Exploring the Area of a Circle by cheredia3

GeoGebra Commands & Parameters

1. Intersect(xAxis, yAxis) → O
2. Segment(E, (x(E) + 4, y(E))) → a
3. Point(a) → F
4. Min((x(F) - x(E)) / (a / 2), 1) → k
5. Point(Segment[(0, 1), (6.28319, 1)]) → H
6. Segment(H, (x(H), 0)) → j
7. Max((x(F) - x(E)) / (a / 2) - 1, 0) → k'
8. CurveCartesian(t - sin(t), 1 - cos(t), t, 0, 6.28319) → b
9. Circle((0, 1), 1) → h
10. Ray((0, 0), (1, 0)) → i
11. Midpoint(a) → J
12. Circle((0, 1), 1) → c_1
13. Segment((0, 0), (6.28319, 0)) → e
14. Segment(G, (x(G), y(G) - 1)) → r
15. CircleArc((0, 1 / (1 - m)), (0, 0), L) → s
16. Sequence((x(O) + sin((i * θ)), y(O) + 1 - cos((i * θ))), i, 0, (2 * n)) → list1
17. Sequence(If[k < 1, (x(O) + ((l * sin((i * φ))) * cos((i * φ)) / sin(φ)), y(O) + ((l * sin((i * φ))) * sin((i * φ)) / sin(φ))), (x(O) + (l * i), y(O))], i, 0, (2 * n)) → list2
18. Rotate((x(O) + 0, y(O) + 1), ((-k) * θ / 2), O) → A
19. Rotate(O, ((-k) * θ / 2), O) → O'
20. Rotate(Element[list1, 1], ((-k) * θ / 2), O) → B
21. Sector(Rotate[Circle[(x(O) + 0, y(O) + 1), O], ((-k) * θ / 2), O], Rotate[O, ((-k) * θ / 2), O], Rotate[Element[list1, 1], ((-k) * θ / 2), O]) → c
22. Rotate((x(O) + 0, y(O) + 1), ((-k) * θ / 2), O) → C
23. Rotate(Element[list1, 1], ((-k) * θ / 2), O) → D
24. Rotate(O, ((-k) * θ / 2), O) → O'_1
25. Arc(Rotate[Circle[(x(O) + 0, y(O) + 1), O], ((-k) * θ / 2), O], O'_1, D) → d
26. Midpoint(j) → I
27. Circle(L, 1 / (1 - m)) → p
28. Circle((0, 0), 1 / (1 - m)) → q
29. Intersect(p, q, 1) → M
30. Sequence(Sector[Rotate[Translate[Circle[(x(O) + 0, y(O) + 1), Element[list1, i]], Vector[Element[list1, i], Element[list2, i]]], (((-((2 * i) - 1)) * k) * θ / 2), Element[list2, i]], Rotate[Translate[Element[list1, i], Vector[Element[list1, i], Element[list2, i]]], (((-((2 * i) - 1)) * k) * θ / 2), Element[list2, i]], Rotate[Translate[Element[list1, i + 1], Vector[Element[list1, i], Element[list2, i]]], (((-((2 * i) - 1)) * k) * θ / 2), Element[list2, i]]], i, 1, n) → list3
31. Sequence(Sector[Rotate[Rotate[Translate[Circle[(x(O) + 0, y(O) + 1), Element[list1, i]], Vector[Element[list1, i], Element[list2, i]]], (((-((2 * i) - 1)) * k) * θ / 2), Element[list2, i]], (180° * k'), (x(O) + (n * l) - sin(θ / 2) / 2, y(O) + cos(θ / 2) / 2)], Rotate[Rotate[Translate[Element[list1, i], Vector[Element[list1, i], Element[list2, i]]], (((-((2 * i) - 1)) * k) * θ / 2), Element[list2, i]], (180° * k'), (x(O) + (n * l) - sin(θ / 2) / 2, y(O) + cos(θ / 2) / 2)], Rotate[Rotate[Translate[Element[list1, i + 1], Vector[Element[list1, i], Element[list2, i]]], (((-((2 * i) - 1)) * k) * θ / 2), Element[list2, i]], (180° * k'), (x(O) + (n * l) - sin(θ / 2) / 2, y(O) + cos(θ / 2) / 2)]], i, n + 1, (2 * n)) → list4
32. Midpoint(e) → N
33. Textfield() → InputBox1
34. Textfield() → InputBox2
35. Point(c_1) → Q
36. Segment(H, Q) → g