Fraction and Geometric Construction Example

GeoGebra Commands & Parameters

1. Point(yAxis) → C
2. Point(Segment[C + (0, h), C + (0, (1.85 * h))]) → B
3. If(t ≤ 0.5, 0, (2 * (t - 0.5))) → t2
4. If(t ≤ 0.5, (2 * t), 1) → t1
5. Point(Segment[B + (0, h), B + (0, (1.85 * h))]) → A
6. Ray((0, 1.9), (0, 2.9)) → f
7. Polygon({A, A + (l, 0), A + (l, h), A + (0, h)}) → poly1
8. Polygon({B, B + (l, 0), B + (l, h), B + (0, h)}) → poly2
9. Sequence(Segment[A + ((i * l / a1), 0), A + ((i * l / a1), h)], i, 1, a1 - 1) → list1
10. Sequence(Segment[B + ((i * l / a2), 0), B + ((i * l / a2), h)], i, 1, a2 - 1) → list2
11. Polygon({A, A + ((b1 * l / a1), 0), A + ((b1 * l / a1), h), A + (0, h)}) → poly3
12. Polygon({B, B + ((b2 * l / a2), 0), B + ((b2 * l / a2), h), B + (0, h)}) → poly4
13. Sequence(Sequence[Segment[A + ((i * l / a1) + (j * l / ((a1 * c1))), 0), A + ((i * l / a1) + (j * l / ((a1 * c1))), h)], j, 1, c1 - 1], i, 0, a1 - 1) → list3, {{}, {}, {}, {}, {}}
14. Sequence(Sequence[Segment[B + ((i * l / a2) + (j * l / ((a2 * c2))), 0), B + ((i * l / a2) + (j * l / ((a2 * c2))), h)], j, 1, c2 - 1], i, 0, a2 - 1) → list4, {{}, {}, {}, {}}
15. If(a1 ≟ a2, true, false) → equald
16. If(equald ∧ (Div[b1 + b2, a1] > 0 ∨ GCD[b1 + b2, a1] > 1), true, If[Div[(b1 * c1) + (b2 * c2), (a1 * c1)] > 0 ∨ GCD[(b1 * c1) + (b2 * c2), (a1 * c1)] > 1, true, false]) → simplify
17. Textfield(a1) → InputBox1
18. Textfield(b1) → InputBox2
19. Textfield(a2) → InputBox3
20. Textfield(b2) → InputBox4
21. Polygon({A', A' + (l, 0), A' + (l, h), A' + (0, h)}) → poly5
22. Polygon({B', B' + ((b2 / a2 * l), 0), B' + ((b2 / a2 * l), h), B' + (0, h)}) → poly6
23. Polygon({A', A' + ((b1 * l / a1), 0), A' + ((b1 * l / a1), h), A' + (0, h)}) → poly7
24. Polygon({B', B' + ((b2 * l / a2), 0), B' + ((b2 * l / a2), h), B' + (0, h)}) → poly8
25. Sequence(Sequence[Segment[A' + ((i * l / a1) + (j * l / ((a1 * c1))), 0), A' + ((i * l / a1) + (j * l / ((a1 * c1))), h)], j, 1, c1 - 1], i, 0, b1 - 1) → list8, {{}, {}, {}}
26. Sequence(Sequence[Segment[B' + ((i * l / a2) + (j * l / ((a2 * c2))), 0), B' + ((i * l / a2) + (j * l / ((a2 * c2))), h)], j, 1, c2 - 1], i, 0, b2 - 1) → list9, {{}, {}}
27. Segment(C - (0, 0.5), C - (0, 1)) → g
28. Segment(C + ((b1 / a1 * l), -0.5), C + ((b1 / a1 * l), -1)) → i
29. Segment(C + ((b1 / a1 * l) + (b2 / a2 * l), -0.5), C + ((b1 / a1 * l) + (b2 / a2 * l), -1)) → j
30. Vector(Midpoint[g], Midpoint[i]) → u
31. Vector(Midpoint[i], Midpoint[g]) → v
32. Vector(Midpoint[i], Midpoint[j]) → w
33. Vector(Midpoint[j], Midpoint[i]) → a
34. Sequence(Segment[A' + ((i * l / a1), 0), A' + ((i * l / a1), h)], i, 0, b1) → list6
35. Sequence(Segment[B' + ((i * l / a2), 0), B' + ((i * l / a2), h)], i, 0, b2) → list7
36. Sequence(Polygon[{C + ((i * l), 0), C + ((i * l) + l, 0), C + ((i * l) + l, h), C + ((i * l), h)}], i, 1, floor(b1 / a1 + b2 / a2)) → list5
37. Segment(B', B' + ((b2 / a2 * l), 0)) → k
38. Segment(B' + ((b2 / a2 * l), h), B' + (0, h)) → m
39. If(b1 / a1 + b2 / a2 ≥ 1, true, false) → improper
40. FractionText(b1 / a1 + b2 / a2) → text19
41. FractionText(b1 / a1 + b2 / a2 - 1) → text20
42. Sequence(Sequence[Segment[C + ((i * l / ((a1 * c1))) + (j * l), 0), C + ((i * l / ((a1 * c1))) + (j * l), h)], i, 1, (a1 * c1) - 1], j, 0, If[b1 / a1 + b2 / a2 ≤ 1, 0, 1]) → list10, {{1.7579424658632512, 1.7579424658632512, 1.7579424658632512, 1.7579424658632512}, {1.7579424658632512, 1.7579424658632512, 1.7579424658632512, 1.7579424658632512}}
43. GCD((a2 * b1) + (a1 * b2), (a1 * a2)) → jakaja