![[Image: ford-circle-1.png]](https://mathematicaloddsandends.wordpress.com/wp-content/uploads/2025/11/ford-circle-1.png)
Summary
A Ford circle is a fascinating geometric construction that gives every rational number its own unique circle. For a fraction written in lowest terms, the circle is placed so that it just touches the x-axis at that fraction, with its size determined by the denominator—the larger the denominator, the smaller the circle. One of the most remarkable properties of Ford circles is that no two circles ever overlap: they either touch each other perfectly or remain completely separate.
Closely connected to Farey sequences, continued fractions, and number theory, Ford circles provide a beautiful visual way to explore the relationships between rational numbers, revealing surprising patterns where geometry and arithmetic come together in an elegant and intuitive way.
ARTICLE
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