Henry Perigal

Henry Perigal, Jr. FRAS MRI (1 April 1801 – 6 June 1898) was a British stockbroker and amateur mathematician, known for his dissection-based proof of the Pythagorean theorem and for his unorthodox belief that the moon does not rotate.[1][2][3][4][5][6]

Biography

Perigal descended from a Huguenot family who emigrated to England in the late 17th century,[4][5][6] and was the oldest of six siblings.[6] After working as a clerk for the Privy Council, he became a bookkeeper in a London stockbrokerage in the 1840s.[5][6] He remained a lifelong bachelor.[1]

Perigal was a member of the London Mathematical Society from 1868 to 1897,[2] and was treasurer of the Royal Meteorological Society for 45 years, from 1853 until his death in 1898.[3] He was elected as a fellow of the Royal Astronomical Society in 1850.[6] He attended the Royal Institution regularly as a visitor for many years, and finally became a member in 1895, at age 94.[1][6]

Although Perigal was long-lived, his father lived even longer, becoming a centenarian.[5]

Mathematics

In his booklet Geometric Dissections and Transpositions (London: Bell & Sons, 1891) Perigal provided a proof of the Pythagorean theorem based on the idea of dissecting two smaller squares into a larger square. The five-piece dissection that he found may be generated by overlaying a regular square tiling whose prototile is the larger square with a Pythagorean tiling generated by the two smaller squares.[1][7] Perigal had the same dissection printed on his business cards, and it also appears on his tombstone.[1][5]

In the same book, Perigal expressed the hope that dissection based methods would also solve the ancient problem of squaring the circle, but that problem had already been shown to be impossible to solve in 1882 by the Lindemann–Weierstrass theorem.

As well as being interested in mathematics, Perigal was an accomplished lathe worker, and made models of mathematical curves for Augustus De Morgan. He believed (falsely) that the moon does not rotate with respect to the fixed stars, and used his knowledge of curvilinear motion in an attempt to demonstrate this belief to others.[1][5]

References

  1. ^ a b c d e f Frederickson, Greg N. (1997), Dissections: Plane & Fancy, Cambridge University Press, p. 31 .
  2. ^ a b "Tucker–Oakes Photograph", LMS Newsletter 391, 2010, http://old.lms.ac.uk/newsletter/391/391_12.html .
  3. ^ a b "Proceedings at the meeting of the society. May 18, 1898. Ordinary Meeting", Quarterly Journal of the Royal Meteorological Society 24 (108): 261, 1898, doi:10.1002/qj.49702410806 .
  4. ^ a b Frederickson, Greg N. (1999), A visit to the monument of Henry Perigal, http://www.cs.purdue.edu/homes/gnf/book/Booknews/perig_m.html .
  5. ^ a b c d e f "On the dissecting table: Henry Perigal 1801 - 1898", Plus magazine 16, December 2000, http://plus.maths.org/content/dissecting-table .
  6. ^ a b c d e f "Obituary Notices : Fellows :- Perigal, Henry", Monthly Notices of the Royal Astronomical Society 59: 226–228, 1899, Bibcode 1899MNRAS..59R.226. 
  7. ^ Nelsen, Roger B. (November 2003), "Paintings, plane tilings, and proofs", Math Horizons: 5–8, http://www-stat.wharton.upenn.edu/~steele/Publications/Books/CSMC/New%20Problems/paintings.pdf . Reprinted in Haunsperger, Deanna; Kennedy, Stephen (2007), The Edge of the Universe: Celebrating Ten Years of Math Horizons, Spectrum Series, Mathematical Association of America, pp. 295–298, ISBN 9780883855553 .