text:
Wikijunior talk:Dinosaurs/Brontosaurus

Controversy
The impression I'm getting here — subject, obviously, to much more study, is that this is basically unsettled, with individual scientists taking strong positions (so that there will be push-back from claiming it's unsettled) but overall consensus in flux. This article could be an opportunity to teach kids about the essence of science, the consideration of rival theories. --Pi zero (discuss • contribs) 02:44, 13 June 2019 (UTC)
 * . A book that taught children how to distinguish probable fact from likely fiction would be enormously useful especially as it is a primary failing of the education system. Starting with the scientific method and how theory is advanced is a good place. Interestingly I read somewhere that Wikipedia demonstrates that even highly controversial subjects can achieve a consensus among opposed editors because they have a common goal - creating a featured article. I feel the germs of an interesting book, if only I had time to write it. QuiteUnusual (discuss • contribs) 08:33, 13 June 2019 (UTC)
 * In very deed. It's been a pet peeve of mine for many years that "popular science" presentations (where I am, mostly on PBS) almost always present prevailing scientific theories as fact; even when discussing a bit of the evidence, they'll say that such-and-such scientist of the past noticed that so-and-so, and therefore theorized that such-and-so, which we now know to be true, but also thought that thus-and-such whereas we later discovered something-or-other and we now know that whatnot.  Which is completely wrong; we don't know anything through science, and the arguments against science are utter bunk.  Basically, not only do opponents of science treat science as if it were a belief system in the same sense that a religion is, but these popular science programs treat it that way too.  A scientific theory is neither absolute truth nor a matter of faith.  A favorite quote of mine is from a Physics Today review (by Freeman Dyson) of a biography (by James Gleick) of Richard Feynman:
 * Gleik sums up Feynman's scientific credo in one sentence, the clearest statement I have seen of the true spirit of science: "He believed in the primacy of doubt, not as a blemish upon our ability to know but as the essence of knowing."
 * --Pi zero (discuss • contribs) 12:22, 13 June 2019 (UTC)

title: Wikijunior talk:Dinosaurs/Brontosaurus


text: User talk:168.229.254.26

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: User talk:168.229.254.26


text: User talk:2401:4900:18F4:A309:4C28:B6FF:FE41:AA67


text:
User talk:Hvn0413

Welcome, Hvn0413!

If you have any questions, you can ask in the assistance reading room or possibly contact me personally. 94rain Talk 08:17, 18 August 2019 (UTC)

title: User talk:Hvn0413


text: User talk:2409:4063:2316:9672:0:0:2248:B0A5


text:
User talk:105.112.39.157

Pls can someone help me I wan t to learn c++ Or python can someone guide me or assist me thanks

title: User talk:105.112.39.157


text:
User talk:Cmhyatt83

Welcome, Cmhyatt83!

If you have any questions, you can ask in the assistance reading room or possibly contact me personally. Viztor (discuss • contribs) 01:27, 14 June 2019 (UTC)

title: User talk:Cmhyatt83


text:
User talk:Btauri

Hello! Some time ago my colleagues published a book on Viquillibres (catalan version of Wikibooks) and Wikilibros (spanish version of Wikibooks) called Guia Jove or Guía Joven (depending on the language), and now I would like to upload the same in an English version that has translate a professional group of translators. The books is a youth guide for professionals who work with youths to promote their participation through motivation. It has different sections and includes topics related to young people's participation, planning socio-educational projects and the use of an intervention area. How can I do it? What steps should I follow? Does it has to be published as a new book or there's an opcion to publish it as just another version of the same? For doing the spanish version, the user Morza helped my colleagues a lot. I already have the authorization and blessing from the authors. Do I need any other permissions? I hope your answers. Thank you. --Btauri (discuss • contribs) 09:19, 14 June 2019 (UTC)

title: User talk:Btauri


text:
User talk:185.84.211.226

Hello, Please refrain from making unconstructive edits to Wikimedia projects. Your edits appear to constitute vandalism and have been reverted. If you would like to experiment, please use the sandbox. Repeated vandalism may result in the loss of editing privileges. Thank you. -- Tomybrz (d)

title: User talk:185.84.211.226


text:
User talk:82.69.20.70

Warning
Hello, I wanted to let you know that one or more of your recent contributions have been undone because they did not appear constructive. If you would like to experiment, please use the sandbox. If you have any questions, you can ask for assistance at the Help Desk. Thanks. -- Tomybrz (d)

title: User talk:82.69.20.70


text: User talk:Mielkemom

title: User talk:Mielkemom


text:
Art Tutorials/General Concepts

Art is subjective, but there are many common principles and concepts used in art.

title: Art Tutorials/General Concepts


text:
User talk:Mattmart1993

Wtf

title: User talk:Mattmart1993


text:
Art Tutorials/Traditional Media/Painting

There are many types of painting mediums - oils, acrylics, watercolor, ink, etc. It should be noted that each type of paint requires different materials.

In General
For all forms of painting other than water-based media, ventilation is important in order to avoid breathing in potentially harmful fumes. This is especially true for pregnant and/or breastfeeding women, people with respiratory issues, and children/teenagers. If you fall into any of those groups, consult a doctor before painting. Take precautions while painting as well.

To start painting, you will need:
 * For solvent-based media, a well-ventilated area - fans and open windows are recommended.
 * Canvases and/or paper. Be aware that there are different canvases/papers made for different mediums, though with care most supports can be used for any paint. Especially for oil-based media, it is important to use a surface primed with a ground such as gesso, as this prevents unwanted chemical reactions with the paint, which can lead to the deterioration of the work.
 * Brushes - Basic brush sets can be found at hobby and art supply stores. Be mindful that many cheaper brush bristles come off easily. Different techniques and types of paint will suggest the use of different brushes: Typically, oil paints will require the stiffest bristles, and watercolors the softest. Brushes for acrylics tend to fall between these two.

Oils
Oils are one of the most popular mediums in painting. While they are widely used, it should be noted that oils (and solvents) are toxic, and one should only use oils in a well-ventilated room, or even outdoors. Because of the toxicity, pregnant and/or breastfeeding women are advised not to use oils and solvents while painting.

What you'll need:
 * Oil paint
 * Solvent/Paint Thinner - Turpentine is a popular one, but is also toxic. There are more environmentally-friendly and healthy solvents out there, and some can even be made at home.
 * Palette for mixing paints - most oil painters use flat palettes of non-absorbent materials, such as glass or metal, though some still use traditional wood palettes. In a pinch, a large ceramic dish can be used.
 * Palette knife - not required, but very useful for mixing paint and for certain application techniques.

Acrylics
Acrylics are a water-based type of paint. No solvents are required, all that is needed for cleanup is water. This makes acrylics a more budget- and health-friendly option, but precautions should still be taken.

What you'll need:
 * Acrylic paint
 * Water
 * Palette for mixing paints - similar to an oil paint palette.
 * Palette knife - useful for mixing paint and for special application techniques.

Watercolor
Watercolors are known for having a very airy and transparent appearance. This effect is achieved by dabbing pigment onto puddles of water on the paper.

What you'll need:
 * Watercolors
 * Palette for mixing paints - watercolor palettes tend to have wells for individual colors and large flat wells for mixing. Most available models are made of plastic or metal.
 * Watercolor paper

Ink
Ink painting is lesser-known, but is popular in parts of Asia like China and Japan. Usually, ink paintings are done in black-and-white.

What you'll need:
 * Ink - Sumi ink and India ink are the most popular. Sumi ink has a more matte appearance while India ink is shiny.
 * Paper


text:
Art Tutorials/Digital Media/Software and Tools

There are many pieces of software and tools available for digital artists to use, both free and premium. With all the software out there, one can start making digital art anytime, anywhere.

Tools:
 * A computer or tablet - One doesn't need one too powerful unless they are making large pieces or getting into 3D work. Starting out, a basic machine is fine.
 * Drawing tablet - This is not a necessity, but many feel that it does help. A drawing tablet allows one to draw like they're using paper.
 * Software

Ms Paint
This piece of software comes free with Windows. Though it lacks many features such as layers and transparency, MS Paint has its uses. It is especially used for pixel art.

Adobe Photoshop
This paid software is one of the most popular out there. It is used by hobbyists and professionals alike.

Paint.NET
This is a free art program that has many features that Ms Paint doesn't, but is not as loaded as Photoshop. The simple UI makes it a viable option for beginners.

Paint Tool SAI
This program has a 30-day free trial, and is utilized by many artists for its brush and linework options.

GIMP
This is a free, open source program, which also has many brushes and filters.

Blender
This is a free program that can be used to make 3d models and scenes.

Maya
This is a paid option, but has a student version.

MakeHuman
This software is for easily generating models of humans.


text:
Art Tutorials/General Concepts/Color

Colors are used extensively in art and visual design. Colors can help to convey messages and draw attention to certain details. Artists can use color most effectively when they understand the basics of colors and what they are.

Hue
Hue is what makes "color", "color". It is determined by wavelength. From red to violet, hue is In painting, a hue is pure, without tint (white) or shade (black) in it.

Cool Colors
Cool colors include blue, green, and violet. They are oftentimes used for a calming or somber effect.

Warm Colors
Warm colors include red, orange, and yellow. They are oftentimes used for an energetic effect.

Neutral Colors
Neutral colors don't show up on color wheels most of the time. They include black (the absconce of color), white (all colors together), and grey. They are called neutral because they can go well with many other colors, and can be present in large quantities without being stressful on the eyes.

Saturation
Saturation is, basically, how much color is in a color. The more saturated a color is, the more muted it is. Muted colors are more dull and "grey" than unsaturated colors. In painting, the addition of white, black, grey, or even a colors compliment (also known as its opposite) can saturate a color. The eyes are drawn to unsaturated colors, but are less drawn to saturated/muted colors. This can be used to place emphasis on certain parts of a piece, like a bright red tree in a dreary city, or a bold green tree frog on a branch.

Value
The value of a color refers its lightness or darkness. Lighter colors have a higher value, and darker colors have a lower value.

