What does cyclotomic mean?
Cyclotomic is a technical adjective from mathematics, describing anything concerned with dividing a circle into equal parts. The term derives from the Greek kyklos (circle) and tomos (a cutting), so it literally means 'circle-cutting.' In modern usage it appears chiefly in number theory and abstract algebra: the cyclotomic polynomials are special integer polynomials whose roots are the complex roots of unity, and cyclotomic fields are number fields built from those roots. These objects are central to classical problems — such as determining which regular polygons can be constructed with compass and straightedge — as well as to modern research in algebraic number theory and cryptography. Because it is a specialist term, cyclotomic carries no everyday connotations; its register is strictly formal and scholarly. For readers interested in the history of mathematics, however, it is a gateway word, marking the point where ancient Greek geometry meets nineteenth-century algebra.
adjectiveRelating to the division of a circle into equal parts; in mathematics, describing polynomials, fields, or extensions connected with the roots of unity obtained by dividing the circle in this way.
- Relating to the division of a circle into equal parts by inscribed regular polygons.
- (Mathematics) Relating to cyclotomic polynomials, cyclotomic fields, or other structures arising from roots of unity.
"The fifth cyclotomic polynomial factors elegantly over the field of complex numbers."
"Euler's work on the division of the circle laid the groundwork for the modern theory of cyclotomic equations."
"She spent her doctoral years studying the Galois group of a cyclotomic field."
Gauss was so proud of proving that a regular 17-sided polygon could be constructed with compass and straightedge — a result rooted in cyclotomic theory — that he reportedly asked for one carved on his tombstone.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of cyclotomic
The word cyclotomic comes from the Greek kyklos, meaning 'circle', and tomos, meaning 'a cutting' or 'slice' — so it literally means 'circle-cutting.' It entered European mathematical vocabulary in the early nineteenth century, when mathematicians such as Gauss studied the division of the circle into equal arcs through roots of unity. The same root tomos gives English cognates such as anatomy, atom, and entropy's sibling term 'entomology' shares only the suffix pattern, but anatomy and atom are true relatives via Greek cutting/slicing terminology.
Related word forms
How cyclotomic is actually used
A technical term used almost exclusively in higher mathematics, particularly number theory and algebra. Outside academic writing it is rare enough that even educated general readers may not know it.
Easily confused with cyclotomic
Cyclothymic refers to a mild form of bipolar mood disorder (alternating elation and depression), whereas cyclotomic is a purely mathematical term about circle division and roots of unity.