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A1.NRNS.1 - Cube Roots Geometric Demonstration

A1.NRNS.1 - Cube Roots Geometric Demonstration
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2019-07-17 21:53
FunctionSequenceSolid GeometryGeometric ConstructionGraphing
This GeoGebra example demonstrates the concept of cube roots through a three-dimensional cube and associated geometric constructions. It integrates core mathematical ideas such as cube roots, cubes, geometric construction, sequences, and summation concepts (e.g., Riemann sums), while also incorporating hyperbolas and isosceles triangles to bridge algebra and geometry. The construction uses GeoGebra commands including Intersect, Circle, Point, Cube, and Sequence, creating multiple points (A1-A10, B1-B10) and cube faces (faceABCD, faceADHE, etc.) and edges (edgeAD, edgeAB). These elements likely illustrate how cube roots vary with parameters. This resource is suitable for high school or early college students to explore the geometric meaning of cube roots, and can serve as a dynamic tool for inquiry-based learning, deepening understanding of radicals and their geometric representations.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, cbrt(n)) → c
  3. Intersect(c, xAxis, 2) → B
  4. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  5. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  6. Sequence(Segment[A + (i * (0, 0, 1)), B + (i * (0, 0, 1))], i, 1, edgeAB) → list1
  7. Sequence(Segment[A + (i * (0, 1, 0)), E + (i * (0, 1, 0))], i, 1, edgeAB) → list2
  8. Sequence(Segment[A + (i * (1, 0, 0)), E + (i * (1, 0, 0))], i, 1, edgeAB) → list3
  9. Sequence(Segment[A + (i * (0, 1, 0)), B + (i * (0, 1, 0))], i, 1, edgeAB) → list4
  10. Sequence(Segment[A + (i * (1, 0, 0)), D + (i * (1, 0, 0))], i, 1, edgeAB) → list5
  11. Sequence(Segment[A + (i * (0, 0, 1)), D + (i * (0, 0, 1))], i, 1, edgeAB) → list6
  12. Sequence(Segment[D + (i * (0, 0, 1)), C + (i * (0, 0, 1))], i, 1, edgeAB) → list7
  13. Sequence(Segment[D + (i * (1, 0, 0)), H + (i * (1, 0, 0))], i, 1, edgeAB) → list8
  14. Sequence(Segment[B + (i * (0, 0, 1)), C + (i * (0, 0, 1))], i, 1, edgeAB) → list9
  15. Sequence(Segment[B + (i * (0, 1, 0)), F + (i * (0, 1, 0))], i, 1, edgeAB) → list10
  16. Sequence(Segment[E + (i * (0, 1, 0)), F + (i * (0, 1, 0))], i, 1, edgeAB) → list11
  17. Sequence(Segment[E + (i * (1, 0, 0)), H + (i * (1, 0, 0))], i, 1, edgeAB) → list12