Dinostratus
Encyclopedia
Dinostratus was a Greek
mathematician
and geometer, and the brother of Menaechmus
. He is known for using the quadratrix
to solve the problem of squaring the circle
.
of Hippias
, for which he proved a special property (Dinostratus' theorem
) that allowed him the squaring of the circle. Due to his work the trisectrix later became known as the quadratrix
of Dinostratus as well. Although Dinostratus solved the problem of squaring the circle, he did not do so using ruler and compass alone, and so it was clear to the Greeks that his solution violated the foundational principles of their mathematics. Over two thousand years later it would be proved impossible to square a circle using straight edge and compass alone.
Greece
Greece , officially the Hellenic Republic , and historically Hellas or the Republic of Greece in English, is a country in southeastern Europe....
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and geometer, and the brother of Menaechmus
Menaechmus
Menaechmus was an ancient Greek mathematician and geometer born in Alopeconnesus in the Thracian Chersonese, who was known for his friendship with the renowned philosopher Plato and for his apparent discovery of conic sections and his solution to the then-long-standing problem of doubling the cube...
. He is known for using the quadratrix
Quadratrix
In mathematics, a quadratrix is a curve having ordinates which are a measure of the area of another curve. The two most famous curves of this class are those of Dinostratus and E. W...
to solve the 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...
.
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 trisectrixTrisectrix
In geometry, a trisectrix is a curve which can be used to trisect an arbitrary angle. Such a method falls outside those allowed by compass and straightedge constructions, so they do not contradict the well known theorem which states that an arbitrary angle cannot be trisected with that type of...
of Hippias
Hippias
Hippias of Elis 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, and lectured on poetry, grammar, history, politics, mathematics, and much else...
, for which he proved a special property (Dinostratus' theorem
Dinostratus' theorem
[File:Quadratrix des Dinostratos.svg|thumb|\frac[File:Quadratrix des Dinostratos.svg|thumb|\frac[File:Quadratrix des Dinostratos.svg|thumb|\frac[[File:Quadratrix des Dinostratos.svg|thumb|\frac[[File:Quadratrix des Dinostratos.svg|thumb|\frac...
) that allowed him the squaring of the circle. Due to his work the trisectrix later became known as the quadratrix
Quadratrix
In mathematics, a quadratrix is a curve having ordinates which are a measure of the area of another curve. The two most famous curves of this class are those of Dinostratus and E. W...
of Dinostratus as well. Although Dinostratus solved the problem of squaring the circle, he did not do so using ruler and compass alone, and so it was clear to the Greeks that his solution violated the foundational principles of their mathematics. Over two thousand years later it would be proved impossible to square a circle using straight edge and compass alone.