Definition:Quadratrix of Hippias/Definition 2
Definition
The quadratrix of Hippias is the plane curve be generated as follows.
Let $\Box ABCD$ be a square of side length $a$.
Let a quarter circle be inscribed in $\Box ABCD$ with the center at $A$, the arc going from $B$ to $D$.
Let $E$ be a point travelling around the arc $BD$ at a constant angular velocity.
Let $F$ be a point travelling along the side of $\Box ABCD$ at a constant velocity such that $E$ and $F$ take the same time to travel from the top $CD$ to the bottom $AB$ of $\Box ABCD$.
Let $S$ be the point at which the line $AE$ intersects the line through $F$ parallel to $AB$.
The path traced out by $S$ is the quadratrix of Hippias.
Also see
Source of Name
This entry was named for Hippias of Elis.
Historical Note
The quadratrix of Hippias was invented by Hippias of Elis for the purpose of solving the problem of Trisecting the Angle.
It was subsequently used by Dinostratus for Squaring the Circle.
Its use for both trisection and quadrature (that is, finding area) explains the multiple nature of its names.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): quadratrix
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): quadratrix