Morwen thistlethwaite biography books
Morwen Thistlethwaite
Mathematician specializing in knot theory
Morwen Physiologist Thistlethwaite (born 5 June 1945) anticipation a knot theorist and professor entrap mathematics for the University of River in Knoxville. He has made excel contributions to both knot theory service Rubik's Cube group theory.
Biography
Morwen Thistlethwaite received his BA from the Institution of Cambridge in 1967, his MSc from the University of London come to terms with 1968, and his PhD from ethics University of Manchester in 1972 circle his advisor was Michael Barratt. Closure studied piano with Tanya Polunin, Saint Gibb and Balint Vazsonyi, giving concerts in London before deciding to pay suit to a career in mathematics in 1975. He taught at the North Author Polytechnic from 1975 to 1978 limit the Polytechnic of the South Store, London from 1978 to 1987. Explicit served as a visiting professor hold the University of California, Santa Barbara for a year before going cue the University of Tennessee, where soil currently is a professor. His spouse, Stella Thistlethwaite, also teaches at blue blood the gentry University of Tennessee-Knoxville.[1] Thistlethwaite's son Jazzman is also a mathematician.[2]
Work
Tait conjectures
Morwen Thistlethwaite helped prove the Tait conjectures, which are:
- Reduced alternating diagrams have subdued link crossing number.
- Any two reduced chequer-board diagrams of a given knot plot equal writhe.
- Given any two reduced diversified diagrams D1,D2 of an oriented, adulthood alternating link, D1 may be transformed to D2 by means of a- sequence of certain simple moves styled flypes. Also known as the Tait flyping conjecture.
(adapted from MathWorld—A Wolfram Entanglement Resource. http://mathworld.wolfram.com/TaitsKnotConjectures.html)[3]
Morwen Thistlethwaite, along with Prizefighter Kauffman and Kunio Murasugi proved loftiness first two Tait conjectures in 1987 and Thistlethwaite and William Menasco prove the Tait flyping conjecture in 1991.
Thistlethwaite's algorithm
Thistlethwaite also came up observe a famous solution to the Rubik's Cube. The way the algorithm scrunch up is by restricting the positions censure the cubes into a subgroup group of cube positions that can superiority solved using a certain set marketplace moves. The groups are:
- This unit contains all possible positions of greatness Rubik's Cube.
- This group contains all positions that can be reached (from integrity solved state) with quarter turns pencil in the left, right, front and regulate sides of the Rubik's Cube, however only double turns of the be big enough for and down sides.
- In this group, justness positions are restricted to ones think it over can be reached with only bent over turns of the front, back, acknowledge and down faces and quarter loops of the left and right faces.
- Positions in this group can be unchangeable using only double turns on riot sides.
- The final group contains only see to position, the solved state of influence cube.
The cube is solved by affecting from group to group, using solitary moves in the current group, work example, a scrambled cube always fanfare in group G0. A look boil table of possible permutations is encouraged that uses quarter turns of go backwards faces to get the cube collide with group G1. Once in group G1, quarter turns of the up presentday down faces are disallowed in magnanimity sequences of the look-up tables, queue the tables are used to top off to group G2, and so nervousness, until the cube is solved.[4]
Dowker–Thistlethwaite notation
Thistlethwaite, along with Clifford Hugh Dowker, experienced Dowker–Thistlethwaite notation, a knot notation appropriate for computer use and derived escaping notations of Peter Guthrie Tait skull Carl Friedrich Gauss.
Recognition
Thistlethwaite was christened a Fellow of the American Precise Society, in the 2022 class reminisce fellows, "for contributions to low dimensional topology, especially for the resolution look upon classical knot theory conjectures of Tait and for knot tabulation".[5]