Tint, Shade, and Tone
Tint, shade, and tone refer to the amount of white, black, and grey in a color respectively. They decrease the intensity of a color. For example, light blue and dark blue are both considered easier on the eyes than a pure blue.

How Colors Go Together
Unless one is making a monochromatic piece (where only one color is used), colors are used in conjunction with one another. In color theory, the color wheel is oftentimes used to demonstrate how colors can be used together.

Complementary Colors
Two colors on opposite ends of the color wheel are complementary. Things like red and green, yellow and violet, and blue and orange are examples of complementary colors. Complementary colors contrast with one another, giving a visually interesting effect.

Analogous Colors
Three colors that sit next to each other on the color wheel are analogous. This can provide a harmonious effect because the colors are so similar to one another.

title: Art Tutorials/General Concepts/Color


text:
Art Tutorials/Photography

Photography is the art of using a camera to capture images of the real world. In 1825, Joseph Nicéphore Niépce took the first permanent photograph in Paris, France using a camera made by Charles and Vincent Chevalier. Today, thousands of people take photos of the world around them, from professional photographers to hobbyists to even those with no interest in photography at all (How many times have you seen someone take a picture of their meal?). While in the early days one would need a big expensive camera to take pictures, a beginner can start by just using their phone.

title: Art Tutorials/Photography


text:
Art Tutorials/Introduction

Making art, especially beginning it, can be both an exciting and daunting task. All artists must start from square one, whether it be their first time picking up a drawing pencil, their first time opening up Photoshop, or their first time holding a camera. This book is here to help teach basic concepts in art, along with how to begin in some of the various forms of art. Keep in mind that while there are principles and concepts and art, ultimately, art is subjective. What is considered terrible in ones eyes can be wonderful in anothers.

This book starts with the basic concepts of art, and then goes into means of making art and required supplies. While it is not necessary to try everything in this book, it is encouraged.

title: Art Tutorials/Introduction


text:
Art Tutorials/Traditional Media/Printmaking

Printmaking is the art of transferring images from one medium to another. Printmaking has been used for centuries to make multiple copies of paintings and other images, as well as to produce decorative objects such as wallpapers and fabrics. There are many forms of printmaking.

=Stencil= Stencils can range from simple paper cutouts used to block certain areas from receiving color, to elaborate photographic resists in silk-screen printing, the most widespread technique in this group. Along with relief printing, stencils are one of the most approachable printmaking techniques due to the simple equipment required to get started.

Silk Screen Printing
=Relief= Relief printing is any where the raised areas of a printing plate are inked and used to make marks on the final support, typically paper. Ukiyo-e woodblock prints are a famous form of relief printmaking, but many other forms exist, including linocuts, wood engravings and collagraphs. As relatively little pressure is required to transfer the ink and other equipment requirements are moderate, these techniques are a popular entry point into printmaking for beginning artists.

Linocut
Linocuts are made by carving away some of the surface of a piece of linoleum, and then inking the remaining uncarved surface and transferring it to a piece of paper (or another substrate if desired). The equipment requirements for getting started are minimal: Also good to have: How you get an image onto the plate is a matter of personal choice. Some artists sketch directly on the plate, some use tracing or carbon paper, some use other methods including stamping, stenciling and projection, but certainly not limited to these. For starters it's probably best to start simply, and to draw the desired image on the plate using soft pencils, markers or anything that will not run off the surface of the linoleum. Once the image is drawn, it's time to carve it into the plate. Using a knife or gouges, carefully cut away any area you want to appear white in the final print. Remember, unlike typical drawing, you're creating white lines on a colored background. This can get a bit of getting used to, and there's no substitute for practice for getting the hang of it. Once you reach a phase where you think the plate is close to being finished, it's good to make a test print. Place a dab of ink about an inch across on your ink plate, and using the roller roll it out into a thin layer. The ink will cover the roller as you do. You want the roller to be generously and uniformly coated. A correctly coated roller will roll on the glass without slipping. With the linoleum face up, you then roll the ink onto the plate. Once you do, place the plate in a clean spot, place a sheet of paper over it, and using a wooden spoon or other tool of choice, rub the entire surface of the paper over the plate to transfer the ink. Since the ink is sticky, you can carefully lift a corner of the paper from the plate from time to time to check how the image is transferring, to see whether any areas require further attention. If you keep most of the paper adhered to the plate, you can replace the corner after inspection without shifting anything and continue rubbing until the image is transferred to your satisfaction. Then carefully lift the paper from the plate and place it on a clean surface printed side up. Now examine the proof print you have made. See whether the image is finished, or whether you want to continue making changes. Chances are that at this stage you will want to make many changes. If so, wipe the ink from the plate and continue working on it. Make another test print once in a while to check your progress. Once you're happy with the image, it's time to make as many copies of it as you want. As with the test prints, roll ink out on your ink plate with the roller, transfer the ink to the plate, place a sheet of paper on it, and rub to transfer the ink to the paper. The ink will take some time to dry, especially if you are using oil-based inks, so having a safe place for the prints to dry is useful. After the ink dries, the prints are finished and ready to sell, give away, or simply enjoy them yourself.
 * a piece of linoleum
 * a sharp knife. While specialized tools (knives, gouges, etc.) are made specifically for linocuts, a simple utility knife could produce very good effects if used with care.
 * an ink roller
 * a flat, non-absorbent surface to roll the ink out on (usually a piece of thick glass or mirror)
 * a tool for applying pressure to the paper to transfer the ink from the plate - while some artist use massive and expensive etching presses for this, a beginner can make do very well with a simple wooden spoon or something similar.
 * ink - water based inks are best for starting out, and they have recently become almost as good as traditional oil-based ones. They are popular because they don't produce hazardous vapors and are a lot easier to clean up.
 * paper - any smooth paper will do, especially for tests, but a heavier, high quality art paper with a smooth surface will produce better finished prints.
 * a bench hook - a piece of thin plywood or hardboard with strips of wood attached to the front bottom and rear top sides, which hooks on to the edge of a table and provides a work surface with a stop that keeps the linoleum from sliding around. Very handy, can be purchased or easily made with very limited tools.
 * linocut gouges - tools for carving out lines and large areas quickly. Gouges come in a variety of shapes and widths, which produce different effects in the finished print.
 * tracing paper or vellum for transferring images to the plate
 * lots of paper towels or rags

Collagraphy
Collagraphy is a technique that uses plates built up from a variety of objects glued onto a substrate, which then can be inked as relief or intaglio, or a combination of the two, depending on the artist's intention. Plates can be made using paper and cardboard cutouts, fabrics, meshes, pieces of wood or metal, as well as found objects, as long as they are flat. When used as a relief plate, it is then inked, and the ink is transferred to paper using moderate pressure from any of a number of possible tools, from spoons and sticks to professional etching presses. For intaglio collagraphy, ink is first applied to the plate, then wiped off the high points to leave it in the crevices of the objects of which it is composed. Such a plate must then be run through a specialized etching press to transfer the ink to paper.

=Intaglio= Intaglio printmaking transfers ink from grooves in a printing plate using the pressure of a printing press. Various techniques exist of creating the grooves, or depressions, ranging from manually engraving them using a graver or drypoint needle, to etching with acid in etchings and aquatints. Due to the need for a printing press, intaglio techniques are not generally practiced outside dedicated print studios.

Mezzotint
=Planographic= Planographic techniques refer mainly to lithography and its derivatives. Lithography depends on the lack of adhesion between a wet printing stone (or plate) and the greasy printing ink used. Heavy pressure from a printing press is used to transfer the image to the final support. As with intaglio, these techniques require extensive, and expensive, equipment, and are typically out of reach for beginning artists.

Xerolithography
An image can be transferred from a paper original printed with water-repellent inks, such as xerographic reproductions (only laser copiers and printers will produce these; inkjet images are not suitable) and some varieties of offset prints such as glossy magazines. The paper plate has to be moistened before being inked in order for the wet paper to repel the ink, which will adhere only to printed areas. The plate is then run through a press in contact with the final medium, transferring the ink. Typically paper plates are suitable for single transfers or very limited editions, as the required moisture and high pressure tends to disintegrate them. One source claims that this technique is suitable for use with a spoon to apply the pressure instead of a printing press[].


text:
Art Tutorials/Digital Media/Digital Painting

Digital painting is the use of software instead of traditional means to make art. Because there is little to no clean-up required, few supplies required, and can be done virtually anywhere, digital painting is widely used and can be considered convenient, sometimes moreso than traditional methods.

What You'll Need
To make digital art, one requires a computer/tablet and an art program. Some may find a drawing tablet, also known as a graphics tablet, to be beneficial. These can be purchased online or at a tech store. They come with two parts: the tablet and pen, and are used like one is drawing on paper. Though they are popular and can simplify the artistic process, they are not necessary, and many artists use a mouse or even a trackpad.

There are many art programs, both free and premium, out there. Keep in mind that premium programs are not necessarily better than free ones.

