Phrase guide

Ford circle

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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1

noun

Meaning 1

Any one of a class of circles with centre at (p/q, 1/(2q2)) and radius 1/(2q2), where p/q is an irreducible fraction (i.e., p and q are coprime integers).

Definition source: English Wiktionary via Wiktextract

Topics: geometry, mathematics, sciences

Examples

  • Every Ford circle is tangent to the horizontal axis y#61;0, and any two Ford circles are either disjoint or meet at a tangent.
  • There is a unique Ford circle associated with every rational number. Additionally, the axis y#61;0 can be considered a Ford circle with infinite radius, corresponding to the case p#61;1,#92;q#61;0.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

Named after American mathematician Lester Randolph Ford, Sr., who wrote about them in 1938.

Across languages

Translations

1 source translations are retained for this English entry.

  • German: Ford-Kreis — any of a class of circles, each unique to a rational number and pairwise either tangent to or disjoint from each other circle