no. >> to others a ruthless dictator that brought the west to the brink of nuclear war. now his legion of faithful followers mourning. but his detractors celebrating in the streets. his death galvanizing the cuban/american diplomacy resumes. >> this special edition of "nightline" will be right back. ?? ?? nobody likes a dog with bad breath. that's why there's oravet dental hygiene chews. oravet's...
@midnight With Chris Hardwick : COM : March 15, 2016 2:40am-3:12am PDT
. i did get a start. that's the end of super zeros. it's time for -- i have a message. hell is real. not the one happening in november when trump becomes president. i know too hard to laugh at isn't it i'm talking about one that's available for the purchase for the astonishingly reasonable price of $999,000. i'm referring to the town of hell, michigan. hell is a unique tourist spot that holds two guinness world records: one, for the world's largest hearse parade, and one for being the only town in michigan willing to acknowledge that it's been abandoned by god. but if nine hundred grand is out of your price range. you can buy one square inch of hell, for $6.66 cents. the number of the beast! plus an additional $2.00. for a total of $8.66. the number of the beast plus shipping and handling! [ applause ] so comedians, let's say you can scrounge up the $999,000 to buy hell, i want you to give me a line from your new tourism campaign slogan to attract people to hell, michigan. we'll get your answers after the break and be right back with more @midnight! [cheers and applause] music throu
. i did get a start. that's the end of super zeros. it's time for -- i have a message. hell is real. not the one happening in november when trump becomes president. i know too hard to laugh at isn't it i'm talking about one that's available for the purchase for the astonishingly reasonable price of $999,000. i'm referring to the town of hell, michigan. hell is a unique tourist spot that holds two guinness world records: one, for the world's largest hearse parade, and one for being the only town...
The Tonight Show Starring Jimmy Fallon : KNTV : June 7, 2016 11:34pm-12:38am PDT
by KNTV
great music from ingrid michaelson! >> steve: hey! [ cheers and applause ] hell no. >> jimmy: guys, it is time to take a look at these stories making headlines today and weigh the good with the bad. it's time for "pros and cons." here we go. [ cheers and applause ] ♪ pros and cons and pros and cons and pros ♪ >> jimmy: thank you, guys. thank you, roots. tonight we'll be taking a look at pros and cons of "the nba finals." >> steve: ooh. >> jimmy: it's the golden state warriors taking on the cleveland cavaliers. lots of fans are excited about the series. so let's take a look at the pros and cons of the nba finals. here we go. pro, it's a matchup between the two best teams in the nba. con, the golden state warriors and lebron james. [ light laughter ] both tough teams. >> steve: both fantastic teams. >> jimmy: both fantastic teams. >> steve: hard working. >> jimmy: pro, players voted steph curry mvp or most valuable player. [ cheers ] con, trump voted him m.a.a. or "my african-american." [ laughter and applause ] >> steve: oh. >> jimmy: a new award? >> steve: is that an award they
great music from ingrid michaelson! >> steve: hey! [ cheers and applause ] hell no. >> jimmy: guys, it is time to take a look at these stories making headlines today and weigh the good with the bad. it's time for "pros and cons." here we go. [ cheers and applause ] ♪ pros and cons and pros and cons and pros ♪ >> jimmy: thank you, guys. thank you, roots. tonight we'll be taking a look at pros and cons of "the nba finals." >> steve: ooh. >>...


1 Transgression speaks to the ungodly within his heart; There is no fear of God before his eyes. 2 For it flatters him in his own eyes Concerning the discovery of his iniquity and the hatred of it. 3 The words of his mouth are wickedness and deceit; He has ceased to be wise and to do good. 4 He plans wickedness upon his bed; He sets himself on a path that is not good; He does not despise evil.