Starting Up
When you first start an art program, you will be greeted with a blank canvas. This canvas can be modified in terms of shape, size, and resolution. Higher resolutions produce smoother results than lower resolutions, and bigger canvases show fewer pixels than smaller ones.


text:
User:MDMinusdr/sandbox

''Wikidata Query Service Examples Help More tools English

Minu SDR 1 Minu SDR #Number of humans in Wikidata 2 SELECT (COUNT(?item) AS ?count) 3 WHERE { 4   ?item wdt:P31/wdt:P279* wd:Q5. 5 } 18:58:31 GMT+3, 14 Jun 2019 Data updated 7 hours ago Query is malformed: Encountered " "min" "Min "" at line 1, column 1. SPARQL-QUERY: queryStr=Minu sdr Mijan sdr

java.util.concurrent.ExecutionException: org.openrdf.query.MalformedQueryException: Encountered " "min" "Min "" at line 1, column 1. Was expecting one of: "base" ...   "prefix" ...    "select" ...    "construct" ...    "describe" ...    "ask" ... at java.util.concurrent.FutureTask.report(FutureTask.java:122) at java.util.concurrent.FutureTask.get(FutureTask.java:206) at com.bigdata.rdf.sail.webapp.BigdataServlet.submitApiTask(BigdataServlet.java:292) at com.bigdata.rdf.sail.webapp.QueryServlet.doSparqlQuery(QueryServlet.java:678) at com.bigdata.rdf.sail.webapp.QueryServlet.doGet(QueryServlet.java:290) at com.bigdata.rdf.sail.webapp.RESTServlet.doGet(RESTServlet.java:240) at com.bigdata.rdf.sail.webapp.MultiTenancyServlet.doGet(MultiTenancyServlet.java:273) at javax.servlet.http.HttpServlet.service(HttpServlet.java:687) at javax.servlet.http.HttpServlet.service(HttpServlet.java:790) at org.eclipse.jetty.servlet.ServletHolder.handle(ServletHolder.java:865) at org.eclipse.jetty.servlet.ServletHandler$CachedChain.doFilter(ServletHandler.java:1655) at org.wikidata.query.rdf.blazegraph.throttling.ThrottlingFilter.doFilter(ThrottlingFilter.java:338) at org.eclipse.jetty.servlet.ServletHandler$CachedChain.doFilter(ServletHandler.java:1642) at ch.qos.logback.classic.helpers.MDCInsertingServletFilter.doFilter(MDCInsertingServletFilter.java:49) at org.eclipse.jetty.servlet.ServletHandler$CachedChain.doFilter(ServletHandler.java:1642) at org.wikidata.query.rdf.blazegraph.filters.ClientIPFilter.doFilter(ClientIPFilter.java:43) at org.eclipse.jetty.servlet.ServletHandler$CachedChain.doFilter(ServletHandler.java:1634) at org.eclipse.jetty.servlet.ServletHandler.doHandle(ServletHandler.java:533) at org.eclipse.jetty.server.handler.ScopedHandler.handle(ScopedHandler.java:146) at org.eclipse.jetty.security.SecurityHandler.handle(SecurityHandler.java:548) at org.eclipse.jetty.server.handler.HandlerWrapper.handle(HandlerWrapper.java:132) at org.eclipse.jetty.server.handler.ScopedHandler.nextHandle(ScopedHandler.java:257) at org.eclipse.jetty.server.session.SessionHandler.doHandle(SessionHandler.java:1595) at org.eclipse.jetty.server.handler.ScopedHandler.nextHandle(ScopedHandler.java:255) at org.eclipse.jetty.server.handler.ContextHandler.doHandle(ContextHandler.java:1340) at org.eclipse.jetty.server.handler.ScopedHandler.nextScope(ScopedHandler.java:203) at org.eclipse.jetty.servlet.ServletHandler.doScope(ServletHandler.java:473) at org.eclipse.jetty.server.session.SessionHandler.doScope(SessionHandler.java:1564) at org.eclipse.jetty.server.handler.ScopedHandler.nextScope(ScopedHandler.java:201) at org.eclipse.jetty.server.handler.ContextHandler.doScope(ContextHandler.java:1242) at org.eclipse.jetty.server.handler.ScopedHandler.handle(ScopedHandler.java:144) at org.eclipse.jetty.server.handler.ContextHandlerCollection.handle(ContextHandlerCollection.java:220) at org.eclipse.jetty.server.handler.HandlerCollection.handle(HandlerCollection.java:126) at org.eclipse.jetty.server.handler.HandlerWrapper.handle(HandlerWrapper.java:132) at org.eclipse.jetty.server.Server.handle(Server.java:503) at org.eclipse.jetty.server.HttpChannel.handle(HttpChannel.java:364) at org.eclipse.jetty.server.HttpConnection.onFillable(HttpConnection.java:260) at org.eclipse.jetty.io.AbstractConnection$ReadCallback.succeeded(AbstractConnection.java:305) at org.eclipse.jetty.io.FillInterest.fillable(FillInterest.java:103) at org.eclipse.jetty.io.ChannelEndPoint$2.run(ChannelEndPoint.java:118) at org.eclipse.jetty.util.thread.strategy.EatWhatYouKill.runTask(EatWhatYouKill.java:333) at org.eclipse.jetty.util.thread.strategy.EatWhatYouKill.doProduce(EatWhatYouKill.java:310) at org.eclipse.jetty.util.thread.strategy.EatWhatYouKill.tryProduce(EatWhatYouKill.java:168) at org.eclipse.jetty.util.thread.strategy.EatWhatYouKill.run(EatWhatYouKill.java:126) at org.eclipse.jetty.util.thread.ReservedThreadExecutor$ReservedThread.run(ReservedThreadExecutor.java:366) at org.eclipse.jetty.util.thread.QueuedThreadPool.runJob(QueuedThreadPool.java:765) at org.eclipse.jetty.util.thread.QueuedThreadPool$2.run(QueuedThreadPool.java:683) at java.lang.Thread.run(Thread.java:748) Caused by: org.openrdf.query.MalformedQueryException: Encountered " "min" "Min "" at line 1, column 1. Was expecting one of: "base" ...   "prefix" ...    "select" ...    "construct" ...    "describe" ...    "ask" ... at com.bigdata.rdf.sail.sparql.Bigdata2ASTSPARQLParser.parseQuery2(Bigdata2ASTSPARQLParser.java:400) at com.bigdata.rdf.sail.webapp.QueryServlet$SparqlQueryTask.call(QueryServlet.java:741) at com.bigdata.rdf.sail.webapp.QueryServlet$SparqlQueryTask.call(QueryServlet.java:695) at com.bigdata.rdf.task.ApiTaskForIndexManager.call(ApiTaskForIndexManager.java:68) at java.util.concurrent.FutureTask.run(FutureTask.java:266) at java.util.concurrent.ThreadPoolExecutor.runWorker(ThreadPoolExecutor.java:1149) at java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:624) ... 1 more Caused by: com.bigdata.rdf.sail.sparql.ast.ParseException: Encountered " "min" "Min "" at line 1, column 1. Was expecting one of: "base" ...   "prefix" ...    "select" ...    "construct" ...    "describe" ...    "ask" ... at com.bigdata.rdf.sail.sparql.ast.SyntaxTreeBuilder.generateParseException(SyntaxTreeBuilder.java:9718) at com.bigdata.rdf.sail.sparql.ast.SyntaxTreeBuilder.jj_consume_token(SyntaxTreeBuilder.java:9585) at com.bigdata.rdf.sail.sparql.ast.SyntaxTreeBuilder.Query(SyntaxTreeBuilder.java:337) at com.bigdata.rdf.sail.sparql.ast.SyntaxTreeBuilder.QueryContainer(SyntaxTreeBuilder.java:212) at com.bigdata.rdf.sail.sparql.ast.SyntaxTreeBuilder.parseQuery(SyntaxTreeBuilder.java:32) at com.bigdata.rdf.sail.sparql.Bigdata2ASTSPARQLParser.parseQuery2(Bigdata2ASTSPARQLParser.java:336) ... 7 more''

title: User:MDMinusdr/sandbox


text:
Baroque Macedonia and the Macedonian Revolts

Table of Contents

 * /Introduction/

 * /Chapter 1 : The struggle for freedom/

 * /Chapter 2 : Early life of a rebellion leader/

 * /Chapter 3 : The gathering of troops/

 * /Chapter 4 : Construction of fortifications/

 * /Chapter 5 : Battle of Kriva Palanka/

 * /Chapter 6 : Victory/

 * /Bibliography/

 * /Author/


text:
QBasic/Advanced Maths

Complex mathematical functions
There are a few trigonometrical operations in QBasic such as:

Most of the other complex calculations do not have appropriate functions in QBasic and hence you have to use functions and make them yourselves.

Some examples taken from the QB64 IDE help page.

title: QBasic/Advanced Maths


text:
User talk:112.215.245.176

JackPotte (discuss • contribs) 17:35, 15 June 2019 (UTC)

title: User talk:112.215.245.176


text:
User talk:2604:6000:100E:A19D:34CF:A579:73F5:9568

Hello, You may be blocked from editing without further warning the next time you vandalize Wikimedia projects. -- Tomybrz (d)


text:
User talk:C.E. user HM J. Y.

Welcome
Welcome to Wikibooks, C.E. user HM J. Y.!

 First steps tutorial Wikibooks is for collaborative development of free textbooks.

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  Getting help   Made a mistake?   Goodies, tips and tricks
 * Read the Using Wikibooks book for a friendly introduction to the project, or our help pages for more information.
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--Pi zero (discuss • contribs) 05:39, 16 June 2019 (UTC)

title: User talk:C.E. user HM J. Y.


text: User talk:109.153.182.211

title: User talk:109.153.182.211


text:
SPARQL/Federated query

Federated query
Federated query is the ability to take a query and provide solutions based on information from many different sources.

A building block is the ability to have one query be able to issue a query on another SPARQL endpoint during query execution.

Example
Federated query comparing Wikidata and UK Parliament database, to show differences of more than 10km in locations of UK parliamentary constituencies (source Wikidata:Wikidata:Status updates/2019 06 10)

SPARQL Federation endpoints
Not all endpoints are allowed by Wikidata Query Service. See the list of allowed endpoints on SPARQL Federation endpoints.

You can nominate more endpoints at the Wikidata:SPARQL federation input.

title: SPARQL/Federated query


text:
VirtualBox/Setting up a Virtual Machine/macOS Catalina

Compatibility
macOS Catalina 10.15.2 and 10.15.3 (and possibly every later version) are only compatible with VirtualBox version 6.1.4 or greater.

