Word.ws English Dictionary

Ford circle

Ford circle noun: 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).

ford circle: any one of a class of circles with centre at (p/q, 1/(2q²)) and radius 1/(2q²), where p/q is an...
Image: Cmglee, CC BY-SA 3.0, via Wikimedia Commons

Noun

Ford circle (plural Ford circles)

  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).
    • 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.

Examples of Ford circle in a sentence

  • A Farey fraction #92;textstyle#92;frackc defines a Ford circle #92;textstyle#92;mathcal#123;C#125;(k,c) in #92;textstyle#92;mathbbC.2008, Jan Manschot, Partition Functions for Supersymmetric Black Holes, Amsterdam University Press, page 78:
  • In fact, one can check that the Ford circles C#95;#123;a#47;b#125; and C#95;#123;c#47;d#125; are tangent if and only if #92;vertad-bc#92;vert#61;1.2016, Ian Short, Mairi Walker, “Even-Integer Continued Fractions and the Farey Tree”, in Jozef Širáň, Robert Jajcay, editors, Symmetries in...

Forms of Ford circle

pluralFord circles

Origin of Ford circle

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

Questions about Ford circle

What does Ford circle mean?
Ford circle means 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).
How do you use Ford circle in a sentence?
A Farey fraction #92;textstyle#92;frackc defines a Ford circle #92;textstyle#92;mathcal#123;C#125;(k,c) in #92;textstyle#92;mathbbC.
What part of speech is Ford circle?
Ford circle is a noun.
What is the plural of Ford circle?
The plural of Ford circle is Ford circles.

Words near Ford circle in the dictionary

  1. forcurses
  2. forcursing
  3. forcut
  4. ford
  5. Ford and Stoke Prior
  6. Ford circle
  7. Ford circles
  8. Ford City
  9. Ford County
  10. Ford Green
  11. Ford Nation

Source and license

Adapted from Wiktionary: Ford circle (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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Cite this entry: “Ford circle.” Word.ws, https://word.ws/ford_circle. Based on Wiktionary, CC BY-SA 4.0.