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Overlapping Circles

Overlapping Circles
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2015-01-30 00:09
CircleSequenceCoordinate Geometry
This example demonstrates a list of overlapping circles with different colors. It involves core math concepts like circles, coordinate geometry, and sequence. The construction uses the Sequence command to generate the list of circles. Suitable for high school mathematics learning, illustrating the combination of sequences and geometric shapes.

GeoGebra Commands & Parameters

  1. Sequence((x - t)^(2) + y^(2) < (1 - t)^(2), t, 0, 1, 0.1) → lista1
  2. Sequence((x - (t * x(A)))^(2) + (y - (t * y(A)))^(2) < (-1 + t)^(2), t, 0, 1, 0.1) → lista2
  3. Sequence((x - (t * x(A)))^(2) + (y + (t * y(A)))^(2) < (-1 + t)^(2), t, 0, 1, 0.1) → lista3
  4. Sequence((x + (t * x(A)))^(2) + (y - (t * y(A)))^(2) < (-1 + t)^(2), t, 0, 1, 0.1) → lista4
  5. Sequence((x + (t * x(A)))^(2) + (y + (t * y(A)))^(2) < (-1 + t)^(2), t, 0, 1, 0.1) → lista5
  6. Sequence((x + t)^(2) + y^(2) < (1 - t)^(2), t, 0, 1, 0.1) → lista6

AI Drawing Prompt Reference

Draw a set of overlapping colored circles generated by a sequence, showing different colors and sizes, with the centers rotating around a common center, and radii changing with position, demonstrating the combination of coordinate geometry and sequences, creating a complex geometric pattern from inner to outer circles.
The prompt above was compiled from the original drawing commands and is for reference only.