Installation script
The following installation script:
 * ...is free and open-source
 * ...requires only VirtualBox with its Extension Pack and dependencies that can be easily installed in a single command with most open-source package managers
 * ...downloads macOS Catalina, Mojave and High Sierra directly from Apple's servers
 * ...installs macOS without modifying the original Apple binaries and without third-party bootloaders
 * ...creates a VM that is compatible with OpenCore and can be exported (with manual modifications) to KVM/QEMU for near-native performance
 * ...runs on Linux, Windows (WSL, Cygwin), and macOS

https://github.com/myspaghetti/macos-guest-virtualbox - Push-button installer of macOS on VirtualBox


text:
User:Salix alba

Operate User:Texvc2LaTeXBot to fix latex syntax. Main page en:w:User:Salix alba.

title: User:Salix alba


text: User:Jake Symons

title: User:Jake Symons


text:
User talk:AskTheRealQuestions

--Pi zero (discuss • contribs) 17:00, 17 June 2019 (UTC)

title: User talk:AskTheRealQuestions


text:
Talk:Shelf:Health sciences

Home Remedies
I suggest that the book "Home Remedies" shouldn´t be categorized as "Freshly started book", since it doesn´t look very empty. I would rather qualify it as "Partly developed book". — Preceding unsigned comment added by 134.176.146.206 (talk • contribs) 20:07, 17 June 2019 (UTC)
 * That's controlled by the book in question, on its main page; in this case, Home Remedies. Completion is specified there by the status template.  Your suggestion is plausible; trying it. --Pi zero (discuss • contribs) 20:39, 17 June 2019 (UTC)

title: Talk:Shelf:Health sciences


text:
User:Musical Inquisit/sandbox

This page will be the guinea pig for anything I don't know how to render or cannot know how it will look until I render it.

Elasticity refers to the percent change to which one value changes, quantity of $$x$$, when another does. Supply and demand change with respect to price; investment and savings change with respect to interest rate. The name is "X elasticity of Y" where a change in X causes a change of magnitude (the elasticity * Y).

Price elasticity of Demand
Let's begin with some definitions. If we want to determine the percent change in price for the demand for a good, we need to understand what we are doing. Let $$Q_{D0}$$ denote the quantity demanded at some arbitrary initial point, and let $$Q_{D}$$ denote the quantity demand at some point close to our initial point that is the final value we get to. To determine the percent change, we have to find a change in the values that we have chosen divided by our old value: if you want to put it in terms of what we learned, it is
 * $$%dQ_{D}={Q_{D} - Q_{D0} \over Q_{D0}}$$, where $$d$$ is simply a letter that denotes a very small change in $$Q$$ (quantity demand).

We learn the above information for one very special reason. That $$%d$$ means something: percentage change. We are looking at the percentage change in quantity demanded. However, we cannot find the percentage in quantity demanded without knowing the prices of goods that correspond to those values. Therefore, let $$P_{D}$$ be the price of $$Q_{D}$$ and $$P_{D0}$$ be the price of $$Q_{D0}$$. To determine the percent change, we have to find a change in the values that we have chosen divided by our old value: if you want to put it in terms of what we learned, it is

 * $$%d P = {P - P_0 \over P_0}$$, where $$P$$ is for price corresponding to $$Q$$.

For any ordered pair $$(Q_{D0},\,P_{D0})$$ and $$(Q_{D},\, P_{D})$$ that corresponds to a demand curve, the price elasticity of demand is $$

Before talking about applications, it is important to get an intuitive understanding of elasticity. Please note the use of elasticity. It is not an arbitrary term. Rather, it brings to mind the rubber band. The maximum stretching distance of the rubber band $$\Delta x$$ can be assigned a value $$a$$ or $$b$$, where $$a>b$$. As a collective, we would say that the rubber band with $$\Delta x=a$$ is relatively more elastic than $$\Delta x=b$$. Similarly, the "stretchiness" of a demand curve represents this fundamental relationship in the form of a percentage change in both quantity demanded and price using the greek letter eta ($$\eta_{D}$$).

Because the demand curve comes in all types of curves (that is downward-sloping), the elasticity must be negative. This does not change anything fundamental to how we interpret the value, yet the absolute value of the price elasticity of demand is often used. Keep in mind that the change is not some constant either but a percentage. This means we are not finding the slope. Instead, we are looking at percentage change. As a result, some strange properties come true. One of them is that moving down along a linear demand curve implies a non-constant elasticity. In fact, the change in the elasticity decreases further and further. A proof for this concept is given below:

 * Given: $${\Delta Q \over \Delta P}={1 \over m}$$ is the reciprocal slope of a linear demand curve with slope $$m$$.
 * Prove: the elasticity $$\eta_{D}$$ of a linear demand curve must be decreasing as price decreases.

Knowing $${\Delta Q \over \Delta P}={1 \over m}$$ is the reciprocal slope, multiplying by $${P \over Q}$$, which is the point $$(Q,P)$$ that is variable, makes the expression equal to the elasticity of demand $$\eta_{D}$$. The reason for this is because

$$\begin{align} \frac{\Delta Q}{\Delta P}\cdot\frac{P}{Q} &= \frac{P\Delta Q}{Q\Delta P} \\ &= \frac{\Delta Q}{Q}\cdot\frac{P}{\Delta P} \\ &= \frac{\tfrac{\Delta Q}{Q}}{\tfrac{\Delta P}{P}} \end{align}$$.

That is,

$$

As you move down the demand curve, $$\Delta P<0$$ and $$\Delta Q>0$$. Ergo, $$\frac{\Delta P}{\Delta Q}<0$$. However, given $${\Delta Q \over \Delta P}$$ is a reciprocal slope of the linear demand curve, the value for $$\Delta Q$$ and $$\Delta P$$ are both constant. Hence, the slope $${1 \over m}$$ must be constant.

Summary: Because $${P\over Q}$$ decreases per every point $$P$$ to point $$Q$$, and $${1 \over m}$$ is constant, the elasticity of demand, $$\eta_{D}$$, along a demand curve must be falling as the price decreases.$$\blacksquare$$

Notice that we were able to derive one more equation relating to the elasticity of demand, $$\eta_{D}$$. However, we did not this proof to show them. By the very fact that$$\left\vert\eta_{D}\right\vert=\left\vert{%dQ_{D} \over %dP_{D}}\right\vert=\left\vert{{Q_{D} - Q_{D0} \over Q_{D0}} \over {P_{D}-P_{D0}\over P_{D0}}}\right\vert\!$$

we can further show one more new truth, simply through rearrangement. Here is the work that leads to the final equation:

 * $$\begin{align}

\left\vert\eta_{D}\right\vert&=\left\vert\frac{P_{D0}\left(Q_{D}-Q_{D0}\right)}{Q_{D0}\left(P_{D}-P_{D0}\right)}\right\vert\\ &=\frac{P_{D0}}{Q_{D0}}\cdot\left\vert\frac{Q_{D}-Q_{D0}}{P_{D}-P_{D0}}\right\vert\\ &=\frac{P_{D0}}{Q_{D0}}\cdot\left\vert\frac{dQ_{D}}{dP_{D}}\right\vert & \left[\text{Recall, }\frac{dQ_{D}}{dP_{D}}<0\text{.}\right] \end{align}$$

$$

Remember and  for later, especially equation 1.

Interpreting the Price Elasticity of Demand
We will look at the following demand curve above for this little exercise in price elasticity of demand. Keep note that the demand function, $$\operatorname{D_{i}}(Q)$$, is the solid, black, downward-sloping line. We will talk about the other two functions later.

Use of Price Elasticity of Demand
Just by knowing a numerical value, one can know more about the type of good that is possibly given in the market. However, before an honest analysis can be given for one particular good, the effects need to be given first before we can move on.

Price elasticity of Supply
By using the same logic for supply, the price elasticity of supply is $${{%\Delta S \over %\Delta P}={{S_{q,f} - S_{q,i} \over S_i} \over {P_f - P_i \over P_i}}}\!$$

where $$S_q$$ denotes the quantity supplied, $$S_{q,i}$$ denotes the quantity supplied at some arbitrary initial point along the demand curve, and $$S_{q,f}$$ denotes the quantity supplied at some final point close to $$S_{q,i}$$.

To reiterate why we determine price elasticity, the percent change can help us determine by how much our good has increased in quantity demanded or quantity supplied and can determine not only the slope but also the iterative change of a good. Say that an ordered pair exists in which $$(S_{q,i},\, P_i)$$ and $$(D_{q,f},\, P_f)$$ corresponds to a supply curve.

Note:
 * $$P_i$$ is initial price
 * $$P_f$$ is final price
 * $$S_{q,i}$$ is initial supply
 * $$S_{q,f}$$ is final supply
 * $$D_i$$ is initial demand
 * $$D_f$$ is final demand
 * $$r_i$$ is initial interest
 * $$r_f$$ is final interest
 * $$I_i$$ is initial investment
 * $$I_f$$ is final investment
 * $$S_i$$ is initial savings
 * $$S_f$$ is final savings

Price elasticity of demand

 * $$= \frac{ %change in D }{ %change in P } = \frac{ \frac{ D_f - D_i }{ ( D_f + D_i ) / 2 } }{ \frac{ P_f - P_i }{ ( P_f + P_i ) / 2 } } $$

Price elasticity of supply

 * $$= \frac{ %change in S }{ %change in P } = \frac{ \frac{ S_f - S_i }{ ( S_f + S_i ) / 2 } }{ \frac{ P_f - P_i }{ ( P_f + P_i ) / 2 } } $$

Interest elasticity of investment

 * $$= \frac{ %change in I }{ %change in r } = \frac{ \frac{ I_f - I_i }{ ( I_f + I_i ) / 2 } }{ \frac{ r_f - r_i }{ ( r_f + r_i ) / 2 } } $$

Interest elasticity of savings

 * $$= \frac{ %change in S }{ %change in r } = \frac{ \frac{ S_f - S_i }{ ( S_f + S_i ) / 2 } }{ \frac{ r_f - r_i }{ ( r_f + r_i ) / 2 } } $$

Cross elasticities
The elasticities mentioned above refer to one object. Cross elasticities refer to the effects of something's price, interest, etc. on something else. This comes into play with substitute and complementary goods and services for the consumer

