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Division Introduction

Division Introduction
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2017-11-24 16:42
FunctionDerivativeGeometric Construction
This example visually demonstrates the basic concept of division. It involves key mathematical concepts such as division, line segments, and derivatives. Using GeoGebra commands like Circle, Sequence, and Zip, the process of division is dynamically illustrated. Suitable for middle school and above students to learn division and related mathematical concepts.

GeoGebra Commands & Parameters

  1. Circle((0, 0), 1) → c
  2. Sequence(Point[{cos(((i * 2) * π / 10)), sin(((i * 2) * π / 10))}], i, 0, 9) → list1
  3. Zip(Segment[(0, 0), A], A, list1) → list2
  4. Sequence(Point[{cos(((i * 2) * π / 100)), sin(((i * 2) * π / 100))}], i, 0, 99) → list3
  5. Sequence(Point[{(0.9 * cos(((i * 2) * π / 100))), (0.9 * sin(((i * 2) * π / 100)))}], i, 0, 99) → list4
  6. Zip(Segment[A, B], A, list3, B, list4) → list5
  7. Point(list3) → A
  8. Point(list3) → B
  9. Sector(c, A, B) → d
  10. Sequence(Point[{cos(((i * 2) * π / 10) + π / 10), sin(((i * 2) * π / 10) + π / 10)}], i, 0, 9) → list6
  11. Zip(Segment[A, (0.85 * A)], A, list6) → list7
  12. Polygon((1.5, -1), (3.5, -1), 4) → squareOutline
  13. Remove(Flatten[Sequence[Sequence[Point[{i, j}], j, -1, 1, 0.2], i, 1.7, 3.5, 0.2]], {(3.5, 1)}) → squarePoints
  14. Mod(100 - (IndexOf[A, list3] - IndexOf[B, list3]), 100) → circleSize
  15. Point(squarePoints) → C
  16. Vertex(squareOutline) → D, E, F, G
  17. Segment(G, F) → f
  18. Segment(F, E) → g
  19. Segment(E, D) → h
  20. Segment(D, G) → i
  21. OrthogonalLine(C, f) → j
  22. OrthogonalLine(C, g) → k
  23. Intersect(j, f) → H
  24. Intersect(k, i) → I
  25. Intersect(j, h) → J
  26. OrthogonalLine(K, k) → l
  27. Intersect(k, l) → L
  28. Flatten(Sequence[Sequence[Point[{i, j}], j, -1, 0.8, 0.2], i, 1.7, 3.5, 0.2]) → backupSquarePoints
  29. Intersect(l, h) → M
  30. Polygon(D, G, K, L, C, J) → poly1, d_1, g_1, k_1, l_1, c_1, j_1
  31. Sequence(Point[{i, -1.5}], i, -1, 3.5 - 0.045, 0.045) → linePoints
  32. Point(linePoints) → N
  33. Segment((-1, -1.5), (3.5, -1.5)) → m
  34. Sequence(Segment[(i, -1.525), (i, -1.475)], i, -1, 3.5, 0.045) → L_2
  35. Vector(N - (0, 0.25), N) → u
  36. Sequence(Segment[(i, -1.55), (i, -1.45)], i, -1 + 0.45 / 2, 3.5, 0.45) → L_3
  37. Sequence(Segment[(i, -1.58), (i, -1.42)], i, -1, 3.5, 0.45) → L_1
  38. Sequence(Segment[(1.5, j), (3.5, j)], j, -0.8, 0.8, 0.2) → L_4
  39. Sequence(Segment[(i, -1), (i, 1)], i, 1.7, 3.3, 0.2) → L_5