Henry Perigal, Jr. FRAS

MRI Magnetic resonance imaging (MRI) is a medical imaging technique used in radiology to generate pictures of the anatomy and the physiological processes inside the body. MRI scanners use strong magnetic fields, magnetic field gradients, and rad ...

(1 April 1801 – 6 June 1898) was a British stockbroker and

amateur An amateur () is generally considered a person who pursues an avocation independent from their source of income. Amateurs and their pursuits are also described as popular, informal, autodidacticism, self-taught, user-generated, do it yourself, DI ...

mathematician, known for his

dissection Dissection (from Latin ' "to cut to pieces"; also called anatomization) is the dismembering of the body of a deceased animal or plant to study its anatomical structure. Autopsy is used in pathology and forensic medicine to determine the cause of ...

-based proof of the

Pythagorean theorem In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite t ...

and for his unorthodox belief that the moon does not rotate......

Biography

Perigal descended from a

Huguenot The Huguenots ( , ; ) are a Religious denomination, religious group of French people, French Protestants who held to the Reformed (Calvinist) tradition of Protestantism. The term, which may be derived from the name of a Swiss political leader, ...

family who emigrated to England in the late 17th century, and was the oldest of six siblings. 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. Perigal was a member of the

London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's Learned society, learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh ...

from 1868 to 1897, and was treasurer of the

Royal Meteorological Society The Royal Meteorological Society is an organization that promotes academic and public engagement in weather and climate science. Fellows of the Society must possess relevant qualifications, but Members can be lay enthusiasts. It publishes vari ...

for 45 years, from 1853 until his death in 1898. He was elected as a

fellow A fellow is a title and form of address for distinguished, learned, or skilled individuals in academia, medicine, research, and industry. The exact meaning of the term differs in each field. In learned society, learned or professional society, p ...

of the

Royal Astronomical Society The Royal Astronomical Society (RAS) is a learned society and charitable organisation, charity that encourages and promotes the study of astronomy, planetary science, solar-system science, geophysics and closely related branches of science. Its ...

in 1850. He attended the

Royal Institution The Royal Institution of Great Britain (often the Royal Institution, Ri or RI) is an organisation for scientific education and research, based in the City of Westminster. It was founded in 1799 by the leading British scientists of the age, inc ...

regularly as a visitor for many years, and finally became a member in 1895, at age 94. Friends with Washington Teasdale and

James Glaisher James Glaisher Fellow of the Royal Society, FRS (7 April 1809 – 7 February 1903) was an English meteorologist, aeronaut and astronomer. Biography Born in Rotherhithe, the son of a London watchmaker, Glaisher was a junior assistant at the C ...

. He was an original member of the British Astronomical Association in 1890; he would be oldest member of the BAA if all the members were gathered together. Although Perigal was long-lived, his father lived even longer, becoming a

centenarian A centenarian is a person who has reached the age of 100. Because life expectancies at birth worldwide are well below 100, the term is invariably associated with longevity. The United Nations estimated that there were 316,600 living centenarian ...

Mathematics

In his booklet ''Geometric Dissections and Transpositions'' (London: Bell & Sons, 1891) Perigal provided a proof of the

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 In mathematics, a prototile is one of the shapes of a tile in a tessellation. Definition A tessellation of the plane or of any other space is a cover of the space by closed shapes, called tiles, that have disjoint interiors. Some of the tiles m ...

is the larger square with a

Pythagorean tiling A Pythagorean tiling or two squares tessellation is a tiling of a Euclidean plane by squares of two different sizes, in which each square touches four squares of the other size on its four sides. Many proofs of the Pythagorean theorem are ...

generated by the two smaller squares.. Reprinted in . Perigal had the same dissection printed on his business cards, and it also appears on his tombstone, which is located within the grounds of St Mary and St Peter, Wennington,

Essex Essex ( ) is a Ceremonial counties of England, ceremonial county in the East of England, and one of the home counties. It is bordered by Cambridgeshire and Suffolk to the north, the North Sea to the east, Kent across the Thames Estuary to the ...

, now the

London Borough of Havering The London Borough of Havering () in East London, England, forms part of Outer London. It has a population of 259,552 inhabitants; the principal town is Romford, while other communities include Hornchurch, Upminster, Collier Row and Rainham, Lo ...

. 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 non-constructive solution has been proposed by

Miklós Laczkovich Miklós Laczkovich (born 21 February 1948) is a Hungarian mathematician mainly noted for his work on real analysis and geometric measure theory. His most famous result is the solution of Tarski's circle-squaring problem in 1989.Ruthen, R. (1989 ...

in 1990.. Perigal also proposed the first 6-pieces solution to the square trisection problem. As well as being interested in mathematics, Perigal was an accomplished

lathe A lathe () is a machine tool that rotates a workpiece about an axis of rotation to perform various operations such as cutting, sanding, knurling, drilling, deformation, facing, threading and turning, with tools that are applied to the w ...

worker, and made models of mathematical curves for

Augustus De Morgan Augustus De Morgan (27 June 1806 – 18 March 1871) was a British mathematician and logician. He is best known for De Morgan's laws, relating logical conjunction, disjunction, and negation, and for coining the term "mathematical induction", the ...

. He falsely believed 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.

References

{{DEFAULTSORT:Perigal, Henry 1801 births 1898 deaths 19th-century English mathematicians