text:
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Armistice Day is on November the 11th every year. It commemorates the end of World War I on the 11th of November 1918. It was on this day that the Allies and Germany signed a ceasefire that was the beginning of the end of the Great War. Hostilities ended on the Western Front, taking effect at eleven o'clock in the morning. This became famously known as "the eleventh hour of the eleventh day of the eleventh month". While it was "all quiet on the Western Front," the war continued for a while longer in other parts of Europe, especially in the former Russian Empire. WWI was called "the War to End All Wars". Most of the world's great powers fought in it. Over 20 million people died, making it one of the deadliest conflicts in history.
Armistice Day is observed all over the world. In many countries, people stop what they are doing for a two-minute moment of silence at 11:00 a.m. This is a sign of respect for those who died. In Britain, there is another name for Armistice Day - Remembrance Sunday. In 1939, the British government moved Armistice Day to the Sunday nearest November 11. In America, the day is also called Veterans Day. Children in Commonwealth countries know these days by another name – Poppy Day. People wear poppies and donate money to charities for soldiers injured in wars. Poppies are a symbol of the blood that filled the trenches. Poppies also bloomed across some of the worst battlefields during the War.
Armistice Day is on November ________________ year. It commemorates the end of World War I on the 11th of November 1918. It ________________ that the Allies and Germany signed a ceasefire that was the beginning ________________ Great War. Hostilities ended on the Western Front, taking effect at eleven o'clock in the morning. This became famously known as "the eleventh hour of the ________________ eleventh month". While it was "all quiet on the Western Front," the war continued ________________ in other parts of Europe, especially in the former Russian Empire. WWI was called "the War to End All Wars". Most of the world's great powers fought in it. Over 20 million people died, ________________ the deadliest conflicts in history.
Armistice Day is observed __________________. In many countries, people stop what they are doing for a two-minute ________________ at 11:00 a.m. This is a sign of respect for those who died. In Britain, there ________________ for Armistice Day - Remembrance Sunday. In 1939, the British government moved Armistice Day to the Sunday nearest November 11. In America, the ________________ Veterans Day. Children in Commonwealth countries know these days by another name – Poppy Day. People wear poppies and ________________ charities for soldiers injured in wars. Poppies are a symbol of the blood that filled the trenches. Poppies also bloomed across ________________ battlefields during the War.
Armistice Day is on November the 11th every year. It commemorates the ____________ of World War I on the 11th of November 1918. It was on this day that the Allies and Germany ____________ a ceasefire that was the beginning of the end of the Great War. Hostilities ____________ on the Western Front, taking effect at eleven o'clock in the morning. This became famously ____________ as "the eleventh hour of the eleventh day of the eleventh month". While it was "all ____________ on the Western Front," the war continued for a while longer in other ____________ of Europe, especially in the former Russian Empire. WWI was called "the War to End All Wars". Most of the world's great powers ____________ in it. Over 20 million people died, making it one of the deadliest ____________ in history.
Armistice Day is ____________ all over the world. In many countries, people stop what they are doing for a two-minute ____________ of silence at 11:00 a.m. This is a sign of ____________ for those who died. In Britain, there is another name for Armistice Day - Remembrance Sunday. In 1939, the British government ____________ Armistice Day to the Sunday ____________ November 11. In America, the day is also called Veterans Day. Children in Commonwealth countries know these days by another name – Poppy Day. People wear poppies and ____________ money to charities for soldiers injured in wars. Poppies are a symbol of the ____________ that filled the trenches. Poppies also ____________ across some of the worst battlefields during the War.
Armistice Day is on November the 11th every year. It commemorates the end / ended of World War I on the 11th of November 1918. It was on this day that the Allies and Germany signing / signed a ceasefire that was the beginning of the end of the Great War. Hostilities ended on the Western Front, taking affect / effect at eleven o'clock in the morning. This became famously known / knowing as "the eleventh hour of the eleventh day of the eleventh month". While it was "all quiet / quite on the Western Front," the war continued for a while longer / length in other parts of Europe, especially in the former Russian Empire. WWI was called "the War to End All Wars". Most of the world's great powers fought them / in it. Over 20 million people died, making it one of the death / deadliest conflicts in history.
Armistice Day is observed all under / over the world. In many countries, people stop what they are doing for a two-minute moment of silent / silence at 11:00 a.m. This is a sign from / of respect for those who died. In Britain, there is the other / another name for Armistice Day - Remembrance Sunday. In 1939, the British government movement / moved Armistice Day to the Sunday nearest November 11. In America, the day is also called Veterans Day. Children in Commonwealth countries know these / them days by another name – Poppy Day. People wear poppies and donate money to charities for soldiers injury / injured in wars. Poppies are a symbol of the blood that filled the trenches. Poppies also bloomed across some of the worst battlefields during / duration the War.
Armistice Day is on November the 11th (1) ____ year. It commemorates the end of World War I on the 11th of November 1918. It was on this day that the Allies and Germany signed a ceasefire that was the beginning of the (2) ____ of the Great War. Hostilities ended on the Western Front, taking (3) ____ at eleven o'clock in the morning. This became famously (4) ____ as "the eleventh hour of the eleventh day of the eleventh month". While it was "all (5) ____ on the Western Front," the war continued for a while longer in other parts of Europe, especially in the former Russian Empire. WWI was called "the War to End All Wars". Most of the world's great powers (6) ____ in it. Over 20 million people died, making it one of the deadliest conflicts in history.
Armistice Day is observed all over the world. In many countries, people stop what they are doing for a two-minute (7) ____ of silence at 11:00 a.m. This is a sign of respect for those who died. In Britain, there is (8) ____ name for Armistice Day - Remembrance Sunday. In 1939, the British government moved Armistice Day to the Sunday (9) ____ November 11. In America, the day is also called Veterans Day. Children in Commonwealth countries know these days by another name – Poppy Day. People wear poppies and donate money to charities for soldiers (10) ____ in wars. Poppies are a (11) ____ of the blood that filled the trenches. Poppies also bloomed across some of the worst battlefields (12) ____ the War.
bloomed across some of the worst battlefields during the War.
powers fought in it. Over 20 million people died, making it one of the deadliest conflicts in history.
end Great The the the of of War beginning.
effect the at morning eleven o'clock Taking in.
all Front quiet on It the was Western.
powers it of great in Most world's fought the.
doing People what are stop they.
is a sign of respect for those who died This.
The Day Veterans called also is day.
poppies charities and donate People money wear to.
the of symbol a are Poppies blood.
Write five questions about Armistice Day in the table. Do this in pairs/groups. Each student must write the questions on his / her own paper.
Write about Armistice Day for 10 minutes. Show your partner your paper. Correct each other's work.
2. INTERNET: Search the Internet and find more information about Armistice Day. Talk about what you discover with your partner(s) in the next lesson.
3. MAGAZINE ARTICLE: Write a magazine article about Armistice Day. Write about what happens around the world. Include two imaginary interviews with people who did something on this day.
4. POSTER: Make your own poster about Armistice Day. Write about what will happen on this day around the world.