Rational and Absolute Value Problem
{Find $$x$$: $$\displaystyle -\frac{x}{2\sqrt{4-x}}+\sqrt{4-x}=0$$ { 4 _5}
 * type="{}"}

{ Recall the Pythagorean Theorem: $$\displaystyle \sqrt{a^{2}+b^{2}}=c$$. ''Note: the below problems are very difficult. Congratulations if you obtain the correct answer.'' }

{A step is a unit movement left (negative), right (positive), down (negative), or up (positive) from the starting point $$\displaystyle O(0,0)$$. Let $$\displaystyle s$$ be the distance travelled while $$\displaystyle D$$ is the distance from $$\displaystyle O$$. Assume the object can only repeat $$\displaystyle R$$ times for only one chosen directional movement, and the object can only move four steps from $$\displaystyle O$$ (e.g. If $$\displaystyle R=1$$, then up, right, up, left is allowed. If $$\displaystyle R=1$$, then up, right, up, up is not allowed because up is repeated twice, and up, right, right, up is not allowed because up is repeated once and right is repeated once). The maximum deviation in distance travelled and displacement for each allowed $$\displaystyle R$$ repetition is indicated by $$\displaystyle T(R)$$. Use the following information to answer items 2 - 3.}

{What is the domain, $$\displaystyle A$$ of $$\displaystyle T(R)$$ that is the most practical to use in this situation? - $$\displaystyle A=\{R|R=0,1,2,3,4\}$$ + $$\displaystyle A=\{R|R=0,1,2,3\}$$ - $$\displaystyle A=\{R|R=1,2,3,4\}$$ - $$\displaystyle A=\{R|R=1,2,3\}$$
 * type="" coef="3"}

{Which of the following best indicates the graph $$T(R)$$? - $$\displaystyle A\times\mathbb{N}$$ - $$\displaystyle A\times\mathbb{Z}$$ - $$\displaystyle A\times\mathbb{Q}$$ + $$\displaystyle A\times\mathbb{R}$$ For Exploration 3-1 through Exploration 3-4, $$f(x)$$ is an absolute value function, and g(x) is any arbitrary function.
 * type="" coef="3"}

Logarithm and Summation Problem
{Find the sum of each of the following:}

{$$\sum_{k=1}^{\infty} \left( e^{-{1 \over 2}^{k+k-2}} \right)$$ - $$e^{4 \over 3}$$ - $$e^{16 \over 3}$$ - $$\frac{e}{e-1}$$ - $$\frac{e^{2}}{e-1}$$ + The series diverges.
 * type=""}

Footnote 1
Allow either $$a$$ or $$b$$ to equal something. We allowed $$a$$ to equal something by adding $$b$$ to both sides of the equation.
 * $$a=3+b$$

From there, substitute back into the system of equations, equation (1), to get:
 * $$n+(3+b)=8$$

After, solve for $$n$$ and substitute that into equation (2):
 * (1):$$n+(3+b)-(3+b)=8-(3+b)$$
 * (1):$$n=8-(3+b)=8-3-b=5-b$$
 * (2):$$(5-b)+b=5$$
 * (2):$$5=5$$

In an attempt to solve for $$b$$, the resultant answer tells us an identity (5 always equals 5). Therefore, b has infinitely many solutions. The same thing also happens with $$a$$. Finally, because $$n$$ is equal to itself, the following is also true:
 * $$\begin{cases}

n+a-a=8-a \\ n+b-b=5-b \end{cases}$$
 * $$\begin{cases}

n=8-a \\ n=5-b \end{cases}$$
 * (4): $$8-a=5-b$$.

The following truth reveals itself. As long $$a-b=3$$, equation (3), and $$8-a=5-b$$, equation (4), the following must be true:
 * $$\begin{cases}

a-b=3 \\ 8-a=5-b \end{cases}$$

However, the same situation results when trying to find one solution set $$(a,b)$$: there are infinitely many solutions. We learn one important lesson: what mathematics means by factor is make it so that all terms can be multiplied by another term. There is no specific term you need to care about.$$\blacksquare$$

Physics 1 Problem
{A crate of mass 100 kg rests on the floor. The coefficient of static friction between the floor and the crate is 0.4. If the applied force is 300 N (parallel to the floor), what is true about the system? Select two choices. + The net force is zero on the object. - The crate will slide, thereby having a kinetic friction. - The acceleration of the crate will be $$7\,\tfrac{\text{m}}{\text{s}^{2}}$$. + The crate's magnitude for the force of static friction is $$300\text{N}$$.
 * type="[]"}

Generalizing the Can Optimization
Given the volume $$L$$ of a cylinder. Prove the minimum of the surface area always has $$h=2r$$ for any chosen $$r>0$$. Never thought you would see a proof? Well, here you go.

Small Problems
Only the most simplified answers will be accepted for "gapfill" responses. Use a calculator when needed.

{Use the following situation below to answer items 1 - 4.}

{''A prison determines its price, in dollars, by the number of exports for the license plates per day, $$x$$, according to the demand function $$p(x)=30-0.01x-0.001x^{2}$$. The marginal cost in terms of cost maintaining the materials $$x$$ is $$MC(x)=0.0111111\left(x^{2}-60x+900\right)$$. The cost of maintaining the prison by itself is $200 because of governmental grants and tax money.''}

{Find the marginal revenue of this situation. $$MR(t)=$${ 30 _7 }$$-$${ 0.02|1/50 _7 }$$t-$${ 0.03|3/100 _7 }$$t^{2}$$
 * type="{}" coef="12"}

{At what price should the license plates be sold at to maximize the economic profit of the prison? ${ 15.20|15.2 _7 }
 * type="{}" coef="6"}

{What is the maximized profit of the prison? ${ 162.18 _7 }
 * type="{}" coef="12"}

{What is the quantity demanded from the government for the license plates? ${ 116|117 _5 }
 * type="{}" coef="6"}

{$$B(w)=120w$$ $$p(x)=\frac{1}{2}x^2-50x+1280.5$$}

{A small business wants to decrease the variable cost of baking bread. The variable cost of each corresponding factor of production is shown, whereby $$B(w)$$ represents the variable cost of hiring $$w$$ working bakers at the shop over 10 hours, and $$p(x)$$ represents the variable cost of producing $$x$$ loaves of bread. The fixed cost of this business is $300. The demand function of the firm is perfectly elastic. The marginal revenue is $300 per loaf of bread. Which of the following are true? Select all that apply - The marginal cost here represents a diminishing returns to scale. + The total revenue function is $$R(x)=300x$$. - We are allowed to change the input $$w$$ for $$B(w)$$ and $$x$$ for $$p(x)$$ to an interstitial variable $$u$$ since by adding $$B(w)$$ and $$p(x)$$, we effectively obtain the variable cost as a function of each unit $$u$$ in the factor of productions. - It is impossible to obtain the marginal cost in this situation because the variables of each function above are different, and therefore do not allow us to find the variable cost in this situation. Without the variable cost, the total cost cannot be found, so the marginal cost cannot be found as a result. + The variable cost must involve two inputs as a function $$V(x,w)$$ or the variable cost needs to have at least one of the functions as a constant added to the variable cost. + For 10 workers, the quantity that allows for maximum profit is 350 loaves of bread. The marginal cost in this situation has a diminishing returns to scale.
 * type"[]"}
 * This would be true if the marginal cost can be calculated. Unfortunately, the calculation requires us to ignore one of the factors herein as a constant.
 * Correct. This is because the demand function is perfectly elastic and is therefore a flat line.
 * Because the two functions require different inputs, the variable cost will be different due to a constant for any input. As such, by adding the two functions as if the variable did not matter would greatly obfuscate the actual correct answer as the marginal cost function would be different and therefore lead to incorrect conclusions.
 * The language here is too strong. While it may be impossible to obtain an actual marginal cost, the variable cost can be obtained as a function of two inputs. Because we are trying to find the marginal cost using two inputs, the marginal cost will be different.
 * For any constant of workers $$c_{w}$$, the maximum profit is obtained at 350 loaves of bread because it is simply a constant added to the variable cost. As long as the total revenue does not increase, the quantity required to obtain a maximum profit is 350 loaves of bread.

{A frictionless inclined ramp, angled at $$30^{\circ}$$, of height $$h=10\text{ m}$$, has a $$15\text{ kg}$$ ball at rest at the top. An initial horizontal velocity $$v_{x0}\tfrac{\text{m}}{\text{s}}$$ is applied to the ball. The ball is slowing down along the ramp due to the air resistance of the room, with a counteracting force $$F_{r}=-kv$$ (parallel to the ramp) where $$k$$ is a constant and $$v$$ is the velocity of the moving object. If $$k=2\tfrac{\text{kg}}{\text{s}}$$, what is the work, $$\Delta E$$, done on the system (to the nearest tenth )? Note: Weight is $$F_{g}=mg$$ and $$\Delta E=W=\int_{0}^{b}F(x)dx$$, where $$x$$ is the horizontal position, $$g=9.81\tfrac{\text{m}}{\text{s}^{2}}$$, and $$b$$ is how you arrive at the desired answer. { 3500.7 _7 } $$\text{Joules (J)}$$.
 * type="{}"}

title: User:Musical Inquisit/sandbox


text: User talk:2A00:23C4:6695:6401:8B2:2F0:9763:E3D


text: User talk:201.191.159.28

title: User talk:201.191.159.28


text: User talk:60.240.190.94

title: User talk:60.240.190.94


text:
Wikibooks:Reading room/Proposals/2019/February

A New Recommender System For Wikibooks (can be extended to WikiMedia in general)
I created a phabricator task for the proposal to improve the existing recommender system used by WikiMedia as a project for GSoC 19 and a mentor asked me to share my proposal here. My proposal includes the followinng tasks:
 * Making a form at the end of each article, so that user can tell if he liked the article or not (maybe star based system) and the categories he wants to tag the article with.
 * Based on this star based system, and the tags provided by users, it will learn new categories for the article.
 * It will recommend new articles, after some time of learning, to users based on their previous activity, in parallel to present system based on edits made by users.
 * learning similarity between different users based on their interests and then it will try to suggest discussion pages where they can discuss similar ideas.

following is the idea on which the proposal is based: “Some people use Wikimedia to gain knowledge rather than making edits and improving what already exists.”

