Number & MeasureGreek → English
Cyclotomic
/ˌsaɪkləˈtɒmɪk/adjective
Relating to the division of a circle into equal parts, and to the polynomials whose roots are the roots of unity.
The Greek roots
κύκλος
kýklos
circle, wheel
τομή
tomḗ
a cutting
Literally: “circle-cutting”
The story of the word
The name is geometry describing algebra: the complex solutions of x to the n equals one sit at equal spacings around the unit circle, cutting it into n arcs. Gauss proved at nineteen that a regular seventeen-sided polygon can be drawn with ruler and compasses, and the theory of cyclotomic fields grew out of that result. The τομή half also cuts through anatomy, dichotomy and the atom, the thing once thought uncuttable.
- How it travelled
- Ancient Greek → mathematical coinage → English
- First recorded
- 19th century
Same family
cyclonedichotomyanatomyatomencyclopedia
In a sentence
The proof reduces to showing the cyclotomic polynomial is irreducible over the rationals.