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text:
Extract sentences by keyword

Write a program
that extracts from a text all sentences that contain a particular
word (case-sensitive).

	Assume that the sentences are separated from each other by
	the character "."
	or "!"
	or "?".

	The words are separated one from another by a non-letter
	character.

	Notе that appearance as substring
	is different than appearance as word. The
	sentence "I am a fan of Motorhead"
	does not contain the word "to".
	It contains the substring "to" which is not
	what we need.

	Print the result sentence text
	without the separators between the sentences ("."
	or "!"
	or "?").

Example

	<COL WIDTH=687>

Input

to

Welcome
			to
			SoftUni! You will learn programming, algorithms, problem solving
			and software technologies. You need to
			allocate for study 20-30 hours weekly. Good luck! I am fan of
			Motorhead. To be or not to
			be - that is the question. TO DO OR NOT?

Output

Welcome
			to
			SoftUni

You
			need to
			allocate for study 20-30 hours weekly

To
			be or not to
			be - that is the question


text:
Biden's American Rescue Plan is Catholic social doctrine in action
House Speaker Nancy Pelosi, D-Calif., and Senate Majority Leader Chuck Schumer, D-N.Y., display the "American Rescue Plan" during the enrollment ceremony on Capitol Hill in Washington March 10, 2021, following passage of President Joe Biden's $1.9 trillion coronavirus disease relief bill. (CNS/Reuters/Erin Scott)
Democratic majorities in both houses of Congress passed the $1.9 billion American Rescue Plan, (ARP) and President Joe Biden signed it into law yesterday. The new law includes efforts to confront the pandemic and the economic consequences of the pandemic, but it also addresses child poverty and other long-standing issues of economic inequality. Biden promised to "build back better," and this law is a major step toward redeeming that promise.
The plan constitutes a decisive repudiation of trickle-down economics in favor of a bottom-up approach to economic stimulus that is far more consistent with Catholic social teaching.
"This legislation is about giving the backbone of this nation — the essential workers, the working people who built this country, the people who keep this country going — a fighting chance," the president said after the House passed the final legislation on Wednesday.
Republicans like to talk about helping the working class, but that help is always derivative. GOP policy the last 40 years has been to cut taxes on the rich and wait for the effects of their increased wealth to trickle down to the rest of us. This neo-liberal approach, with its idolization of market forces, has been denounced by every pope since Leo XIII in 1891. Pope Francis' 2013 apostolic exhortation, Evangelii Gaudium, epitomizes the church's hostility to the neo-liberal, trickle-down approach:
Some people continue to defend trickle-down theories which assume that economic growth, encouraged by a free market, will inevitably succeed in bringing about greater justice and inclusiveness in the world. This opinion, which has never been confirmed by the facts, expresses a crude and naïve trust in the goodness of those wielding economic power and in the sacralized workings of the prevailing economic system.
It is not impossible to see Biden, the kid from Scranton, using such words, but I am glad the kid from Buenos Aires beat him to it.
The differences in the tax provisions between the just-passed ARP and President Donald Trump's 2017 Tax Cuts and Jobs Act (TCJA) are stark. According to the Tax Policy Center's analysis of the new law:
Simply in terms of whose taxes are cut, the bill is in stark contrast to the 2017 Tax Cuts and Jobs Act. In 2021, low- and moderate-income households (those making $91,000 or less) would receive nearly 70 percent of the tax benefits from the [ARP]. Among families with children, those low- and middle-income households would get nearly three-quarters of the benefit. By contrast, nearly half of the TCJA's 2018 tax cuts went to households in the top 5 percent of the income distribution (who made about $308,000 that year).
They estimate that the biggest beneficiaries of Biden's proposal are those in the lowest two economic quartiles, while the benefits of the Trump tax cuts went overwhelmingly to the top quartile.
Republicans are trying to remake themselves as the party of the working class, but they are having trouble making the switch. Senators Mike Lee and Marco Rubio recently issued a joint statement regarding efforts to expand the Child Tax Credit. They note that the Child Tax Credit was included in the 2017 TCJA.
They now oppose efforts to turn the credit into an "allowance," akin to a universal basic income for children, because it would decouple the benefit from the requirement that a parent be working. "An essential part of being pro-family is being pro-work. Congress should expand the Child Tax Credit without undercutting the responsibility of parents to work to provide for their families," they state.
