Background
Perigal descended from a Huguenot family who emigrated to England in the late 17th century, and was the oldest of six siblings.
Perigal descended from a Huguenot family who emigrated to England in the late 17th century, and was the oldest of six siblings.
He attended the Royal Institution regularly as a visitor for many years, and finally became a member in 1895, at age 94.
After working as a clerk for the Privy Council, he became a bookkeeper in a London stockbrokerage in the 1840s. He remained a lifelong bachelor. He was elected as a fellow of the Royal Astronomical Society in 1850.
Although Perigal was long-lived, his father lived even longer, becoming a centenarian.
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.
Perigal had the same dissection printed on his business cards, and it also appears on his tombstone. In the same book, Perigal expressed the hope that dissection based methods would also solve the 1925 Tarski"s problem of circle-squaring by dissection.
That problem had been shown to be impossible to solve in a constructive way in 1963.
Nevertheless a no-constructive solution has been proposed by Miklós Laczkovich in 1990. Perigal also propose the first 6-pieces solution to the square trisection problem. 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
Perigal was a member of the London Mathematical Society from 1868 to 1897, and was treasurer of the Royal Meteorological Society for 45 years, from 1853 until his death in 1898. He was an original member of the British Astronomical Association in 1890. He would be oldest member of the Bachelor of Applied Arts if all the members were gathered together.
