MATHEMATICIAN

Life
Nicomedes lived in Alexandria and Pergamum, after Eratosthenes and before Geminus. His work is cited by Proclus, Pappus and Eutocius.


Work
He worked on the problem of the trisection of the angle (division of any angle into three equal parts). His solution, by construction using a special curve which he called a conchoid, is presented in his treatise on conchoids.

"On conchoidal lines": An algebraic curve of the 4th degree, a conchoid is a plane curve generated by a line rotating about a fixed point crossing a fixed line not containing the fixed point. With the instrument he constructed to describe this line, Nicomedes succeeded in devising a mechanical solution to the problem of the trisection of the angle, by the use of an "inclination" or "verging", that is, a straight section so placed that having passed though a given point on one line it is intercepted at a given length by another line.

Nicomedes also worked on the problem of the duplication of the cube, that is, the geometric solution of the cubic equation x³ = 2a³ (the Delian problem). He solved it by construction, using his conchoidal line.