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Demonstration of Upper and Lower Sums/Riemann Sum by Martin Flashman

Demonstration of Upper and Lower Sums/Riemann Sum by Martin Flashman
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2017-12-30 10:48
CircleFunctionCalculusGeometric Construction
This example demonstrates how to calculate the upper sum, lower sum, and Riemann sum of a function by constructing rectangles. It involves core mathematical concepts such as upper and lower sums, Riemann sum, similar triangles, correlation, rectangles, and incircle. The construction uses GeoGebra commands/objects like Point, Vector, Textfield, Segment, Line, Derivative, Intersect, Polygon, Sequence. Suitable for high school calculus students to understand the geometric meaning of Riemann integration.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Vector(A, B) → f_2
  3. Textfield(f) → inputBox1
  4. Vector(x_1, y_1) → v
  5. Segment(f_a, F) → c
  6. Segment(E, F) → d
  7. Segment(A, x_1) → e
  8. Segment(B, y_1) → g
  9. Segment(B, y_1) → h
  10. Line(x_1, y_1) → i
  11. Textfield(f) → inputBox2
  12. Derivative(f) → q
  13. Segment(C, D) → b
  14. Segment((0, y(A) - δ), (0, y(A) + δ)) → m
  15. Point(m) → G
  16. Point(m) → H
  17. Point(yAxis) → I
  18. Vector(I, J) → u
  19. Intersect(n, p) → K
  20. Intersect(a, p) → L
  21. Intersect(a, r) → M
  22. Intersect(n, r) → N
  23. Polygon(K, L, M, N) → poly1, k_1, l_1, m_1, n_1
  24. Textfield(ε) → inputBox3
  25. Textfield(δ) → inputBox4
  26. Textfield(f) → InputBox1
  27. Sequence(Vector[(0, xk), (2, f(xk))], xk, y(A) - δ, y(A) + δ, δ / 8) → arrowlist