field_of_work morwen thistlethwaite
In ___MASK40___ , knot theory is the study of mathematical knots . While inspired by knots which appear in daily life in shoelaces and rope , a mathematician ' s knot differs in that the ends are joined together so that it cannot be undone . In mathematical language , a knot is an embedding of a circle in 3 - dimensional Euclidean space , R ( in ___MASK40___ , a circle isn ' t bound to the classical geometric concept , but to all of its homeomorphisms ). Two mathematical knots are equivalent if one can be transformed into the other via a deformation of R upon itself ( known as an ambient isotopy ); these transformations correspond to manipulations of a knotted string that do not involve cutting the string or passing the string through itself . Ern Rubik ( born 13 July 1944 ) is a Hungarian inventor , architect and professor of ___MASK70___ . He is best known for the ___MASK33___ of mechanical puzzles including Rubik ' s Cube ( 1974 ), Rubik ' s Magic , , and Rubik ' s Snake . In ___MASK100___ , Euclidean space encompasses the two - dimensional Euclidean plane , the three - dimensional space of Euclidean ___MASK100___ , and certain other spaces . It is named after the Ancient Greek mathematician Euclid of Alexandria . The term " Euclidean " distinguishes these spaces from other types of spaces considered in modern ___MASK100___ . Euclidean spaces also generalize to higher dimensions . In the mathematical field of ___MASK40___ , a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function . Homeomorphisms are the isomorphisms in the category of topological spaces  that is , they are the mappings that preserve all the topological properties of a given space . Two spaces with a homeomorphism between them are called homeomorphic , and from a topological viewpoint they are the same . The word " homeomorphism " comes from the Greek words "  " (" homoios ") = similar and "  " (" morph ") = shape , form . Professor ( commonly abbreviated as " prof .") is an academic rank at universities and other post - secondary ___MASK73___ and ___MASK48___ institutions in most countries . Literally , " professor " derives from Latin as a " person who professes " being usually an expert in arts or sciences , a teacher of the highest rank . In ___MASK1___ , ___MASK40___ ( from the Greek  , " place ", and  , " study ") is concerned with the properties of space that are preserved under continuous deformations , such as stretching and bending , but not tearing or gluing . This can be studied by considering a collection of subsets , called open sets , that satisfy certain properties , turning the given set into what is known as a topological space . Important topological properties include connectedness and compactness . ___MASK70___ ( Latin " architectura ", from the Greek  " arkhitekton " " architect ", from  - " chief " and  " builder ") is both the process and the product of planning , designing , and constructing buildings and other physical structures . Architectural works , in the material form of buildings , are often perceived as cultural symbols and as works of ___MASK96___ . Historical civilizations are often identified with their surviving architectural achievements . Morwen B . Thistlethwaite is a knot theorist and professor of ___MASK1___ for the University of Tennessee in Knoxville . He has made important contributions to both ___MASK76___ and Rubik ' s Cube group theory . Rubik ' s Cube is a 3 - D combination puzzle invented in 1974 by Hungarian sculptor and professor of ___MASK70___ Ern Rubik . Originally called the Magic Cube , the puzzle was licensed by Rubik to be sold by Ideal Toy Corp . in 1980 via businessman Tibor Laczi and Seven Towns founder Tom Kremer , and won the German Game of the Year special award for Best Puzzle that year . As of January 2009 , 350 million cubes had been sold worldwide making it the world ' s top - selling puzzle game . It is widely considered to be the world ' s best - selling toy . In the mathematical subject of ___MASK40___ , an ambient isotopy , also called an " h - isotopy ", is a kind of continuous distortion of an " ambient space ", a manifold , taking a submanifold to another submanifold . For example in knot theory , one considers two knots the same if one can distort one knot into the other without breaking it . Such a distortion is an example of an ambient isotopy . More precisely , let " N " and " M " be manifolds and " g " and " h " be embeddings of " N " in " M ". A continuous map is defined to be an ambient isotopy taking " g " to " h " if " F " is the identity map , each map " F " is a homeomorphism from " M " to itself , and " F "  " g " = " h ". This implies that the orientation must be preserved by ambient isotopies . For example , two knots which are mirror images of each other are in general not equivalent . In ___MASK1___ , an embedding ( or imbedding ) is one instance of some mathematical structure contained within another instance , such as a group that is a subgroup . A circle is a simple closed shape in Euclidean ___MASK100___ . It is the set of all points in a plane that are at a given distance from a given point , the centre ; equivalently it is the curve traced out by a point that moves so that its distance from a given point is constant . The distance between any of the points and the centre is called the radius . In ___MASK45___ and mathematics , the dimension of a mathematical space ( or object ) is informally defined as the minimum number of coordinates needed to specify any point within it . Thus a line has a dimension of one because only one coordinate is needed to specify a point on itfor example , the point at 5 on a number line . A surface such as a plane or the surface of a cylinder or sphere has a dimension of two because two coordinates are needed to specify a point on itfor example , both a latitude and longitude are required to locate a point on the surface of a sphere . The inside of a cube , a cylinder or a sphere is three - dimensional because three coordinates are needed to locate a point within these spaces .