MathPlotAI Logo MathPlotAI

Exploration of Circle Area

Exploration of Circle Area
Loading the math board and drawing, please wait…
2020-04-01 13:25
CircleFunctionGeometric Construction
This example demonstrates exploring the area of a circle through geometric construction. Key mathematical concepts include the properties of circles and the area formula. Using GeoGebra commands such as Intersect, Point, Segment, and Circle, the example dynamically shows the changes in the area of a circle. Suitable for middle school and above students to learn geometry and area calculation.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Segment(A, C) → f
  4. Circle(B, C) → c
  5. Sequence(Rotate[C, (n * θ), B], n, 1, a) → l1
  6. Segment(B, C) → g
  7. Sequence(Segment[Rotate[B, (n * θ), B], Rotate[C, (n * θ), B]], n, 1, a) → l2
  8. Sequence(Sector[c, ((n - 1) * θ), (n * θ)], n, 1, a) → l3
  9. Sequence(Sector[c, ((n - 1) * θ) + 180°, (n * θ) + 180°], n, 1, a) → l4
  10. Sequence((x(C) + 1 + (n * m), 0), n, 0, a) → l6
  11. Sequence((x(C) + 1 + (n * m) + m / 2, 0), n, 0, a - 1) → l5
  12. Sequence((x(C) + 1 + (n * m) + m / 2, (4 * cos(θ / 2))), n, 0, a - 1) → l7
  13. Sequence((x(C) + 1 + (n * m), (-4 * cos(θ / 2))), n, 1, a) → l9
  14. Sequence(Sector[Circle[(x(C) + 1 + ((n + 1) * m), (-4 * cos(θ / 2))), 4], (x(C) + 1 + ((n + 1) * m) + m / 2, 0), (x(C) + 1 + (n * m) + m / 2, 0)], n, 0, a - 1) → l15
  15. Vector((0, 0), (0, fit)) → u
  16. Translate(l15, u) → l15'
  17. Sequence(Sector[Circle[(x(C) + 1 + (n * m) + m / 2, 0), 4], (x(C) + 1 + (n * m), (-4 * cos(θ / 2))), (x(C) + 1 + ((n + 1) * m), (-4 * cos(θ / 2)))], n, 0, a - 1) → l8
  18. Segment((x(C) + 1, (-4 * cos(θ / 2))), (x(C) + 1 + (a * m), (-4 * cos(θ / 2)))) → h
  19. Segment((x(C) + 1 + m / 2, 0), (x(C) + 1 + m / 2, (-4 * cos(θ / 2)))) → i