My idea of recommender system serves people who surf Wikimedia to learn new things along with those who know a particular topic and mostly visit articles surrounding that topic only and it will help people to discover new people who are interested in similar topics and in this way we can become part of larger group dynamics and discussions.

 * Current recommender system:
 * The current recommender system is mostly based on the edits made by the user. So, this method doesn’t serve those who want to learn new things and have no prior knowledge about the articles they want to visit.
 * The second method on which current recommender system works is by user providing their interests.
 * In the current recommender system, there is no way by which the system can learn new categories that should be assigned to the page and which may be skipped out by the person who has tagged the article with categories.
 * New idea of recommender system:
 * This recommender system learns categories liked by new users. The recommender system suggests new articles to users based on these categories assigned to new users.
 * It will also learn categories to be assigned to new articles based on the ratings given by old user.
 * It will adapt to changes in interests of users. If a user is interested in new type of categories, it will change the categories assigned to user automatically.
 * We can also add a feature that helps a user assign new categories to articles. This will help us to track user’s interests and change categories liked by him accordingly and it will help learning the categories of articles easily. This will also help us to tackle the emergence of new categories.
 * By knowing similarities between users, we can make them part of larger discussions.
 * Also, we can ask new users about their fields of interest and show initial results (results before learning) accordingly.
 * This recommender system can run in parallel to the old one. So, some of the suggestions will be based on this system and others will be given by old one.

(User:Chaitanya kharyaldiscuss) 18:09, 17 February 2019 (UTC)


text:
Fractals/Mathematics/binary

Binary fraction in the theory of discrete dynamical systems ( number conversions and binary expansion of the decimal fraction ) =Notation=

general math notation
A binary fraction is a sum of negative powers of two

 * $$ b_0.b_1 b_2 b_3\dots. = \sum_{i=0}^\infty b_i 2^{-i} = b_0 2^0 + b_1 2^{-1} + b_2 2^{-2} +  b_3 2^{-3}  + \dots $$

 * $$b_i2^{-i} = \frac{b_i}{2^i}$$

Subscript number denotes number base ( radix of the positional numeral system)

 * $$0.1_2 = 0.5_{10}$$

 * $$0.1_{10} = (0.0\overline{0011})_2$$

Sometimes round brackets are used for greater clarity:

 * $$(0.1)_{10} = 0.1_{10} $$

Infinitely repeating part of binary expansion denoted by
 * round brackets
 * overline

infinite sequence is denoted by ellipsis ( = 3 dots)

 * $$0.10(00101010) = 0.10\overline{00101010} = 0.10001010100010101000101010001010100010101000101010 \dots$$

exponent ( superscript) with or without brackets: '''
 * denotes how many times the series repeats
 * will be used to indicate symbols (or groups of symbols) that are to be '''repeated a finite number of times
 * $$0.11(11101010) = 0.11(11(10)^3) $$

 * $$0.((001)^{88}010)_2 = 0.(001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001010)$$

 * $$ 0.(01^3) = 0.(0111)$$

The leading zero is sometimes omitted

 * $$.1 = 0.1$$

Trailing zeros to the right of a radix point (a small dot .), do not affect the value of a number and here will be omitted:

 * $$0.1(0) = 0.1$$

Special notation
Special notation used in programs:
 * program Mandel uses: 0p01 which in general math notation is 0.0(01). Generally apb = 0.a(b)
 * program Book program uses: .0(01) which in general math notation is 0.0(01). Generally .a(b) = 0.a(b)

preperiod and period
Preperiod is used in 2 meanings :
 * T = preperiod of critical point $$z_{cr} = 0$$
 * t = preperiod of critical value $$z_{cv} = c$$

Note that :

$$ t = T - 1$$

Period p is the same for critical value and critical point

Preperiod:
 * preperiod of critical value
 * Wolf Jung uses : "... the usual convention is to use the preperiod of the critical value. This has the advantage, that the angles of the critical value have the same preperiod under doubling as the point, and the same angles are found in the parameter plane."
 * preperiod of critical point
 * Pastor uses preperiod of critical point : "all the Misiurewicz points are given with one unit more in their preperiods, therefore this $$M_{2,1}$$ is given as $$M_{3,1}$$"
 * Demidov
 * Claude Heiland-Allen

=Key words=
 * period
 * smallest length of periodic part of binary expansion ( binary sequence )
 * lentgh of the orbit of the angle (decimal ratio) under doubling map = period under doubling map
 * preperiod
 * smallest length of preperiodic part of binary expansion ( binary sequence )

=Types of binary expansions=

Binary expansion can be :
 * finite - decimal ratio number with even denominator which is a power of 2. Note that it has also equal infinite preperiodic representation
 * infinite
 * periodic : preperiod = 0, period > 0, rational number with odd denominator which is not a power of 2
 * preperiodic ( = eventually periodic) : preperiod > 0, period > 0, rational number with even denominator
 * aperiodic : preperiod = 0, period = 0 ( or infinity), irrational number

If the decimal number is rational number check it's form. Is it is in the lowest terms ( irreducible = reduced = numerator and denominator are coprime )?

How to find expansion type
=Description =

finite
A decimal ratio m/n has a finite binary representation if and only if it can be written as a fraction whose denominator n is a power of 2 ( also even):

$$\frac{m}{n} = \frac{m}{2^t}$$

for some integer m and some non-negative integer t."

In other words :
 * fractions in binary arithmetic terminate only if 2 is the only prime factor in the denominator = dyadic rational.
 * The dyadic rationals are precisely those numbers possessing finite binary expansions

It is because of binary fraction construction:

 * $$ r=b_0.b_1 b_2 b_3\dots. = \sum_{i=0}^\infty \frac{b_i}{2^i} = \frac{b_0}{2^0} + \frac{b_1}{2^1} + \frac{b_2}{2^2} +\frac{b_3}{2^3}  + \dots $$

Binary expansion of the unitary fraction:

$$r = \frac{1}{2^t} = 0.\overbrace{b...b}^{t-1}1 = 0.0^{t-1}1$$

This finite binary expansion has second equal representation: infinite and preperiodic ! Because this 2 representations have different preperiod and period then in the theory of discrete dynamical systems is better to use infinite version.

infinite

 * periodic : preperiod = 0, period > 0
 * preperiodic : preperiod > 0, period > 0
 * aperiodic : preperiod = 0, period = 0

periodic
Here decimal number is a rational number with odd denominator.

There are 2 possible types ( complete classification):
 * denominator is a odd prime (prime number other then 2)
 * denominator is an odd composite number

There is special case which is not exclusive from th.e other two cases : denominator is integer one less than a power of two:

 * $$r = \frac{1}{2^p-1} = 0.((0)^{p-1}1)$$

So binary fraction has:
 * period = p
 * preperiod = 0

Binary fraction 1/(2^p-1) has the same form in binary expansion as fraction 1/(2^p), but repeating.

Example 1/(2^5)=0.00001 and 1/(2^5-1)=0.(00001)

denominator is an odd prime
Rational number with odd prime denominator ( prime number other then 2 )

Period of binary expansion of reduced rational fraction m/n is equal to the multiplicative order of 2 modulo n:

$$ k = Period_2(m/n) = {ord}_n(2)$$

The longest possible period k is:

$$ k = n-1$$

when 2 is a primitive root of denominator n :

Im Maxima CAS one can use :
 * ifactors(n)
 * zn_order(2,n)
 * zn_primroot_p(2,n)

1/9949 computed with the knowledgedoor calculator: convert_a_ratio_of_integers ( it allows for computations up to 100000 fractional digits in the new number):

