1. Description

2. See also

3. References

4. External links

A conchoid is a curve derived from a fixed point O, another curve, and a length d. It was invented by the ancient Greek mathematician Nicomedes.^[1]

Description

For every line through O that intersects the given curve at A the two points on the line which are d from A are on the conchoid. The conchoid is, therefore, the cissoid of the given curve and a circle of radius d and center O. They are called conchoids because the shape of their outer branches resembles conch shells.

The simplest expression uses polar coordinates with O at the origin. If

expresses the given curve, then

expresses the conchoid.

If the curve is a line, then the conchoid is the conchoid of Nicomedes.

For instance, if the curve is the line , then the line's polar form is

and therefore the conchoid can be expressed parametrically as

A limaçon is a conchoid with a circle as the given curve.

The so-called conchoid of de Sluze and conchoid of Dürer are not actually conchoids. The former is a strict cissoid and the latter a construction more general yet.

See also

• Cissoid
• Strophoid

References

• {{cite book | author=J. Dennis Lawrence | title=A catalog of special plane curves | publisher=Dover Publications | year=1972 | isbn=0-486-60288-5 | pages=36, 49–51, 113, 137 }}

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