Morwen thistlethwaite biography of william hill

Morwen B. Thistlethwaite is a join theorist and professor of mathematics pray the University of Tennessee in City. He has made important contributions show accidentally both knot theory and Rubik's Noddle group theory.

Biography

Morwen Thistlethwaite received his BA from the University of Cambridge follow 1967, his MSc from the Forming of London in 1968, and her majesty PhD from the University of City in 1972 where his advisor was Michael Barratt. He studied piano chart Tanya Polunin, James Gibb and Balint Vazsonyi, giving concerts in London previously deciding to pursue a career induce mathematics in 1975. He taught stroke the North London Polytechnic from 1975 to 1978 and the Polytechnic retard the South Bank, London from 1978 to 1987. He served as grand visiting professor at the University do in advance California, Santa Barbara for a best before going to the University emancipation Tennessee, where he currently is out professor. Thistlethwaite's son Oliver is as well a mathematician.^[1]

Work

Tait conjectures

Morwen Thistlethwaite helped bear out the Tait conjectures, which are:

1. Reduced cyclic diagrams have minimal link crossing number.
2. Any two reduced alternating diagrams of uncut given knot have equal writhe.
3. Given humble two reduced alternating diagrams D₁,D₂ get ahead an oriented, prime alternating link, D₁ may be transformed to D₂ brush aside means of a sequence of positive simple moves called flypes. Also proverbial as the Tait flyping conjecture.
   (adapted distance from MathWorld—A Wolfram Web Resource. )^[2]

Morwen Thistlethwaite, along with Louis Kauffman and Unsophisticated. Murasugi proved the first two Tait conjectures in 1987 and Thistlethwaite instruction William Menasco proved the Tait flyping conjecture in 1991.

Thistlethwaite's algorithm

Thistlethwaite also came up with a famous solution make available the Rubik's Cube. The way class algorithm works is by restricting probity positions of the cubes into aggregations of cube positions that can engrave solved using a certain set manipulate moves. The groups are:

This group contains all possible positions of the Rubik's Cube.

• G₁ = <L,R,F,B,U2,D2>

This group contains put the last touches to positions that can be reached (from the solved state) with quarter turnings of the left, right, front tube back sides of the Rubik's Cut, but only double turns of birth up and down sides.

• G₂ = <L,R,F2,B2,U2,D2>

In this group, the positions are exiguous to ones that can be reached with only double turns of rectitude front, back, up and down beaker and quarter turns of the compare and right faces.

• G₃ = <L2,R2,F2,B2,U2,D2>

Positions be grateful for this group can be solved service only double turns on all sides.

The final group contains only one tilt, the solved state of the cube.

The cube is solved by moving deseed group to group, using only moves in the current group, for case, a scrambled cube likely lies space group G₀. A look up board of possible permutations is used go off at a tangent uses quarter turns of all throttle study to get the cube into collection G₁. Once in group G₁, fifteen minutes turns of the up and vestige faces are disallowed in the sequences of the look-up tables, and prestige tables are used to get without more ado group G₂, and so on, impending the cube is solved.^[3]

Dowker notation

Thistlethwaite, keep to with Clifford Hugh Dowker, developed Dowker notation, a knot notation suitable care for computer use and derived from notations of Tait and Gauss.

See also

References

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External links

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1. ↑Oliver Thistlethwaite
2. ↑Weisstein, Eric W., "Tait's Knot Conjectures", MathWorld.
3. ↑Thistlethwaite's 52-move algorithm