MathPlotAI Logo MathPlotAI

Which Rectangle is Largest?

Which Rectangle is Largest?
Loading the math board and drawing, please wait…
2023-03-03 00:09
FunctionCoordinate GeometryOptimization
This example demonstrates exploring the area change of rectangles through parallel translations, involving core math concepts like quadratic functions, translations, limits, set theory, 3D vectors, and rational numbers. It uses commands such as Point, Segment, Sequence, Polygon, Sum, First, If for construction, suitable for high school mathematics teaching on quadratic function transformations and optimization.

GeoGebra Commands & Parameters

  1. Point(xAxis) → P
  2. Segment(O, P) → Laufsteg
  3. Point(Laufsteg) → Zug
  4. Point(yAxis) → Q
  5. Sequence((k * x(P) / n), k, 0, n) → xWertetabelle, {0, 0.6, 1.2, 1.7999999999999998, 2.4, 3, 3.5999999999999996, 4.2, 4.8, 5.3999999999999995, 6}
  6. Polygon(Zug, B, C, O) → Rechteck, a, b, c, o
  7. Sequence((Element[xWertetabelle, k], (Element[xWertetabelle, k] * g(Element[xWertetabelle, k]))), k, 1, n + 1) → Punktetabelle
  8. Sum(Aktuell) → m
  9. First(Punktetabelle, m) → TeilPunktetabelle
  10. Sequence(g((k * x(P) / n)), k, 0, n) → yWertetabelle, {5, 4.5, 4, 3.5, 3, 2.5, 2, 1.4999999999999996, 1, 0.5, 0}
  11. If(x(Zug) > Element[xWertetabelle, 2], "" + (Element[xWertetabelle, 2]), "") → A2
  12. If(x(Zug) > Element[xWertetabelle, 1], "" + (Element[xWertetabelle, 1]), "") → A1
  13. If(x(Zug) > Element[xWertetabelle, 3], "" + (Element[xWertetabelle, 3]), "") → A3
  14. If(x(Zug) > Element[xWertetabelle, 4], "" + (Element[xWertetabelle, 4]), "") → A4
  15. If(x(Zug) > Element[xWertetabelle, 5], "" + (Element[xWertetabelle, 5]), "") → A5
  16. If(x(Zug) > Element[xWertetabelle, 1], "" + (y(Element[Punktetabelle, 1])), "") → C1
  17. If(x(Zug) > Element[xWertetabelle, 2], "" + (y(Element[Punktetabelle, 2])), "") → C2
  18. If(x(Zug) > Element[xWertetabelle, 3], "" + (y(Element[Punktetabelle, 3])), "") → C3
  19. If(x(Zug) > Element[xWertetabelle, 4], "" + (y(Element[Punktetabelle, 4])), "") → C4
  20. If(x(Zug) > Element[xWertetabelle, 5], "" + (y(Element[Punktetabelle, 5])), "") → C5
  21. If(x(Zug) > Element[xWertetabelle, 6], "" + (y(Element[Punktetabelle, 6])), "") → C6
  22. If(x(Zug) > Element[xWertetabelle, 7], "" + (y(Element[Punktetabelle, 7])), "") → C7
  23. If(x(Zug) > Element[xWertetabelle, 8], "" + (y(Element[Punktetabelle, 8])), "") → C8
  24. If(x(Zug) > Element[xWertetabelle, 9], "" + (y(Element[Punktetabelle, 9])), "") → C9
  25. If(x(Zug) > Element[xWertetabelle, 10], "" + (y(Element[Punktetabelle, 10])), "") → C10
  26. If(x(Zug) > Element[xWertetabelle, 11], "" + (y(Element[Punktetabelle, 11])), "") → C11
  27. If(x(Zug) > Element[xWertetabelle, 6], "" + (Element[xWertetabelle, 6]), "") → A6
  28. If(x(Zug) > Element[xWertetabelle, 7], "" + (Element[xWertetabelle, 7]), "") → A7
  29. If(x(Zug) > Element[xWertetabelle, 8], "" + (Element[xWertetabelle, 8]), "") → A8
  30. If(x(Zug) > Element[xWertetabelle, 9], "" + (Element[xWertetabelle, 9]), "") → A9
  31. If(x(Zug) > Element[xWertetabelle, 10], "" + (Element[xWertetabelle, 10]), "") → A10
  32. If(x(Zug) > Element[xWertetabelle, 11], "" + (Element[xWertetabelle, 11]), "") → A11
  33. If(x(Zug) > Element[xWertetabelle, 1], "" + (Element[yWertetabelle, 1]), "") → B1
  34. If(x(Zug) > Element[xWertetabelle, 2], "" + (Element[yWertetabelle, 2]), "") → B2
  35. If(x(Zug) > Element[xWertetabelle, 3], "" + (Element[yWertetabelle, 3]), "") → B3
  36. If(x(Zug) > Element[xWertetabelle, 4], "" + (Element[yWertetabelle, 4]), "") → B4
  37. If(x(Zug) > Element[xWertetabelle, 5], "" + (Element[yWertetabelle, 5]), "") → B5
  38. If(x(Zug) > Element[xWertetabelle, 6], "" + (Element[yWertetabelle, 6]), "") → B6
  39. If(x(Zug) > Element[xWertetabelle, 7], "" + (Element[yWertetabelle, 7]), "") → B7
  40. If(x(Zug) > Element[xWertetabelle, 8], "" + (Element[yWertetabelle, 8]), "") → B8
  41. If(x(Zug) > Element[xWertetabelle, 9], "" + (Element[yWertetabelle, 9]), "") → B9
  42. If(x(Zug) > Element[xWertetabelle, 10], "" + (Element[yWertetabelle, 10]), "") → B10
  43. If(x(Zug) > Element[xWertetabelle, 11], "" + (Element[yWertetabelle, 11]), "") → B11
  44. If(x(Zug) > xA_{frueher}, true, false) → Vorwärts

AI Drawing Prompt Reference

Draw a rectangular grid where rectangles start from the origin, with width along the x-axis and height along the y-axis, and area equal to width times height. By parallel translation, rectangles can be moved along the x-axis or y-axis to show area changes. The figure includes a coordinate system, rectangle points, area calculation points, and a series of marked points to identify rectangles of different sizes. The construction order is to first establish the coordinate system and initial rectangle, then generate a series of translated rectangles, and finally mark key points to display area relationships.
The prompt above was compiled from the original drawing commands and is for reference only.