MathPlotAI Logo MathPlotAI

Comparing Ratios with a Water Dye Simulation

Comparing Ratios with a Water Dye Simulation
Loading the math board and drawing, please wait…
2023-03-22 02:59
Coordinate GeometryGeometric Construction
This example demonstrates how to use ratios to simulate water dye color mixing. The key mathematical concepts involve proportions and proportion equations, along with geometric principles like similar triangles. Construction uses GeoGebra commands such as Shuffle, Element, and Corner to build the visual representation. It is suitable for students in grades 6-8 to understand proportional reasoning in real-world applications and develop geometric intuition.

GeoGebra Commands & Parameters

  1. Shuffle(Sequence[2, 16] \ {11, 13, 17, 19}) → randomX, {10, 8, 2, 7, 12, 4, 15, 3, 5, 6, 16, 9, 14}
  2. Element(randomX, Mod[countQuestion, Length[randomX]] + 1) → X
  3. Shuffle(KeepIf[Mod[ii, X] ≟ 0 ∨ Mod[X, ii] ≟ 0, ii, Sequence[2, 16] \ {X}]) → randomY, {5, 2}
  4. Element(randomY, 1) → Y
  5. Shuffle(Sequence[6]) → randomColor, {5, 3, 4, 1, 2, 6}
  6. Element(randomColor, Mod[countQuestion, Length[randomColor]] + 1) → color
  7. Corner(5) → AppSize
  8. Shuffle(KeepIf[IsInteger[(ii * Y / X)] ∧ (ii * Y / X) ≤ 20, ii, Sequence[2, 20]]) → randoma, {18, 2, 6, 4, 14, 20, 12, 16, 10, 8}
  9. Segment(Vertex[glass1Base], Vertex[glass1Top]) → glass1Left
  10. Mirror(glass1Left, yAxis) → glass1Right
  11. Translate(glass1Left, displacement) → glass2left
  12. Translate(glass1Right, displacement) → glass2Right
  13. Translate(glass1Base, displacement) → glassBase2
  14. Translate(glass1Top, displacement) → glassTop2
  15. Translate(liquidheight2, displacement) → liquidheight2InPlace
  16. Element(randoma, 1) → a
  17. Polygon({(-1, 0), (1, 0), Intersect[glass1Right, Line[(0, h1), (1, h1)]], Intersect[glass1Left, Line[(0, h1), (1, h1)]]}) → q1
  18. Translate(c, displacement) → c'
  19. Translate(e, displacement) → e'
  20. Polygon({Translate[(-1, 0), displacement], Translate[(1, 0), displacement], Intersect[glass2Right, Line[(0, h2), (1, h2)]], Intersect[glass2left, Line[(0, h2), (1, h2)]]}) → q2
  21. Min(X, Y) → smaller
  22. Polygon({(1, -1.5), (2, -1.5), (2, -0.5), (1, -0.5)}) → q3
  23. Polygon({(2, -1.5), (2, -0.5), (3, -0.5), (3, -1.5)}) → q4
  24. Polygon({(1, -1.5), (1, -0.5), (3, -0.5), (3, -1.5)}) → q5
  25. If(dropCount2 < b, "\text{Too light...}", dropCount2 ≟ b, "\text{Match!}", "\text{Too dark...}") → feedback
  26. Text(feedback, (2, -1.5), true, true, 0, -1) → feedbackPositioned
  27. expandQuad(PulsC1, PulsC2, PulsC3, PulsC4, (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingObject

AI Drawing Prompt Reference

Draw a geometric representation of water dye mixing to demonstrate ratio concepts. Include two glasses with colored liquids, showing proportions through geometric principles and similar triangles. Randomly generate colors and ratios, using shapes to depict liquid heights and relationships, with feedback indicating if the mixture is too light, matches, or is too dark.
The prompt above was compiled from the original drawing commands and is for reference only.