Henry Perigal
Encyclopedia
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.
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
from 1868 to 1897, and was treasurer of the Royal Meteorological Society
for 45 years, from 1853 until his death in 1898. He was elected as a fellow
of the Royal Astronomical Society
in 1850. He attended the Royal Institution
regularly as a visitor for many years, and finally became a member in 1895, at age 94.
Although Perigal was long-lived, his father lived even longer, becoming a centenarian
.
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 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.
Royal Astronomical Society
The Royal Astronomical Society is a learned society that began as the Astronomical Society of London in 1820 to support astronomical research . It became the Royal Astronomical Society in 1831 on receiving its Royal Charter from William IV...
MRI
Royal Institution
The Royal Institution of Great Britain is an organization devoted to scientific education and research, based in London.-Overview:...
(1 April 1801 – 6 June 1898) was a British stockbroker and amateur
Amateur
An amateur is generally considered a person attached to a particular pursuit, study, or science, without pay and often without formal training....
mathematician, known for his dissection-based proof of the Pythagorean theorem
Pythagorean theorem
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a relation in Euclidean geometry among the three sides of a right triangle...
and for his unorthodox belief that the moon does not rotate.
Biography
Perigal descended from a HuguenotHuguenot
The Huguenots were members of the Protestant Reformed Church of France during the 16th and 17th centuries. Since the 17th century, people who formerly would have been called Huguenots have instead simply been called French Protestants, a title suggested by their German co-religionists, the...
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
Privy Council of the United Kingdom
Her Majesty's Most Honourable Privy Council, usually known simply as the Privy Council, is a formal body of advisers to the Sovereign in the United Kingdom...
, 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
London Mathematical Society
-See also:* American Mathematical Society* Edinburgh Mathematical Society* European Mathematical Society* List of Mathematical Societies* Council for the Mathematical Sciences* BCS-FACS Specialist Group-External links:* * *...
from 1868 to 1897, and was treasurer of the Royal Meteorological Society
Royal Meteorological Society
The Royal Meteorological Society traces its origins back to 3 April 1850 when the British Meteorological Society was formed as a society the objects of which should be the advancement and extension of meteorological science by determining the laws of climate and of meteorological phenomena in general...
for 45 years, from 1853 until his death in 1898. He was elected as a fellow
Fellow
A fellow in the broadest sense is someone who is an equal or a comrade. The term fellow is also used to describe a person, particularly by those in the upper social classes. It is most often used in an academic context: a fellow is often part of an elite group of learned people who are awarded...
of the Royal Astronomical Society
Royal Astronomical Society
The Royal Astronomical Society is a learned society that began as the Astronomical Society of London in 1820 to support astronomical research . It became the Royal Astronomical Society in 1831 on receiving its Royal Charter from William IV...
in 1850. He attended the Royal Institution
Royal Institution
The Royal Institution of Great Britain is an organization devoted to scientific education and research, based in London.-Overview:...
regularly as a visitor for many years, and finally became a member in 1895, at age 94.
Although Perigal was long-lived, his father lived even longer, becoming a centenarian
Centenarian
A centenarian is a person who is or lives beyond the age of 100 years. Because current average life expectancies across the world are less than 100, the term is invariably associated with longevity. Much rarer, a supercentenarian is a person who has lived to the age of 110 or more, something only...
.
Mathematics
In his booklet Geometric Dissections and Transpositions (London: Bell & Sons, 1891) Perigal provided a proof of the Pythagorean theoremPythagorean theorem
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a relation in Euclidean geometry among the three sides of a right triangle...
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
Prototile
In the mathematical theory of tessellations, a prototile is one of the shapes of a tile in a tessellation.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 may be congruent to one or more others...
is the larger square with a Pythagorean tiling
Pythagorean tiling
In geometry, the Pythagorean tiling or two squares tessellation is a tessellation of the plane by squares of two different sizes, in which each square touches four squares of the other size on its four sides. A tiling of this type may be formed by squares of any two different sizes...
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 ancient problem of squaring the circle
Squaring the circle
Squaring the circle is a problem proposed by ancient geometers. It is the challenge of constructing a square with the same area as a given circle by using only a finite number of steps with compass and straightedge...
, but that problem had already been shown to be impossible to solve in 1882 by the Lindemann–Weierstrass theorem
Lindemann–Weierstrass theorem
In mathematics, the Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendence of numbers. It states that if 1, ..., are algebraic numbers which are linearly independent over the rational numbers ', then 1, ..., are algebraically...
.
As well as being interested in mathematics, Perigal was an accomplished lathe
Lathe
A lathe is a machine tool which rotates the workpiece on its axis to perform various operations such as cutting, sanding, knurling, drilling, or deformation with tools that are applied to the workpiece to create an object which has symmetry about an axis of rotation.Lathes are used in woodturning,...
worker, and made models of mathematical curves for Augustus De Morgan
Augustus De Morgan
Augustus De Morgan was a British mathematician and logician. He formulated De Morgan's laws and introduced the term mathematical induction, making its idea rigorous. The crater De Morgan on the Moon is named after him....
. 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.