cissoid
Definition
- Noun:
- A plane curve: In mathematics, a "cissoid" is a specific type of plane curve generated from two given curves (typically a circle and a line) by a geometric construction. More precisely, it is the locus of points such that the distance from a fixed point (the pole) to a point on the curve equals the distance from that point to a fixed line (the directrix), often defined in relation to a circle and a tangent line.
Usage Examples
- Noun:
- The cissoid of Diocles is a classic example of a cubic curve studied in ancient Greek geometry. (A specific cissoid curve with historical significance.)
- In analytic geometry, the equation of a cissoid can be expressed in polar coordinates as r = 2a sin²θ / cosθ. (The mathematical formula for a cissoid curve.)
Advanced Usage
"Cissoid of Diocles": A specific cissoid curve named after the Greek mathematician Diocles, used to solve the problem of doubling the cube. It is the locus of points satisfying a particular relationship between a circle and a line.
- The cissoid of Diocles was discovered in the 2nd century BC as a tool for geometric constructions. (Historical mathematical curve.)
"Cissoid curve": A general term for any curve formed by the cissoid construction method.
- The cissoid curve has a cusp at the pole and an asymptote at the directrix. (Geometric properties of the curve.)
Variants and Related Words
Cissoidal (adj): Relating to or having the form of a cissoid.
- The cissoidal shape appears in certain algebraic equations. (Describing a curve with cissoid properties.)
Cissoid of Diocles (n): The specific cissoid curve named after Diocles.
- The cissoid of Diocles is one of the earliest known transcendental curves. (Historical mathematical curve.)
Synonyms
- Curve: a continuous line in geometry (general term).
- Locus: a set of points satisfying a given condition (mathematical synonym for the definition).
Related Idioms
- (The word "cissoid" is a technical mathematical term and does not appear in idiomatic expressions.)