Nicomedes

Nicomedes

Born: about 300 BC in Greece
Died: about 240 BC

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Nicomedes is known for his discovery of the curve the Conchoid of Nicomedes
(x - b)^2(x^2 + y^2) - a^2x^2 = 0
(not a notation Nicomedes would have recognised!) which can be used in both the trisection of an angle and the duplication of a cube.

Nicomedes recognised three distinct forms in this family. The conchoid has x = b as an asymptote and the area between either branch and the asymptote is infinite.

Nicomedes also used the quadratrix, discovered by Hippias, to solve the problem of squaring the circle. Pappus tells us

For the squaring of the circle there was used by Nicomedes, Dinostratus and certain other later persons a certain curve which took its name from this property, for it is called by them square-forming in other words the quadratrix.
References elsewhere in this archive:

Show me the Conchoid

References:

  1. Dictionary of Scientific Biography
  2. G Loria, Le scienze esatte nell'antica Grecia (Milan, 1914), 404-410.
  3. T L Heath, A History of Greek Mathematics I (Oxford, 1921), 260-262. 
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JOC/EFR February 1996