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Constructing Near 1000

Constructing Near 1000
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2016-04-18 21:10
PolygonCoordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the geometric construction and numerical calculation using polygons to achieve a sum close to 1000. It involves core math concepts like addition, logic operations, natural numbers, integers, dilation, histograms, and prism volumes. Key GeoGebra commands and objects used include Polygon, Segment, If, Mod, Div, and Sequence. Suitable for middle school and above students to learn geometric constructions, numerical computations, and spatial reasoning.

GeoGebra Commands & Parameters

  1. Polygon((0, 0), (0.9, 0), 4) → poly1
  2. Polygon((2, 0), (2.9, 0), 4) → poly3
  3. Polygon((1, 0), (1.9, 0), 4) → poly2
  4. Polygon((0, 1), (0.9, 1), 4) → poly4
  5. Polygon((1, 1), (1.9, 1), 4) → poly5
  6. Polygon((2, 1), (2.9, 1), 4) → poly6
  7. Polygon((0, 2), (0.9, 2), 4) → poly7
  8. Polygon((1, 2), (1.9, 2), 4) → poly8
  9. Polygon((2, 2), (2.9, 2), 4) → poly9
  10. Segment(J, K) → a
  11. If(IsInRegion[A, poly9], 1, If[IsInRegion[B, poly9], 2, If[IsInRegion[C, poly9], 3, If[IsInRegion[D, poly9], 4, If[IsInRegion[E, poly9], 5, If[IsInRegion[F, poly9], 6, If[IsInRegion[G, poly9], 7, If[IsInRegion[H, poly9], 8, If[IsInRegion[I, poly9], 9, 0]]]]]]]]) → nineSum
  12. If(IsInRegion[A, poly8], 1, If[IsInRegion[B, poly8], 2, If[IsInRegion[C, poly8], 3, If[IsInRegion[D, poly8], 4, If[IsInRegion[E, poly8], 5, If[IsInRegion[F, poly8], 6, If[IsInRegion[G, poly8], 7, If[IsInRegion[H, poly8], 8, If[IsInRegion[I, poly8], 9, 0]]]]]]]]) → eightSum
  13. If(IsInRegion[A, poly7], 1, If[IsInRegion[B, poly7], 2, If[IsInRegion[C, poly7], 3, If[IsInRegion[D, poly7], 4, If[IsInRegion[E, poly7], 5, If[IsInRegion[F, poly7], 6, If[IsInRegion[G, poly7], 7, If[IsInRegion[H, poly7], 8, If[IsInRegion[I, poly7], 9, 0]]]]]]]]) → sevenSum
  14. If(IsInRegion[A, poly6], 1, If[IsInRegion[B, poly6], 2, If[IsInRegion[C, poly6], 3, If[IsInRegion[D, poly6], 4, If[IsInRegion[E, poly6], 5, If[IsInRegion[F, poly6], 6, If[IsInRegion[G, poly6], 7, If[IsInRegion[H, poly6], 8, If[IsInRegion[I, poly6], 9, 0]]]]]]]]) → sixSum
  15. If(IsInRegion[A, poly5], 1, If[IsInRegion[B, poly5], 2, If[IsInRegion[C, poly5], 3, If[IsInRegion[D, poly5], 4, If[IsInRegion[E, poly5], 5, If[IsInRegion[F, poly5], 6, If[IsInRegion[G, poly5], 7, If[IsInRegion[H, poly5], 8, If[IsInRegion[I, poly5], 9, 0]]]]]]]]) → fiveSum
  16. If(IsInRegion[A, poly4], 1, If[IsInRegion[B, poly4], 2, If[IsInRegion[C, poly4], 3, If[IsInRegion[D, poly4], 4, If[IsInRegion[E, poly4], 5, If[IsInRegion[F, poly4], 6, If[IsInRegion[G, poly4], 7, If[IsInRegion[H, poly4], 8, If[IsInRegion[I, poly4], 9, 0]]]]]]]]) → fourSum
  17. If(IsInRegion[A, poly3], 1, If[IsInRegion[B, poly3], 2, If[IsInRegion[C, poly3], 3, If[IsInRegion[D, poly3], 4, If[IsInRegion[E, poly3], 5, If[IsInRegion[F, poly3], 6, If[IsInRegion[G, poly3], 7, If[IsInRegion[H, poly3], 8, If[IsInRegion[I, poly3], 9, 0]]]]]]]]) → threeSum
  18. If(IsInRegion[A, poly2], 1, If[IsInRegion[B, poly2], 2, If[IsInRegion[C, poly2], 3, If[IsInRegion[D, poly2], 4, If[IsInRegion[E, poly2], 5, If[IsInRegion[F, poly2], 6, If[IsInRegion[G, poly2], 7, If[IsInRegion[H, poly2], 8, If[IsInRegion[I, poly2], 9, 0]]]]]]]]) → twoSum
  19. If(IsInRegion[A, poly1], 1, If[IsInRegion[B, poly1], 2, If[IsInRegion[C, poly1], 3, If[IsInRegion[D, poly1], 4, If[IsInRegion[E, poly1], 5, If[IsInRegion[F, poly1], 6, If[IsInRegion[G, poly1], 7, If[IsInRegion[H, poly1], 8, If[IsInRegion[I, poly1], 9, 0]]]]]]]]) → oneSum
  20. Mod(onesPlace, 10) → SAone
  21. Mod(tensPlace + Div[onesPlace, 10], 10) → SAten
  22. Mod(Div[tensPlace + Div[onesPlace, 10], 10] + hundredsplace, 10) → SAhund
  23. Div(Div[tensPlace + Div[onesPlace, 10], 10] + hundredsplace, 10) → SAthou
  24. Sequence(Point[{i, 4}], i, -3, 5) → anchors
  25. Div(onesPlace, 10) → SAtensCarry
  26. Div(tensPlace + Div[onesPlace, 10], 10) → SAhundredsCarry
  27. Segment(J - (1, 2.9), K - (0, 2.9)) → d

AI Drawing Prompt Reference

Draw a geometric pattern composed of multiple squares with increasing side lengths, arranged in three rows from left to right. Label numbers 1 to 9 within each square, using different colors or fills. Connect specific points based on the numbers inside the squares to form lines, creating a complex geometric design that illustrates the relationship between numbers and shapes.
The prompt above was compiled from the original drawing commands and is for reference only.