Where was this concern about the responsibility to work in some other provisions of the 2017 tax reform? According to testimony from Chye-Ching Huang of the Center on Budget and Policy Priorities, that law, among other regressive effects, lowered corporate tax rates by 40%, mostly helping investors and top-level executives who receive stocks as part of their compensation, and doubled the exemption for the estate tax. So, investment income and dying get lower tax rates period, but the poor need to demonstrate they work hard?
A worker in Minneapolis washes away chalked messages on US Bank Plaza March 8, 2021. (CNS/Reuters/Nicholas Pfosi)
If I were a Republican, I would be rooting for Rubio. His "common good conservatism" is ethically thin by my lights, but it is vastly superior to the cult of Trump that dominates the GOP. Rubio's pitch to the working class is not entirely rooted in resentments, to be sure. His aspirational rhetoric is something more Democrats need to learn to mimic.
Still, he refuses to recognize the degree to which he is reflexively allergic to economic policies that depart from the trickle-down policies of the past 40 years. Marco: Reagan is dead and buried. Thatcher is dead and buried. It is time to chart a new course.
That new course extends beyond economics; the pandemic has revived the need for government in ways no other event could have. As E.J. Dionne wrote this week in The Washington Post, "There is nothing magical about the renewed popularity of government action. The pandemic flattened the private sector economy and demanded a mobilization of resources only government could command. The disparate health and economic impacts of covid-19 turned inequality from an abstract question into a life-or-death proposition."
This willingness to deploy the authority of the state to address issues of justice raised by the pandemic also enjoys a prominent pedigree in Catholic social teaching. Here, St. Pope John Paul II's teaching in Centesimus Annus comes to mind and seems exactly on point as we consider the need to repair our health, education and economic infrastructures:
It is the task of the State to provide for the defence and preservation of common goods such as the natural and human environments, which cannot be safeguarded simply by market forces. Just as in the time of primitive capitalism the State had the duty of defending the basic rights of workers, so now, with the new capitalism, the State and all of society have the duty of defending those collective goods which, among others, constitute the essential framework for the legitimate pursuit of personal goals on the part of each individual.
Health, education and basic welfare are among the collective goods that the state is charged with providing when the market fails to do so. As John Paul II continued in that same paragraph:
Certainly the mechanisms of the market offer secure advantages: they help to utilize resources better; they promote the exchange of products; above all they give central place to the person's desires and preferences, which, in a contract, meet the desires and preferences of another person. Nevertheless, these mechanisms carry the risk of an "idolatry" of the market, an idolatry which ignores the existence of goods which by their nature are not and cannot be mere commodities.
I could have found countless citations from other encyclicals. The economic catastrophe occasioned by the pandemic requires government intervention, and such intervention is perfectly consistent with the teaching of the Catholic Church.
Fratelli Tutti, specifically written with the experience of the pandemic in mind, pointed toward the kinds of policies that the ARP contains, as well as the moral demand that we not revert to the unjust socio-economic structures that existed before COVID-19, but instead use this moment to rebuild a more just and humane society.
Biden and the Democrats have placed a big bet. If this stimulus package fails to stimulate the economy, if unemployment is still horrifically high next year, if children are still unable to go to schools in some cities because the poor ventilation in the school buildings make them viral incubators, if child poverty continues at its unconscionably high rate, the Democrats will pay a political price for this American Rescue Plan, and they will deserve to pay a price. And if it works, the Republicans might pay a price for having been bystanders at a time when so many of our fellow citizens are in profound pain. Whatever the political calculus, we all can hope that it works and, as Catholics, take some pride in the fact that our values and habits of ethical thought have played a role in coming to the nation's aid.


text:
Aflao è una città del Ghana nella Regione del Volta.

