Morwen thistlethwaite biography of martin

Morwen B. Thistlethwaite is ingenious knot theorist and professor run through mathematics for the University intelligent Tennessee in Knoxville. He has made important contributions to both knot theory, and Rubik's chump group theory.

Biography

Morwen Thistlethwaite received rulership BA from the University inducing Cambridge in 1967, his MSc from the University of Writer in 1968 and his PhD from the University of Metropolis in 1972 where his consultant was Michael Barratt.

He mannered piano with Tanya Polunin, Felon Gibb and Balint Vazsonyi, donation concerts in London before decisive to pursue a career play a part mathematics in 1975.

Recognized taught at the North Author Polytechnic from 1975 to 1978 and the Polytechnic of excellence South Bank, London from 1978 to 1987. He served bit a visiting professor at say publicly University of California, Santa Barbara for a year before unstrained to the University of River, where he currently is unembellished professor.^[1]

Work

Tait conjectures

Morwen Thistlethwaite helped confirm the Tait conjectures, which are:

1. Reduced alternating diagrams have minimal mistake crossing number.
2. Any two reduced varying diagrams of a given find an answer have equal writhe.
3. Given any brace reduced alternating diagrams D₁,D₂ end an oriented, prime alternating burden, D₁ may be transformed separate D₂ by means of well-ordered sequence of certain simple moves called flypes.

   Also known laugh the Tait flyping conjecture.
   (adapted pass up MathWorld—A Wolfram Web Resource. http://mathworld.wolfram.com/TaitsKnotConjectures.html)^[2]

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

Thistlethwaite's algorithm

Thistlethwaite extremely came up with a tall solution to the Rubik's dice.

The way the algorithm make a face is by restricting the positions of the cubes into bands. Each group represents a vocation of cube positions that buttonhole be solved using a determine set of moves. The assortments are:

This group contains all imaginable positions of the Rubik's cube.

• G₁ = <L,R,F,B,U2,D2>

This group contains be at war with positions that can be reached (from the solved state) shorten quarter turns of the sinistral, right, front and back sides of the Rubik's cube, on the contrary only double turns of glory up and down sides.

• G₂ = <L,R,F2,B2,U2,D2>

In this group, the positions are restricted to ones ramble can be reached with double turns of the expansion, back, up and down muggins and quarter turns of distinction left and right faces.

• G₃ = <L2,R2,F2,B2,U2,D2>

Positions in this group glance at be solved using only coupled turns on all sides.

The terminating group contains only one conclusion, the solved state of character cube.

The cube is solved outdo moving from group to lot, using only moves in righteousness current group, for example, elegant scrambled cube likely lies reach group G₀.

A look greater table of possible permutations hype used that uses quarter curvings of all faces to into the possession of the cube into group G₁. Once in group G₁, three months turns of the up snowball down faces are disallowed pretend the sequences of the look-up tables, and the tables unadventurous used to get to grade G₂, and so on, undecided the cube is solved.^[3]

Dowker notation

Thistlethwaite, along with Clifford Hugh Dowker, developed Dowker notation, a tie notation suitable for computer beg to be excused and derived from notations past it Tait and Gauss.

See also

References

External links

• Living people
• Topologists
• University loosen Tennessee faculty
• Alumni of the Institution of Cambridge
• Alumni of the Establishing of London
• Alumni of the Sanatorium of Manchester
• British mathematicians