Nicomedes (mathematician)
Encyclopedia
Ancient Greek
Ancient Greek is the stage of the Greek language in the periods spanning the times c. 9th–6th centuries BC, , c. 5th–4th centuries BC , and the c. 3rd century BC – 6th century AD of ancient Greece and the ancient world; being predated in the 2nd millennium BC by Mycenaean Greek...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
.
Life and work
Almost nothing is known about his life apart from references in his works. We know that he lived around the time of EratosthenesEratosthenes
Eratosthenes of Cyrene was a Greek mathematician, poet, athlete, geographer, astronomer, and music theorist.He was the first person to use the word "geography" and invented the discipline of geography as we understand it...
or after, because he criticized Eratosthenes' method of doubling the cube
Doubling the cube
Doubling the cube is one of the three most famous geometric problems unsolvable by compass and straightedge construction...
. It is also known that Apollonius of Perga
Apollonius of Perga
Apollonius of Perga [Pergaeus] was a Greek geometer and astronomer noted for his writings on conic sections. His innovative methodology and terminology, especially in the field of conics, influenced many later scholars including Ptolemy, Francesco Maurolico, Isaac Newton, and René Descartes...
called a curve of his creation a "sister of the conchoid
Conchoid
Conchoid can refer to:*Conchoid curve, an equation discovered by the mathematician Nicomedes*Conchoidal fracture, a breakage pattern characteristic to certain glasses and crystals...
," suggesting that he was naming it after Nicomedes' already famous curve. Consequently, it is believed that Nicomedes lived after Eratosthenes
Eratosthenes
Eratosthenes of Cyrene was a Greek mathematician, poet, athlete, geographer, astronomer, and music theorist.He was the first person to use the word "geography" and invented the discipline of geography as we understand it...
and before Apollonius of Perga
Apollonius of Perga
Apollonius of Perga [Pergaeus] was a Greek geometer and astronomer noted for his writings on conic sections. His innovative methodology and terminology, especially in the field of conics, influenced many later scholars including Ptolemy, Francesco Maurolico, Isaac Newton, and René Descartes...
.
Like many geometers of the time, Nicomedes was engaged in trying to solve the problems of doubling the cube
Doubling the cube
Doubling the cube is one of the three most famous geometric problems unsolvable by compass and straightedge construction...
and trisecting the angle, both problems we now understand to be impossible using the tools of classical geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
. In the course of his investigations, Nicomedes created the conchoid
Conchoid
Conchoid can refer to:*Conchoid curve, an equation discovered by the mathematician Nicomedes*Conchoidal fracture, a breakage pattern characteristic to certain glasses and crystals...
of Nicomedes; a discovery that is contained in his famous work entitled On conchoid lines. Nicomedes discovered three distinct types of conchoids, but what these conchoids were is unknown. Pappus
Pappus of Alexandria
Pappus of Alexandria was one of the last great Greek mathematicians of Antiquity, known for his Synagoge or Collection , and for Pappus's Theorem in projective geometry...
wrote: "Nicomedes trisected any rectilinear angle by means of the conchoidal curves, the construction, order and properties of which he handed down, being himself the discoverer of their peculiar character.".
Nicomedes also used the Hippias
Hippias
Hippias of Elis was a Greek Sophist, and a contemporary of Socrates. With an assurance characteristic of the later sophists, he claimed to be regarded as an authority on all subjects, and lectured on poetry, grammar, history, politics, mathematics, and much else...
' quadratrix
Quadratrix
In mathematics, a quadratrix is a curve having ordinates which are a measure of the area of another curve. The two most famous curves of this class are those of Dinostratus and E. W...
to square the circle
Squaring the circle
Squaring the circle is a problem proposed by ancient geometers. It is the challenge of constructing a square with the same area as a given circle by using only a finite number of steps with compass and straightedge...
, since according to Pappus, "For the squaring of the circle there was used by Dinostratus, Nicomedes, and certain other later persons a certain curve which took its name from this property, for it is called by them square-forming". Eutocius mentions that Nicomedes "prided himself inordinately on his discovery of this curve, contrasting it with Eratosthenes's mechanism for finding any number of mean proportionals, to which he objected formally and at length on the ground that it was impracticable and entirely outside the spirit of geometry."