Thorold Gosset

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John Herbert de Paz Thorold Gosset (16 October 1869[1] – December 1962) was an English lawyer and an amateur mathematician. In mathematics, he is noted for discovering and classifying the semiregular polytopes in dimensions four and higher, and for his generalization of Descartes' theorem on tangent circles to four and higher dimensions.

Biography

Thorold Gosset was born in

called to the bar of the Inner Temple in June 1895, and graduated LLM in 1896.[1] In 1900 he married Emily Florence Wood,[4] and they subsequently had two children, named Kathleen and John.[5]

Mathematics

According to

vertex-uniform, as well as the analogous honeycombs, which he regarded as degenerate polytopes. In 1897 he submitted his results to James W. Glaisher, then editor of the journal Messenger of Mathematics. Glaisher was favourably impressed and passed the results on to William Burnside and Alfred Whitehead. Burnside, however, stated in a letter to Glaisher in 1899 that "the author's method, a sort of geometric intuition" did not appeal to him. He admitted that he never found the time to read more than the first half of Gosset's paper. In the end Glaisher published only a brief abstract of Gosset's results.[7]

Gosset's results went largely unnoticed for many years. His semiregular polytopes were rediscovered by

H.S.M. Coxeter
who gave both Gosset and Elte due credit.

Coxeter introduced the term Gosset polytopes for three semiregular polytopes in 6, 7, and 8 dimensions discovered by Gosset: the 221, 321, and 421 polytopes. The vertices of these polytopes were later seen to arise as the roots of the exceptional Lie algebras E6, E7 and E8.

A new and more precise definition of the Gosset Series of polytopes has been given by Conway in 2008.[9]

See also

  • Gosset graph
  • Scott Vorthmann with David Richter in this article are displaying and presenting computerized vZome images of Gosset's Polytopes built with vZome program and which are including the 3_21 polytope of Coxeter of 27 nodes which interested Pierre Etevenon in France.[10]

References

  1. ^ a b "Gosset, John Herbert de Paz Thorold (GST888JH)". A Cambridge Alumni Database. University of Cambridge.
  2. ^ UK Census 1871, RG10-863-89-23
  3. ^ "Register of Marriages". St George Hanover Square 1a. General Register Office for England and Wales. January–March 1868: 429. {{cite journal}}: Cite journal requires |journal= (help)
  4. ^ "Register of Marriages". St George Hanover Square 1a. General Register Office for England and Wales. June–September 1900: 1014. {{cite journal}}: Cite journal requires |journal= (help)
  5. ^ UK Census 1911, RG14-181-9123-19
  6. ISBN 0-486-61480-8
    . A brief account of Gosset and his contribution to mathematics is given on page 164.
  7. ^ Gosset, Thorold (1900). "On the regular and semi-regular figures in space of n dimensions". Messenger of Mathematics. 29: 43–48.
  8. ISBN 1-4181-7968-X
    .
  9. ISBN 978-1-56881-220-5
    . A new account of Gosset Series is given on pages 411-413.
  10. ^ Gosset’s Polytopes, vzome.com
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