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Fraction Division Geometric Demonstration by ericchowyl

Fraction Division Geometric Demonstration by ericchowyl
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2016-10-17 13:59
FunctionTrigonometryCoordinate Geometry
This example demonstrates the concept of fraction division. It involves core mathematical concepts such as fractions and division. Using GeoGebra commands like Segment, Point, Sequence, etc., a geometric model of fraction division is constructed. Suitable for middle school and above students to learn the geometric meaning of fraction division.

GeoGebra Commands & Parameters

  1. Segment(A, (x(A) + 1, y(A))) → l1
  2. Point(Segment[(x(A), y(A)), (x(A) + 1, y(A))]) → P
  3. Segment(B, (x(B) + 1, y(B))) → l2
  4. Point(Segment[(x(B) + 2 / 6, y(B)), (x(B) + 1, y(B))]) → Q
  5. Point(Segment[(x(C) + 1 / 6 - 0.005, y(C)), (x(Q) - 1 / 6, y(C))]) → R
  6. Segment(C, (x(C) + 1, y(C))) → l3
  7. Sequence(Circle[((2.5 * (i - 1)), 0), 1], i, 1, a) → list1
  8. Sequence(Sequence[CircleSector[((f * sin((((2 * k) - 1) * θ / 2))) + (2.5 * (m - 1)), (f * cos((((2 * k) - 1) * θ / 2)))), ((f * sin((((2 * k) - 1) * θ / 2))) + sin((k * θ)) + (2.5 * (m - 1)), (f * cos((((2 * k) - 1) * θ / 2))) + cos((k * θ))), ((f * sin((((2 * k) - 1) * θ / 2))) + sin(((k - 1) * θ)) + (2.5 * (m - 1)), (f * cos((((2 * k) - 1) * θ / 2))) + cos(((k - 1) * θ)))], k, 1, b], m, 1, a) → list4
  9. Sequence(CircleSector[(((-f) * sin((((2 * k) - 1) * θ / 2))) + (2.5 * a), (f * cos((((2 * k) - 1) * θ / 2)))), (((-f) * sin((((2 * k) - 1) * θ / 2))) - sin(((k - 1) * θ)) + (2.5 * a), (f * cos((((2 * k) - 1) * θ / 2))) + cos(((k - 1) * θ))), (((-f) * sin((((2 * k) - 1) * θ / 2))) - sin((k * θ)) + (2.5 * a), (f * cos((((2 * k) - 1) * θ / 2))) + cos((k * θ)))], k, 1, c) → list5
  10. CircleSector(((2.5 * a), 0), ((2.5 * a), 1), ((2.5 * a) - sin((c * θ)), cos((c * θ)))) → s1_1
  11. Sequence(Segment[((2.5 * a), 0), ((2.5 * a) - sin((j * θ)), cos((j * θ)))], j, 1, c - 1) → list2
  12. Sequence(Segment[((2.5 * a), 0), ((2.5 * a) - sin((j * θ)), cos((j * θ)))], j, c + 1, b - 1) → list3
  13. CircleSector(((2.5 * a), 0), ((2.5 * a) - sin((c * θ)), cos((c * θ))), ((2.5 * a), 1)) → s2
  14. Segment(D, (x(D) + 1, y(D))) → l4
  15. Point(Segment[(x(D) + 1 / 5, y(D)), (x(D) + 1, y(D))]) → S
  16. Sequence(Sequence[CircleSector[(((-f) * sin((((2 * k) - 1) * θ / 2))) + (2.5 * (m - 1)), (f * cos((((2 * k) - 1) * θ / 2)))), (((-f) * sin((((2 * k) - 1) * θ / 2))) - sin(((k - 1) * θ)) + (2.5 * (m - 1)), (f * cos((((2 * k) - 1) * θ / 2))) + cos(((k - 1) * θ))), (((-f) * sin((((2 * k) - 1) * θ / 2))) - sin(((k - 1) * θ) + θ / d) + (2.5 * (m - 1)), (f * cos((((2 * k) - 1) * θ / 2))) + cos(((k - 1) * θ) + θ / d))], k, 1, b], m, 1, a) → list6
  17. Sequence(CircleSector[(((-f) * sin((((2 * k) - 1) * θ / 2))) + (2.5 * a), (f * cos((((2 * k) - 1) * θ / 2)))), (((-f) * sin((((2 * k) - 1) * θ / 2))) - sin(((k - 1) * θ)) + (2.5 * a), (f * cos((((2 * k) - 1) * θ / 2))) + cos(((k - 1) * θ))), (((-f) * sin((((2 * k) - 1) * θ / 2))) - sin(((k - 1) * θ) + θ / d) + (2.5 * a), (f * cos((((2 * k) - 1) * θ / 2))) + cos(((k - 1) * θ) + θ / d))], k, 1, c) → list7
  18. Sequence(Sequence[Sequence[Segment[(((-f) * sin((((2 * k) - 1) * θ / 2))) + (2.5 * (m - 1)), (f * cos((((2 * k) - 1) * θ / 2)))), (((-f) * sin((((2 * k) - 1) * θ / 2))) - sin(((k - 1) * θ) + (n * θ / d)) + (2.5 * (m - 1)), (f * cos((((2 * k) - 1) * θ / 2))) + cos(((k - 1) * θ) + (n * θ / d)))], n, 1, d - 1], k, 1, b], m, 1, a) → list8
  19. Sequence(Sequence[Segment[(((-f) * sin((((2 * k) - 1) * θ / 2))) + (2.5 * a), (f * cos((((2 * k) - 1) * θ / 2)))), (((-f) * sin((((2 * k) - 1) * θ / 2))) - sin(((k - 1) * θ) + (n * θ / d)) + (2.5 * a), (f * cos((((2 * k) - 1) * θ / 2))) + cos(((k - 1) * θ) + (n * θ / d)))], n, 1, d - 1], k, 1, c) → list9
  20. Polygon((0.016528925619834656, -3), (1.2165289256198346, -3), (1.2165289256198346, -1.3), (0.016528925619834656, -1.3)) → poly1, e, g, h, i
  21. GCD((a * b) + c - ((floor(((a * b) + c) / ((b * d))) * b) * d), (b * d)) → k
  22. Segment(A, P) → j
  23. Segment(C, R) → l
  24. Segment(B, Q) → m
  25. Segment(D, S) → n

AI Drawing Prompt Reference

Create a geometric model to demonstrate the concept of fraction division. Start by drawing two line segments AB and CD, then mark points P on AB, Q and R on CD. Draw a series of circles and arcs, including circles centered on the x-axis and arcs around the origin. Finally, connect points A and P, C and R, B and Q, and D and S to form the geometric model.
The prompt above was compiled from the original drawing commands and is for reference only.