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Körperix Robot: Random Geometry & Difference Quotient Generator

Körperix Robot: Random Geometry & Difference Quotient Generator
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2024-09-05 16:16
FunctionSolid GeometrySlider AnimationGraphing
In collections Rauminhalt zusammengesetzter Körper - Quader und Würfel
This interactive GeoGebra example demonstrates a robot named 'Körperix' that generates random math problems through variable manipulation. Core mathematical concepts include: ①construction and volume calculation of solid figures (cubes, cuboids); ②coordinate representation of rectangles and polygons; ③numerical calculation of difference quotients and slopes; ④random sampling from normal distribution. Construction uses Sequence and Shuffle for generating random question lists, Point/Vector/Translate for geometric transformations, Dilate for scaling, Polygon/Rectangle for object creation, and dy/dx calculation for slope (difference quotient). Suitable for middle to high school mathematics, demonstrating variable applications in geometry, intuitive understanding of function slopes, and interactive random problem generation in probability & statistics.

GeoGebra Commands & Parameters

  1. Vector(pointVec) → vec
  2. Textfield(input1) → InputBox1
  3. Textfield(input2) → InputBox2
  4. Defined((input1 * input2)) → fixed
  5. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {4, 4, 5, 10, 6, 4, 7, 9, 2, 9, 9, 8, 4, 10, 4, 3, 4, 1, 9, 1, 8, 3, 3, 10, 9, 0, 4, 6, 4, 7, 10, 2, 3, 2, 1, 0, 5, 10, 3, 2, 5, 10, 4, 8, 0, 1, 2, 3, 1, 4, 8, 1, 9, 9, 2, 4, 5, 0, 6, 7, 9, 3, 2, 1, 8, 2, 2, 6, 3, 2, 4, 6, 10, 3, 5, 4, 2, 2, 6, 7, 3, 2, 9, 7, 5, 5, 3, 10, 0, 9, 2, 4, 9, 1, 5, 1, 9, 1, 2, 3}
  6. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  7. Translate(object01L0BG1, vec) → object01L0BG1'
  8. Sequence(Segment[Vertex[object01L0BG1(1), i], Vertex[object01L0BG1'(1), i]], i, 1, 10) → object01L1Lines
  9. RemoveUndefined(Sequence[If[i ∈ {2, 3, 4, 5, 6}, object01L1Lines(i)], i, 1, 10]) → object01L2LinesManual
  10. Translate(object02L0BG1, vec) → object02L0BG1'
  11. Sequence(Segment[Vertex[object02L0BG1(1), i], Vertex[object02L0BG1'(1), i]], i, 1, 10) → object02L1Lines
  12. RemoveUndefined(Sequence[If[i ∈ {2, 6, 7, 8}, object02L1Lines(i)], i, 1, 10]) → object02L2LinesManual
  13. Translate(object03L0BG1, vec) → object03L0BG1'
  14. Sequence(Segment[Vertex[object03L0BG1(1), i], Vertex[object03L0BG1'(1), i]], i, 1, 10) → object03L1Lines
  15. Translate(object04L0BG1, vec) → object04L0BG1'
  16. Sequence(Segment[Vertex[object04L0BG1(1), i], Vertex[object04L0BG1'(1), i]], i, 1, 10) → object04L1Lines
  17. RemoveUndefined(Sequence[If[i ∈ {1, 5, 6}, object04L1Lines(i)], i, 1, 10]) → object04L1LinesManual
  18. Translate({Segment[pointObject04P1, pointObject04P6], Segment[pointObject04P6, pointObject04P5]}, vec) → object04L4BGKontur
  19. Translate(object06L0BG1, vec) → object06L0BG1'
  20. Sequence(Segment[Vertex[object06L0BG1(1), i], Vertex[object06L0BG1'(1), i]], i, 1, 10) → object06L1Lines
  21. RemoveUndefined(Sequence[If[i ∈ {1, 3, 4, 5, 7, 8}, object06L1Lines(i)], i, 1, 10]) → object06L1LinesManual
  22. Translate({PolyLine[{pointObject06P3, pointObject06P4, pointObject06P5}], PolyLine[{pointObject06P7, pointObject06P8, pointObject06P1}]}, vec) → object06L4BGKontur
  23. Point(object06L4BGKontur) → pointObject06P9
  24. Point(object06L0BG1) → pointObject06P10
  25. Dilate(listFrame1, 0.97, Midpoint[pointFrame1, pointFrame3]) → listFrame2
  26. Dilate(listFrame1, 1.02, Midpoint[pointFrame1, pointFrame3]) → listFrame3
  27. Join({{Segment[pointObject02P7, pointObject02P4]}, {Segment[pointObject02P7 + vec, pointObject02P4 + vec]}}) → object02HintKontur
  28. Join({{Segment[pointObject02P6, pointObject02P6 + vec]}, {Segment[pointObject02P6 + vec, pointObject02P7 + vec]}, object02L2Kontur3}) → object02HintKonturDashed
  29. RemoveUndefined(Sequence[If[i ∈ {2, 3, 4, 5, 6}, object03L1Lines(i)], i, 1, 10]) → object03L1LinesManual
  30. Sequence(Rotate[Segment[CenterFBRay + (0.5, 0), CenterFBRay + (1, 0)], i°, CenterFBRay], i, 0, 360, 30) → Flashlight
  31. Polygon(pointlips1, pointlips2, pointlips3, pointlips4) → lips, f_1, g_1, h_1, i_1

AI Drawing Prompt Reference

Draw a “robot-style” geometry problem generator on a coordinate plane: build several panel frames from pairs of segment outlines created by translating the same contour by a single vector, so different faces appear as shifted copies; connect/overlay a few contour hint lines to suggest structure along the panel edges; create a flashlight-like beam by rotating a segment around a fixed center through angles over a full turn; add a lips or facial polygon region composed of multiple polygon points; keep all parts consistent with the same translation and slight scaling relationships so the robot panels look coordinated.
The prompt above was compiled from the original drawing commands and is for reference only.