Dinostratus ( el, Δεινόστρατος; c. 390 – c. 320 BCE) was a
Greek
Greek may refer to:
Greece
Anything of, from, or related to Greece, a country in Southern Europe:
*Greeks, an ethnic group.
*Greek language, a branch of the Indo-European language family.
**Proto-Greek language, the assumed last common ancestor ...
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
and
geometer
A geometer is a mathematician whose area of study is geometry.
Some notable geometers and their main fields of work, chronologically listed, are:
1000 BCE to 1 BCE
* Baudhayana (fl. c. 800 BC) – Euclidean geometry, geometric algebra
* ...
, and the brother of
Menaechmus :''There is also a Menaechmus in Plautus' play, ''The Menaechmi''.''
Menaechmus ( el, Μέναιχμος, 380–320 BC) was an ancient Greek mathematician, geometer and philosopher born in Alopeconnesus or Prokonnesos in the Thracian Chersonese, wh ...
. He is known for using the
quadratrix
In geometry, a quadratrix () is a curve having ordinates which are a measure of the area (or quadrature) of another curve. The two most famous curves of this class are those of Dinostratus and Ehrenfried Walther von Tschirnhaus, E. W. Tschirnhaus, ...
to solve the problem of
squaring the circle
Squaring the circle is a problem in geometry first proposed in Greek mathematics. It is the challenge of constructing a square with the area of a circle by using only a finite number of steps with a compass and straightedge. The difficulty ...
.
Life and work
Dinostratus' chief contribution to mathematics was his solution to the problem of squaring the circle. To solve this problem, Dinostratus made use of the
trisectrix
In geometry, a trisectrix is a curve which can be used to trisect an arbitrary angle with ruler and compass and this curve as an additional tool. Such a method falls outside those allowed by compass and straightedge constructions, so they do not c ...
of
Hippias
Hippias of Elis (; el, Ἱππίας ὁ Ἠλεῖος; late 5th century BC) was a Greek sophist, and a contemporary of Socrates. With an assurance characteristic of the later sophists, he claimed to be regarded as an authority on all subjects, ...
, for which he proved a special property (
Dinostratus' theorem
In geometry, Dinostratus' theorem describes a property of Hippias' trisectrix, that allows for the squaring the circle if the trisectrix can be used in addition to straightedge and compass. The theorem is named after the Greek mathematician Dinost ...
) that allowed him the squaring of the circle. Due to his work the trisectrix later became known as the
quadratrix
In geometry, a quadratrix () is a curve having ordinates which are a measure of the area (or quadrature) of another curve. The two most famous curves of this class are those of Dinostratus and Ehrenfried Walther von Tschirnhaus, E. W. Tschirnhaus, ...
of Dinostratus as well.
Although Dinostratus solved the problem of squaring the circle, he did not do so using
ruler and compass
In geometry, straightedge-and-compass construction – also known as ruler-and-compass construction, Euclidean construction, or classical construction – is the construction of lengths, angles, and other geometric figures using only an ideali ...
alone, and so it was clear to the Greeks that his solution violated the foundational principles of their mathematics.
Over 2,200 years later
Ferdinand von Lindemann
Carl Louis Ferdinand von Lindemann (12 April 1852 – 6 March 1939) was a German mathematician, noted for his proof, published in 1882, that (pi) is a transcendental number, meaning it is not a root of any polynomial with rational coefficien ...
would prove that it is impossible to square a circle using straight edge and compass alone.
Citations and footnotes
References
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External links
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{{Authority control
Ancient Greek mathematicians
Ancient Greek geometers
4th-century BC Greek people
390s BC births
320s BC deaths
4th-century BC mathematicians