È la prima città della costa orientale dopo il confine con il Togo.

Il principale gruppo etnico è quello degli Anlo, del gruppo degli Ewe.

Altri progetti

Centri abitati della regione del Volta

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Scotty (Simon Pegg) and Bones (Karl Urban) are stranded on Starbase Earhart, a remote outpost just outside of Federation Space, after the Enterprise is destroyed by an unknown force of ruthless aliens. Halfway into their five year mission, they must now face off against a new and unexpected villain that they quickly learn has a storied and powerful hatred of the Federation and all that it stands for.
The Enterprise's mission was to explore strange new worlds and seek out new life and new civilizations. In Star Trek: Beyond our heroes find themselves on a strange planet where members of the crew have been taken hostage by a ruthless villain named Krall (Idris Elba). It's up to Captain Kirk (Chris Pine) to rescue his crew and prove that the Federation's belief in unity is not a weakness, but a strength.


text:
Sara Netanyahu in court on June 16.
Sara Netanyahu, wife of Israel's prime minister, sentenced for corruption
By Ephrat Livni June 16, 2019
Israeli prime minister Benjamin Netanyahu has a lot of problems. He has been accused of corruption, failed to assemble a coalition after winning a recent election and now must campaign in another race in September. To make matters worse, his wife is now officially a convicted criminal.
Sara Netanyahu was accused of aggravated fraud and breach of public trust last June. Netanyahu ordered gourmet takeout to the residence even though her government-funded kitchen had its own chef, flouting state rules and forcing the public pay for meals.
Prosecutors argued the prime minister and his wife were not entitled to the $96,000 in take-out ordered between 2010 and 2013, according to the indictment. Ultimately, she pled guilty to lesser charges and today (June 16) was sentenced.
The prime minister's wife faced up to five years in prison on the initial charges against her. In a negotiated settlement, she agreed to plea to "intentionally exploiting the mistake of another" by misleading officials who authorized the expenses, unaware that she already benefited from chefs on the government payroll, AP reports. Her overspending charges were reduced to $50,000, and she has agreed to pay $2,800 in fines and return about $12,500 to the state.
Prosecutor Erez Padan said that the prosecution made "significant concessions" to resolve the case, explaining, "Like in every plea deal, all sides make concessions, at times not easy ones. Netanyahu's consent to be convicted shows she assumes responsibility." He said the deal was struck because there were difficulties obtaining evidence in the matter, according to Haaretz.
"Sara Netanyahu is today paying a heavy and painful personal cost to put an end to this witch hunt, and I hope that indeed this is the end of the story," Netanyahu's attorney, Yossi Cohen, said after the sentencing hearing.
As unseemly as Sara's food crime may appear, it's small time compared to the accusations that her husband faces. Benjamin Netanyahu has been accused of bribery and breach of public trust for allegedly accepting lavish gifts from rich friends and promoting desired legislation in exchange for favorable media coverage.
Netanyahu has repeatedly tried to push back a pre-indictment hearing, most recently claiming that upcoming elections in September make an October hearing impossible. But Israeli Attorney-General Avichai Mandelblit refused further delays, and the hearing is expected on October 2.


Come out to get involved and learn about the events we will be hosting at W&M this year. Food will be served (including vegetarian options) in room 127.
Seminar Title: "Response of Planktonic Foraminifera to Seasonal Upwelling and Acidfication Along the California Margin"
Organizations that were allocated funding during the annual budget distribution process (held in early spring 2017), must send their financial manager and/or primary contact to one of three budget distribution workshops.
Come out and meet the producers of WMTV and learn more information about working for William & Mary's student run TV station.


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text:
Q: Angular router causes 404 when page is refreshed Basically title, I would like the router to be able to reroute to a certain page via URL. I would like to be able to move to all my "pages" but I can't find all that much information on how that can be achieved.
https://grimzero.github.io/Portfolio to https://grimzero.github.io/Portfolio/About
To clarify, my router has no issues on my page, I would just like that the page doesnt throw a 404 when it is refreshed somewhere other than the main page.

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