Dinostratus' theorem
Encyclopedia
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 Dinostratus
who proved it around 350 BC when he attempted to square the circle himself.
The theorem states that Hippias' trisectrix divides one of the sides of its associated square in a ratio of
.
Arbitrary points on Hippias' trisectrix itself however cannot be constructed by circle and compass alone but only a dense subset. In particular it is not possible to construct the exact point where the trisectrix meets the edge of of the square. For this reason Dinostratus' approach is not considered a "real" solution of the classical problem of squaring the cricle.
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...
if the trisectrix can be used in addition to straightedge and compass. The theorem is named after the Greek mathematician Dinostratus
Dinostratus
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.- Life and work :...
who proved it around 350 BC when he attempted to square the circle himself.
The theorem states that Hippias' trisectrix divides one of the sides of its associated square in a ratio of
.Arbitrary points on Hippias' trisectrix itself however cannot be constructed by circle and compass alone but only a dense subset. In particular it is not possible to construct the exact point where the trisectrix meets the edge of of the square. For this reason Dinostratus' approach is not considered a "real" solution of the classical problem of squaring the cricle.