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Sharing Juice Glasses

Sharing Juice Glasses
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2018-11-29 00:54
VectorFunctionGeometric Construction
This example demonstrates dynamic juice distribution among multiple glasses using GeoGebra, showcasing geometric transformations and quantitative relationships. Core math concepts include division, unit circle, quadratic functions, 3D vectors, polynomial functions, and symmetry. Construction highlights the use of commands like Polygon, CountIf, and If, creating objects (A_3 to D_2) and locus lines (L series). Suitable for high school mathematics teaching to visualize functions, vectors, and geometric transformations.

GeoGebra Commands & Parameters

  1. Polygon(A_3, B_3, C_3, D_3) → q3, a_2, b_2, c_9, d_2
  2. Polygon(A_2, B_2, C_2, D_2) → q2, a_1, b_1, c_8, d_1
  3. CountIf(IsInRegion[T, q2], T, {L_{v1}, L_{v2}, L_{v3}, L_{v4}, L_{v5}, L_{v6}, L_{v7}}) → vazios_{t2}
  4. CountIf(IsInRegion[T, q3], T, {L_{v1}, L_{v2}, L_{v3}, L_{v4}, L_{v5}, L_{v6}, L_{v7}}) → vazios_{t3}
  5. CountIf(IsInRegion[T, q3], T, {L_{c1}, L_{c2}, L_{c3}, L_{c4}, L_{c5}, L_{c6}, L_{c7}}) → cheios_{t3}
  6. CountIf(IsInRegion[T, q2], T, {L_{c1}, L_{c2}, L_{c3}, L_{c4}, L_{c5}, L_{c6}, L_{c7}}) → cheios_{t2}
  7. CountIf(IsInRegion[T, q3], T, {L_{m1}, L_{m2}, L_{m3}, L_{m4}, L_{m5}, L_{m6}, L_{m7}}) → meios_{t3}
  8. CountIf(IsInRegion[T, q2], T, {L_{m1}, L_{m2}, L_{m3}, L_{m4}, L_{m5}, L_{m6}, L_{m7}}) → meios_{t2}
  9. Polygon(A_1, B_1, C_1, D_1) → q1, a, b, c, d
  10. CountIf(IsInRegion[T, q1], T, {L_{c1}, L_{c2}, L_{c3}, L_{c4}, L_{c5}, L_{c6}, L_{c7}}) → cheios_{t1}
  11. CountIf(IsInRegion[T, q1], T, {L_{m1}, L_{m2}, L_{m3}, L_{m4}, L_{m5}, L_{m6}, L_{m7}}) → meios_{t1}
  12. CountIf(IsInRegion[T, q1], T, {L_{v1}, L_{v2}, L_{v3}, L_{v4}, L_{v5}, L_{v6}, L_{v7}}) → vazios_{t1}
  13. If(cheios_{t1} ≟ 3 ∧ meios_{t1} ≟ 1 ∧ vazios_{t1} ≟ 3 ∧ cheios_{t2} ≟ 3 ∧ meios_{t2} ≟ 1 ∧ vazios_{t2} ≟ 3 ∧ cheios_{t3} ≟ 1 ∧ meios_{t3} ≟ 5 ∧ vazios_{t3} ≟ 1, 1, 0) → s_1
  14. If(IsInRegion[L_{c1}, q1], s_1 ≟ 1) → e
  15. If(cheios_{t1} ≟ 1 ∧ meios_{t1} ≟ 5 ∧ vazios_{t1} ≟ 1 ∧ cheios_{t2} ≟ 3 ∧ meios_{t2} ≟ 1 ∧ vazios_{t2} ≟ 3 ∧ cheios_{t3} ≟ 3 ∧ meios_{t3} ≟ 1 ∧ vazios_{t3} ≟ 3, 1, 0) → s_2
  16. If(cheios_{t1} ≟ 3 ∧ meios_{t1} ≟ 1 ∧ vazios_{t1} ≟ 3 ∧ cheios_{t2} ≟ 1 ∧ meios_{t2} ≟ 5 ∧ vazios_{t2} ≟ 1 ∧ cheios_{t3} ≟ 3 ∧ meios_{t3} ≟ 1 ∧ vazios_{t3} ≟ 3, 1, 0) → s_3
  17. If(cheios_{t1} ≟ 3 ∧ meios_{t1} ≟ 1 ∧ vazios_{t1} ≟ 3 ∧ cheios_{t2} ≟ 2 ∧ meios_{t2} ≟ 3 ∧ vazios_{t2} ≟ 2 ∧ cheios_{t3} ≟ 2 ∧ meios_{t3} ≟ 3 ∧ vazios_{t3} ≟ 2, 1, 0) → s_4
  18. If(cheios_{t1} ≟ 2 ∧ meios_{t1} ≟ 3 ∧ vazios_{t1} ≟ 2 ∧ cheios_{t2} ≟ 3 ∧ meios_{t2} ≟ 1 ∧ vazios_{t2} ≟ 3 ∧ cheios_{t3} ≟ 2 ∧ meios_{t3} ≟ 3 ∧ vazios_{t3} ≟ 2, 1, 0) → s_5
  19. If(cheios_{t1} ≟ 2 ∧ meios_{t1} ≟ 3 ∧ vazios_{t1} ≟ 2 ∧ cheios_{t2} ≟ 2 ∧ meios_{t2} ≟ 3 ∧ vazios_{t2} ≟ 2 ∧ cheios_{t3} ≟ 3 ∧ meios_{t3} ≟ 1 ∧ vazios_{t3} ≟ 3, 1, 0) → s_6

AI Drawing Prompt Reference

Create a dynamic juice distribution visualization using geometric shapes. Draw multiple glasses with different levels of juice (red for full, blue for half-full, green for empty) across three tiers. Use polygons to represent the glasses and lines to indicate the flow of juice. The construction should highlight geometric transformations and symmetry, demonstrating functions, vectors, and their relationships in a visually engaging way suitable for high school mathematics teaching.
The prompt above was compiled from the original drawing commands and is for reference only.