1/9949 = 0.(0.000000000000011010010110010100100110010000110010100010010100000 000011000101100111011010011110111101111011000001010110000010111001 010000111100110101000010000011010101010000101010101101101011111001 000001101101111011000111111011101000000010110101001001011101100111 000011011011011011111001100010101001110100110111110000100111001101 101110001001111100011111001101100100010001100100110000110111010001 010100101101010000101110000000011110011101110011110100001111011010 011011101011001000011100100011111100100100111110011100110001111100 011011111010110001101100110010101010100010111110110100101010001011 000110100101111111011111111000110010111001010111100010011010001011 100111100001111001001111101101110010000100010000100010111001000011 110001101010101110111010111011111111100000101101011111100010100100 000011111111010000001111100010101010101001100100011001110011101111 010011001110100100011111111110111110001000001100100000010110000001 101010001101111111000010001111101011101110010100101001100011100101 000111000110000110101100111111011011010110111101010110110010101001 101110010010001011011101101001100001100001010111011111000111011001 000010101111110010111011011011010010000001001010111011011110100100 110011101111101101100100111001000110001111110000101010100000100000 101110101110100101100001110110110001100111110110011110101011110011 101011001011101111010110100001010111000100110001000100011100011111 000000011001000111010001101000011110000000001010101101000100010111 100010110100100001111100001000001010000010010000000110000100101001 001111110100010111101001011010000111000101101100010110101010110101 000110001010110100011110101001010101100101010000001001110001110010 001001001100101110110000001110111011001001001010101011000000100111 111011110101001101111111011100100110000000010100100101011100000101 111001000111011110110011101000010011010011000110010101100001100011 000000111000011001110010000101111001111100001011011100110100110100 111000001010111101100010010100011010101111000001100001100100101010 010001101100001011001001000100000101011011011110010111101000100101 011010011100011111110101000101110000011110001010000011000100110010 101101110101110001011001011100010001011010111000011111100010111110 011010010011110110100000010101001100111101100100110010100000101010 100111000110010011111000001001101110011111010110100111111100101001 111010101000101001000111100101011001001101011100110111010010111110 000110100011000111000011101000100111000011110101110010001110001000 111010100111011010000100100111100110011011000101010000010110111100 111100011100010101001000000001011000111011010101100001001000101010 100011110011100001010011010111101000001011000100000111111001100100 010011001110001010001001101010010111110111011001111110000010000001 010001100001000011101110010111111100010110001001111001001100011010 111111011111011110011100100100110001010001100111101001010011100001 100000100010110010011110001100100001001010101110010011011010100000 100111010100010011101111000110000011011010001100110110100100110111 000010100000001001101011001100100100000011001010100011100110010110 001001000100011111110001110010111101111001010111111100110000100000 001101110010101011110010000001110010011100111101011110001100111011 100001000010111001101011010011001001101000010100000111110010111110 101110000100100101111101000001110010110111010011110010110011001100 010011100101001101101011101011110110100011100111111111100010010110 111000110100111101000111001001011001011111100100001101011101010001 101001010010101100110011111001100101111100100111011100100010101101 100010000000101001111111100100110100111110110000100010101011111000 100111010111100110100001101010110101100000100001001001000100111010 001000000111100100001010001010011111000100100000100110011111100111 000101111001100001110101001000001110100100000101101000101001100001 111011101101110011101101101001110101010010000110111011110011111110 111100011110110011001101111100111110100000000100101111000000101100 111000000001000101001010100110000100011100000100101010000100100001 000000110101111011101100001010010100010111011100001110111100110010 100011111101011001101011000101111110011110000000111111011001101101 100100000100011001100110100100001000111011011100000110101101110100 001000000000001001111000010111101110010110010010111100110111100000 001001010000110110001111011100111001110001000100000010001000101011 110010110110011111000110001001111111110010000000001001000011101011 000101001001110001010111110010111000001000011111011100011000110101 001010010010010011101100100111111101011110100111010001110101101001 001010011101110101011101101000101100110100101110010010100101110011 111110000111110010001010000001011011011001011011011100101110001111 010011000001011001010101101011110101101110111011010110010101110101 010011110000010101000110010111111111101000111100011101111110100001 010011110001111110011111101010011000101100000110100111001110100010 110110100101101011101111001001010110001100110001101000101011001011 010101000000001100110000110011111110100010001000011110100111101100 001011111101110000101110100111111111111100101101001101011011001101 111001101011101101011111111100111010011000100101100001000010000100 111110101001111101000110101111000011001010111101111100101010101111 010101010010010100000110111110010010000100111000000100010111111101 001010110110100010011000111100100100100100000110011101010110001011 001000001111011000110010010001110110000011100000110010011011101110 011011001111001000101110101011010010101111010001111111100001100010 001100001011110000100101100100010100110111100011011100000011011011 000001100011001110000011100100000101001110010011001101010101011101 000001001011010101110100111001011010000000100000000111001101000110 101000011101100101110100011000011110000110110000010010001101111011 101111011101000110111100001110010101010001000101000100000000011111 010010100000011101011011111100000000101111110000011101010101010110 011011100110001100010000101100110001011011100000000001000001110111 110011011111101001111110010101110010000000111101110000010100010001 101011010110011100011010111000111001111001010011000000100100101001 000010101001001101010110010001101101110100100010010110011110011110 101000100000111000100110111101010000001101000100100100101101111110 110101000100100001011011001100010000010010011011000110111001110000 001111010101011111011111010001010001011010011110001001001110011000 001001100001010100001100010100110100010000101001011110101000111011 001110111011100011100000111111100110111000101110010111100001111111 110101010010111011101000011101001011011110000011110111110101111101 101111111001111011010110110000001011101000010110100101111000111010 010011101001010101001010111001110101001011100001010110101010011010 101111110110001110001101110110110011010001001111110001000100110110 110101010100111111011000000100001010110010000000100011011001111111 101011011010100011111010000110111000100001001100010111101100101100 111001101010011110011100111111000111100110001101111010000110000011 110100100011001011001011000111110101000010011101101011100101010000 111110011110011011010101101110010011110100110110111011111010100100 100001101000010111011010100101100011100000001010111010001111100001 110101111100111011001101010010001010001110100110100011101110100101 000111100000011101000001100101101100001001011111101010110011000010 011011001101011111010101011000111001101100000111110110010001100000 101001011000000011010110000101010111010110111000011010100110110010 100011001000101101000001111001011100111000111100010111011000111100 001010001101110001110111000101011000100101111011011000011001100100 111010101111101001000011000011100011101010110111111110100111000100 101010011110110111010101011100001100011110101100101000010111110100 111011111000000110011011101100110001110101110110010101101000001000 100110000001111101111110101110011110111100010001101000000011101001 110110000110110011100101000000100000100001100011011011001110101110 011000010110101100011110011111011101001101100001110011011110110101 010001101100100101011111011000101011101100010000111001111100100101 110011001001011011001000111101011111110110010100110011011011111100 110101011100011001101001110110111011100000001110001101000010000110 101000000011001111011111110010001101010100001101111110001101100011 000010100001110011000100011110111101000110010100101100110110010111 101011111000001101000001010001111011011010000010111110001101001000 101100001101001100110011101100011010110010010100010100001001011100 011000000000011101101001000111001011000010111000110110100110100000 011011110010100010101110010110101101010011001100000110011010000011 011000100011011101010010011101111111010110000000011011001011000001 001111011101010100000111011000101000011001011110010101001010011111 011110110110111011000101110111111000011011110101110101100000111011 011111011001100000011000111010000110011110001010110111110001011011 111010010111010110011110000100010010001100010010010110001010101101 111001000100001100000001000011100001001100110010000011000001011111 111011010000111111010011000111111110111010110101011001111011100011 111011010101111011011110111111001010000100010011110101101011101000 100011110001000011001101011100000010100110010100111010000001100001 111111000000100110010010011011111011100110011001011011110111000100 100011111001010010001011110111111111110110000111101000010001101001 101101000011001000011111110110101111001001110000100011000110001110 111011111101110111010100001101001001100000111001110110000000001101 111111110110111100010100111010110110001110101000001101000111110111 100000100011100111001010110101101101101100010011011000000010100001 011000101110001010010110110101100010001010100010010111010011001011 010001101101011010001100000001111000001101110101111110100100100110 100100100011010001110000101100111110100110101010010100001010010001 000100101001101010001010101100001111101010111001101000000000010111 000011100010000001011110101100001110000001100000010101100111010011 111001011000110001011101001001011010010100010000110110101001110011 001110010111010100110100101010111111110011001111001100000001011101 110111100001011000010011110100000010001111010001011)

Nonunitary fraction ( numerator is greater then 1 ) have :
 * the same period k ( length of periodic part )
 * if $$k = \phi(n) $$
 * then periodic part cyclically shifted with respect to the corresponding unitary fraction
 * else there are $$\phi(n)/k $$ different cycles ( periodic parts) all of length k

where
 * $$\phi $$ is the Euler totient function. In Maxima CAS it is totient(n)

denominator is an odd composite number
period of binary expansion of $ \frac{m}{n}$= period of the angle $$ \frac{m}{n}$$ under doubling map

Hard case: 1/99007599 = 1 / (3*33002533), written as a binary fraction, have a period of nearly 50 million 0’s and 1’s

Tests:
 * knowledgedoor calculator - "There are more than 100000 fractional digits in the new number. We are sorry, but we had to abort the calculation to control the loading on our server."
 * In Maxima CAS : zn_order(2,99007599) = 33002532

preperiodic
Here denominator n of fraction r

 * $$r = \frac{m}{n}$$

is even:

 * $$n = 2^tq$$

and q is odd.

Cases by preperiod and period
$$\{t,p\} $$ where t is preperiod and p period
 * $$\{1,1\} = 0.0(1) = 1/2 = 0.5$$
 * $$\{1,2\}$$
 * $$ 0.0(01) = 1/6 = 2/12 = 0.1666666666666667$$
 * $$ 0.0(10) = 1/3 = 4/12 = 0.3333333333333333$$
 * $$ 0.1(01) = 2/3 = 8/12 = 0.6666666666666667$$
 * $$ 0.1(10) = 5/6 = 10/12 = 0.8333333333333333$$
 * $$\{2,1\}$$
 * $$ 0.00(1) = 1/4 = 0.25$$
 * $$ 0.10(1) = 3/4 = 0.75$$
 * $$\{2,2\}$$
 * $$ 0.00(01) = 1/12 = 0.0833333333333333$$
 * $$ 0.01(10) = 5/12 = 0.4166666666666667$$
 * $$ 0.10(01) = 7/12 = 0.5833333333333333$$
 * $$\{4,4\}$$
 * $$ 0.0110(1001) = 99/240 = 0.4125$$
 * $$ 0.1001(0110) = 141/240 = 0.5875$$
 * $$\{5,2\}$$
 * $$ 0.01101(10) = 41/96 = 0,42708333333333333$$

Cases by q type

 * q = 1, dyadic fractions. It is equal infinite representation of finite binary fraction. See black rows int the table below
 * q is a prime number, See green rows int the table below
 * q = 2^p - 1 then period = p
 * if q is not integer one less the a power of two then period p = ( minimal length of repeating part) $$p =\phi(q) $$
 * q is a composite number, period p "is the same as for the denominator q. It is either Phi(q) or a strict divisor of  Phi(q) . You can determine it numerically when you double  1/q  again and again until you get  1/q." ( Wolf Jung ). See red rows int the table below

q is an integer one less than the power of two
If q is an integer one less than the power of two ( even):

 * $$q = 2^p-1$$

then fraction r has a form:

 * $$r = \frac{m}{n} = \frac{m}{2^t(2^p-1) } = 0.\overbrace{b...b}^{t}(\overbrace{b...b}^{p})$$

has:
 * period ( minimal length of repeating part) $$p$$
 * preperiod ( length of non-repeating part) = t

