MathPlotAI Logo MathPlotAI

Exploration 3.5: Interval and Riemann Sum

Exploration 3.5: Interval and Riemann Sum
Loading the math board and drawing, please wait…
2019-07-05 19:51
CalculusIntegralTransformation
In collections Exploring Feyman's Triangle
This example illustrates the concept of intervals and Riemann sums. By constructing geometric transformations and function graphs, users can intuitively understand the calculation method of Riemann sums and their application in integration. Mainly uses Segment, Dilate, Intersect, Polygon, Rotate, etc., GeoGebra commands. Suitable for high school mathematics teaching and learning integration concepts.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(C, B) → g
  3. Segment(A, C) → h
  4. Dilate(C, 1 / 3, A) → C'
  5. Dilate(A, 1 / 3, B) → A'
  6. Dilate(B, 1 / 3, C) → B'
  7. Segment(B, C') → i
  8. Segment(A, B') → j
  9. Segment(A', C) → k
  10. Intersect(k, i) → E
  11. Intersect(j, i) → D
  12. Intersect(k, j) → F
  13. Polygon(B, A, C) → t1, c, b, a
  14. Polygon(E, D, F) → t2, f_1, d, e
  15. Dilate(B, 1 / 2, A) → X
  16. Dilate(A, 1 / 2, C) → Y
  17. Dilate(B, 1 / 2, C) → Z
  18. Polygon(X, E, B) → t3, b_1, x_1, d_1
  19. Polygon(Z, F, C) → t4, c_1, z_1, f_2
  20. Polygon(D, A, Y) → t5, y_1, e_1, a_1
  21. Rotate(X, (-(180°)), X) → X'
  22. Rotate(E, (-(180°)), X) → E'
  23. Rotate(B, (-(180°)), X) → B'_1
  24. Polygon(X', E', B'_1) → t3', b'_1, x', d'
  25. Rotate(D, (-(180°)), Y) → D'
  26. Rotate(A, (-(180°)), Y) → A'_1
  27. Rotate(Y, (-(180°)), Y) → Y'
  28. Polygon(D', A'_1, Y') → t5', y', e', a'_1
  29. Rotate(Z, (-(180°)), Z) → Z'
  30. Rotate(F, (-(180°)), Z) → F'
  31. Rotate(C, (-(180°)), Z) → C'_1
  32. Polygon(Z', F', C'_1) → t4', c'_1, z', f'

AI Drawing Prompt Reference

Draw a triangle formed by three line segments. From each vertex, draw a line segment to the opposite side, creating three smaller triangles. Scale and translate these smaller triangles, then rotate parts of the figure to create overlapping geometric shapes, illustrating the concept of intervals and Riemann sums.
The prompt above was compiled from the original drawing commands and is for reference only.