MathPlotAI Logo MathPlotAI

Venn Diagram Construction by Steve Phelps

Venn Diagram Construction by Steve Phelps
Loading the math board and drawing, please wait…
2017-01-01 05:42
FunctionCoordinate GeometryGeometric Construction
This example demonstrates how to construct Venn diagrams using GeoGebra, involving set operations, logical relationships, and analytical geometry. Key commands and objects used include Point, Circle, Intersect, Integral, IntegralBetween, Polygon, PolyLine, LaTeX, Random. Suitable for high school and above students to learn about set theory and geometric constructions.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Circle(A, 2) → c
  3. Intersect(c, xAxis, 2) → B
  4. Circle(B, 2) → d
  5. Intersect(c, d, 2) → C
  6. Circle(C, 2) → e
  7. Intersect(c, d, 1) → D
  8. Intersect(d, e, 1) → E
  9. Intersect(c, e, 2) → F
  10. Intersect(c, xAxis, 1) → G
  11. Intersect(d, xAxis, 2) → H
  12. Integral(h, -3, -1) → a
  13. IntegralBetween(h, g, -1, 0) → b
  14. Integral(hh, -3, -2) → i
  15. Integral(p, -2, -1) → j
  16. IntegralBetween(g, p, -1, 0) → k
  17. IntegralBetween(h, p, 0, 1) → l
  18. IntegralBetween(g, h, 0, 1) → m
  19. Integral(g, 1, 3) → n
  20. Integral(gg, 2, 3) → o
  21. Integral(p, 1, 2) → q
  22. IntegralBetween(hh, pp, -2, 0) → r
  23. IntegralBetween(gg, pp, 0, 2) → s
  24. IntegralBetween(p, hh, -2, -1) → t
  25. IntegralBetween(gg, hh, -1, 0) → u
  26. IntegralBetween(hh, gg, 0, 1) → v
  27. IntegralBetween(p, gg, 1, 2) → w
  28. Integral(p, -1, 1) → a_1
  29. Integral(gg, -1, 0) → b_1
  30. Polygon((-4.5, 2.5), (4.5, 2.5), (4.5, -5), (-4.5, -5)) → poly1, f_1, g_1, h_1, i_1
  31. PolyLine((-4.5, 2.5), (4.5, 2.5), (4.5, -5), (-4.5, -5), (-4.5, 2.5)) → j_1
  32. Integral(hh, 0, 1) → ccc
  33. LaTeX("A \cap \left( B' \cup C' \right)") → B1
  34. LaTeX("A \cap C' ") → B2
  35. LaTeX("\left(A \cup B \right) \cap C' ") → B3
  36. LaTeX("A") → B4
  37. LaTeX("A \cap B") → B5
  38. LaTeX("A \cap B \cap C") → B6
  39. LaTeX("A \cap C") → B8
  40. LaTeX("B \cap C") → B9
  41. LaTeX("B \cap \left( A' \cup C' \right)") → B10
  42. LaTeX("C \cap \left( A' \cup B' \right)") → B11
  43. LaTeX("A \cap B \cap C'") → B12
  44. LaTeX("A \cap B' \cap C") → B13
  45. LaTeX("A' \cap B \cap C") → B14
  46. LaTeX("\left( B \cup C \right)' ") → B15
  47. LaTeX("\left( A \cup C \right)' ") → B16
  48. LaTeX("\left( A \cup B \right)' ") → B17
  49. LaTeX("A' ") → B18
  50. LaTeX("B' ") → B19
  51. LaTeX("C' ") → B20
  52. LaTeX("\left(B \cup C \right) \cap A' ") → B21
  53. LaTeX("\left(A \cup C \right) \cap B' ") → B22
  54. LaTeX("\left( A \cup B \cup C \right)' ") → B7
  55. Random(1, 22) → pick

AI Drawing Prompt Reference

Draw a Venn diagram with two intersecting circles to illustrate set operations like intersections and unions. Start by creating two circles with radius 2 that intersect on the x-axis. Then, add several points inside and outside the circles, connecting them with lines to form closed polygonal regions. Finally, include LaTeX formulas around the diagram to label different set operations, such as A∩B, A∪B, etc.
The prompt above was compiled from the original drawing commands and is for reference only.