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Ford Circles

Ford Circles
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2018-11-25 05:48
CircleSequence
This example illustrates the concept of Ford circles, involving fractions and circles. Using GeoGebra commands such as Circle and Sequence, it dynamically demonstrates the construction of multiple circles. Suitable for middle school and above students to learn about fractions and geometric shapes.

GeoGebra Commands & Parameters

  1. Circle((P / Q, 1 / ((2 * Q^(2)))), (P / Q, 0)) → d
  2. FordC(p, q) → e
  3. Sequence(FordC[P + (i * p), Q + (i * q)], i, (-m), m) → L_1
  4. Max((2 * Max[1 / q^(2), 1 / Q^(2)]), abs(p / q - P / Q)) → w

AI Drawing Prompt Reference

Draw a sequence of Ford circles where each circle's center is on the x-axis and its radius is 1 divided by the square of the center's x-coordinate, illustrating the relationship between fractions and circles. Distribute the circle centers evenly from -m to m, color each circle differently, and ensure all circles have a radius no smaller than twice the maximum of the larger value between the square of the reciprocal of the denominators and the square of the reciprocal of Q, and the absolute difference between the current circle's x-coordinate and P/Q.
The prompt above was compiled from the original drawing commands and is for reference only.