Examples:
 * $$\frac{1}{6} = \frac{1}{2*3} = \frac{1}{2(2^2-1)} = {0.0(01)}_2$$
 * $$\frac{7}{24} = \frac{7}{2^3*3} = \frac{7}{2^3(2^2-1)} = {0.010(01)}_2$$
 * $$\frac{9}{56} = \frac{9}{2^3*7} = \frac{9}{2^3(2^3-1)} = {0.001(010)}_2$$

How to check if q is an integer one less than the power of two:
 * $$ q = 2^k -1 $$
 * $$ q+1 = 2^k $$
 * $$ k = {log}_2(q+1) $$

In Maxima cas one can use function

Give_k(q):=float(log(q+1)/log(2));

If k is near integer ( fractional part is 0 or near 0)
 * then $$ q = 2^k -1 $$ and use above method
 * else use below method

q is a prime number
If $$q \ne 2^k-1$$then fraction r

 * $$r = \frac{m}{n} = \frac{m}{2^tq} = 0.\overbrace{b...b}^{t}(\overbrace{b...b}^{k})$$

where :
 * q is odd
 * $$\phi $$ is the Euler totient function. In Maxima CAS it is totient(n)

has:
 * period ( minimal length of repeating part) $$k =\phi(q) $$
 * preperiod ( length of non-repeating part) = t

Examples:

 * $$\frac{9}{20} = \frac{9}{2^25} = {0.01(1100)}_2 $$ here period $$ = \phi(5) = 4$$ and preperiod  t = 1

 * $${0.1416}_{10} = \frac{1416}{10000} = \frac{117}{1250} = \frac{117}{2(5^4)} = {0.0(00101111111011000101011011010101110011111010101011001101100111 101000001111100100001001011010111011100110001100011111100010100000 100100000010110111100000000011010001101101110001011101011000111000 100001100101100101001010111101001111000011011000010001001101000000 010011101010010010101000110000010101010011001001100001011111000001 101111011010010100010001100111001110000001110101111101101111110100 100001111111110010111001001000111010001010011100011101111001101001 101011010100001011000011110010011110111011)}_2$$

here:
 * period $$ = \phi(5^4) = 500$$
 * preperiod = 1

aperiodic
If expansion is:
 * infinite
 * aperiodic ( period = 0 or infinity )

then it is an irrational number.

Irrational number features (not a complete classification) :
 * normality - normal number in wikipedia / non-normal number ( sequence)
 * linearizability: not linearizable / linearizable, check Brjuno condition
 * Transcendental(non-algebraic) /algebraic

Applications
 * internal angle

normal
Random sequences
 * pseudorandom
 * true random

Examples from |Gaussian Random Number Generator:
 * 10 bytes: 10001000111010111111001111010111101000110001010110010010011111100101110101011001
 * 15 bytes: 100110100001100101010100001010100110110000100111001100110001101100101111100001001111101001011011101011110100011011000000
 * 20 bytes: 1010100101110110001100111101101001001100001011111011001010000100100110010000001010110000101100100111111111011000001001110110000110111011100001101110001000101110

Binary Champernowne constant C2 = 110111001011101111000100110101011110011011110111110000100011001010011101001010110110101111

non-normal
Binary Liouville's constant (binary Liouville number ):

$$L = \sum_{n=1}^{\infty}2^{-n!} = \frac{1}{2^{1!}} + \frac{1}{2^{2!}} + \cdots + \frac{1}{2^{n!}} + \cdots = \frac{1}{2} + \frac{1}{2^2} + \frac{1}{2^6} + \cdots +  \frac{1}{2^{n!}} + \cdots = 0.11000100000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001\ldots$$

where:
 * ! denotes factorial
 * $$ \sum$$ denotes sum of infinite series

So binary digits on position:

$$1, 2, 6, 24, 120, 720, 5040, 40 320, 362 880, 39 916 800, 479 001 600\ldots$$

are 1, others are 0.

the Thue–Morse sequence = binary expansion of Prouhet–Thue–Morse constant:

 * $$ \tau = \sum_{i=0}^{\infty} \frac{t_i}{2^{i+1}} = {0.01101001100101101001011001101001\ldots}_2 $$

where:
 * $$t_i$$ is the ith element of the Prouhet–Thue–Morse sequence

It obtained by starting with 0 and successively appending the Boolean complement of the sequence obtained thus far.

Define a sequence of strings of 0 and 1 as follows:
 * $$t_0 = 0$$
 * $$ t_{n+1} = t_n \overline{t_n}$$

where:
 * $$\overline{t}$$ means change all the 0’s in x to 1’s and vice-versa

First 5 sequences
 * $$ t_0= 0$$
 * $$ t_1= 01$$
 * $$ t_2= 0110$$
 * $$ t_3= 01101001$$
 * $$ t_4 = 0110100110010110$$

The Rabbit constant (The limiting Rabbit Sequence) given by the continued fraction

$$R = [0, 2^{F_0}, 2^{F_1}, 2^{F_2}, 2^{F_3}, ...] = 0.1011010110110...$$

where:
 * $$F_n$$ are Fibonacci numbers with $$F_0$$ taken as 0

=Multiple representations= The representations are:
 * equal in general meaning, because give the same decimal fraction
 * nonequal here, because have different period/preperiod of binary fraction, so describe different dynamical system

Periodic
periodic angles have multiple possible ways of writing down, one of which is special in having the smallest period

$$ 1/3 = .0101010101010101... = .(01) = .(0101) = .(010101) = ... $$

So "period" really means minimal possible period

Orbit of 1/3 under doubling map is periodic {1/3, 2/3 }

preperiodic
preperiodic angles have multiple possible ways of writing down ( infinite forms), one of which is special in having the smallest preperiod:

$$ \frac{1}{6} = 0.0(01) = 0.00(10) = 0.001(01) = ...$$

$$\frac{3}{14} = 0.0(011) = 0.00(110)$$

$$\frac{1}{5} = 0.0\overline{0110}=0.\overline{0011}$$

finite

 * every nonzero terminating binary number ( = rational number with odd denominator which is a power of 2 )   has two equal representations
 * The binary expansions of dyadic rationals are not unique; there is one finite and one infinite representation of each dyadic rational other than 0 (ignoring terminal 0s). For example, 0.112 = 0.10111...2, giving two different representations for 3/4. The dyadic rationals are the only numbers whose binary expansions are not unique.

$$ 0.0^{t-1}1_2 = 0.0^{t}(1)_2 $$

Examples:
 * "The angle 1/4  or  01 has  preperiod = 2  and  period = 1." program from program Mandel. Here finite version is used

=Relation between binary numbers and the dynamical systems =

Maps
 * binary fraction, doubling map = left shift = Bernoulli shift
 * complex number, complex quadratic map

Doubling map
"The map $$\lambda : \mathbb{R}/\mathbb{Z} \to J_c$$  is called the Caratheodory semiconjugacy, with the associated identity $$\lambda(2*t) = f_c(\lambda(t))$$ in the degree 2 case. This identity allows us to easily track forward iteration of external rays and their landing points in $$J_c$$ by doubling the angle of their associated external rays modulo 1." Mary Wilkerson

Orbits of fraction under doubling map for :
 * decimal rational fractions
 * fractions with odd denominators are periodic
 * fractions with even denominators are preperiodic
 * decimal irrational fractions are non periodic and dense

the relationship between external angles and binary decomposition rendering for quadratic polynomials
 * Removing the first bit is the same as doubling mod 1

when tracing external ray and passing dwell band ( boundary of escape time level set): of binary expansion of external angle
 * inwards ( toward Julia/Mandelbrot set): add bit at the end
 * outwards ( toward point at infinity): add the bit at the beginning

external angles
There are two kinds of rational angles ( decimal fractions):
 * When the denominator is odd, the sequence of binary digits will be periodic, and the angle is periodic under doubling. The dynamic ray with this angle lands at a periodic point of the Julia set. The parameter ray lands at the root of a hyperbolic component.
 * When the denominator is even, the sequence of binary digits will be preperiodic, and the angle is preperiodic under doubling. The dynamic ray lands at a preperiodic point of the Julia set, and the parameter ray lands at a Misiurewicz point.

Relation between point and external angle ? Using binary decomposition:
 * start with an unknown location and finds the external angles from the image
 * start with angles and find the location that matches

The external arguments of the rays landing at z = −0.15255 + 1.03294i are:

$$(\theta^- _{20}, \theta^+_{20} ) = (0.\overline{00110011001100110100}, 0.\overline{00110011001101000011})$$

where:

$$\theta^- _{20} = 0.\overline{00110011001100110100}_2 = 0.\overline{20000095367522590181913549340772}_{10} = \frac{209716}{1048575} = \frac{209716}{2^{20}-1}$$

collecting bits
Collecting bits of binary expansion of external angle when tracing externla rays on the binary decomposition of exterior of the Mandelbrot/Julia set

See also
 * binary decomposition
 * parameter plane
 * dynamic plane
 * reading bits from binary decomposition = collecting bits of external angle's binary expansion

patterns
Patterns are sculpted in the intricate shape of the boundary the Mandelbrot set when zooming ( especially deep zooming). Zooming are reflected in the complex dynamics, in particular in the binary expansions of the pairs of external rays landing on the cusp of each baby Mandelbrot set copy at the centre of each phase.

=Conversions=
 * Convert binary fraction to decimal ratio
 * convert decimal fraction to binary
 * knowledgedoor calculators

Can all decimal fractions be converted exactly to binary?
Not all. Only those for which denominator is a power of 2 ( finite ) have exact decimal representation. "In every other case, there will be an error in the representation. The error's magnitude depends on the number of digits used to represent it."

decimal to binary
=See also=
 * Bit numbering in wikipedia
 * Bit_manipulation in wikipedia
 * ENT A Pseudorandom Number Sequence Test Program in C by John Walker
 * Continued fraction representation of real number

=References=
 * Binary Numbers by Jamie King on YT

title: Fractals/Mathematics/binary


text:
User talk:203.57.215.167

--Eihel (discuss • contribs) 02:02, 19 June 2019 (UTC)

title: User talk:203.57.215.167