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Finding Missing Values in Venn Diagrams

Finding Missing Values in Venn Diagrams
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2023-09-07 22:50
Probability & StatisticsGeometric ConstructionSlider Animation
This example demonstrates how to interpret Venn diagrams involving three sets and calculate the missing value in the figure. Key math concepts include set operations and probability & statistics. Construction highlights the use of GeoGebra commands and objects like Shuffle, Element, If, Sequence, Take, Textfield, Corner, PointToPixels, onboardingTextOffset, Vector, Ellipse, Translate. Suitable for students in grades 6-8 to practice solving problems using Venn diagrams.

GeoGebra Commands & Parameters

  1. Shuffle({1, 2, 3, 4, 5, 6, 7}) → allUnknown, {3, 6, 7, 5, 1, 4, 2}
  2. Shuffle({1, 2, 3}) → allCaseNum, {1, 3, 2}
  3. Element(allUnknown, Mod[countQuestion, Length[allUnknown]] + 1) → currentUnknown
  4. Element(allCaseNum, Mod[countQuestion, Length[allCaseNum]] + 1) → caseNum
  5. If(caseNum ≟ 1, 1823, caseNum ≟ 2, 1094, 492) → h
  6. If(caseNum ≟ 1, 367, caseNum ≟ 2, 1150, 61) → g
  7. If(caseNum ≟ 1, 77, caseNum ≟ 2, 207, 92) → f
  8. If(caseNum ≟ 1, 406, caseNum ≟ 2, 218, 333) → d
  9. If(caseNum ≟ 1, 76, caseNum ≟ 2, 237, 456) → b
  10. If(caseNum ≟ 1, 458, caseNum ≟ 2, 1079, 312) → c
  11. If(caseNum ≟ 1, 362, caseNum ≟ 2, 316, 1788) → a
  12. Sequence(Random[0, 99] / 100, A, 1, 200) → allRandomSeeds, {0.38, 0.45, 0.07, 0.91, 0.74, 0.84, 0.15, 0.22, 0.18, 0, 0.62, 0.55, 0.86, 0.93, 0.81, 0.2, 0.04, 0.43, 0.52, 0.41, 0.01, 0.62, 0.26, 0.4, 0.71, 0.87, 0.44, 0.4, 0.76, 0.6, 0.2, 0.02, 0.14, 0.65, 0.71, 0.58, 0.79, 0.67, 0.84, 0.03, 0.72, 0.67, 0.67, 0.81, 0.41, 0.16, 0.55, 0.83, 0.85, 0.47, 0.53, 0.35, 0.97, 0.99, 0.11, 0.18, 0.5, 0.17, 0.84, 0.9, 0.17, 0.39, 0.8, 0.5, 0.5, 0.45, 0.08, 0.04, 0.88, 0.93, 0.29, 0.14, 0.84, 0.74, 0.91, 0, 0.65, 0.72, 0.9, 0.43, 0.53, 0.36, 0.2, 0.5, 0.99, 0.31, 0.97, 0.33, 0.33, 0.9, 0.56, 0.66, 0.24, 0.4, 0.27, 0.29, 0.42, 0.52, 0.54, 0.21, 0.52, 0.39, 0.05, 0.37, 0.02, 0.58, 0.32, 0.02, 0.13, 0.85, 0.97, 0.34, 0.2, 0.51, 0.3, 0.46, 0.82, 0.89, 0.44, 0.25, 0.79, 0.58, 0.32, 0.12, 0.25, 0.37, 0.2, 0.18, 0.64, 0.15, 0.33, 0.97, 0.79, 0.18, 0.84, 0.4, 0.38, 0.87, 0.28, 0.24, 0.85, 0.83, 0.09, 0.06, 0.49, 0.11, 0.75, 0.91, 0.54, 0.53, 0.65, 0.35, 0.17, 0.16, 0.63, 0.55, 0.01, 0.21, 0.31, 0.46, 0.26, 0.38, 0.45, 0.19, 0.89, 0.2, 0.03, 0.81, 0.19, 0, 0.17, 0.26, 0.97, 0.9, 0.77, 0.98, 0.49, 0.84, 0.14, 0.8, 0.67, 0.39, 0.67, 0.93, 0.35, 0.73, 0.11, 0.41, 0.83, 0.6, 0.4, 0.91, 0.32, 0.88, 0.94, 0.49, 0.39, 0.9, 0.58, 0.58}
  13. Take(allRandomSeeds, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
  14. Textfield(input1) → InputBox1
  15. Textfield(input2) → InputBox2
  16. Corner(5) → layoutAppSize
  17. PointToPixels(Corner[onboardingDisplayText, 2], Corner[1], Corner[3], Corner[5]) → layoutOnboarding
  18. onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], onboardingCase, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset
  19. Vector(A, J) → u
  20. Vector(A, T) → v
  21. Ellipse(A, B, C) → co
  22. Translate(co, v) → mo
  23. Translate(co, u) → lu

AI Drawing Prompt Reference

Draw a Venn diagram with three ellipses to represent three sets. The diagram includes other parts obtained by translation and scaling to simulate set intersections. The construction order is: first create a list of random seeds, then select one random seed, then draw the base ellipse, then translate and scale it to get other ellipses, and finally combine them into a complete Venn diagram structure.
The prompt above was compiled from the original drawing commands and is for reference only.