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SEMCV Calendar Math Problems May 2019 n.1-2

SEMCV Calendar Math Problems May 2019 n.1-2
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2018-12-12 23:15
TrigonometrySolid GeometryGeometric Construction
This example demonstrates the mathematical problems 1-2 from the SEMCV calendar of May 2019, focusing on geometric constructions and property analysis. Key math concepts include rotation, summation, numerical calculations, and trigonometry. Construction highlights involve GeoGebra commands such as Point, Cube, Midpoint, Segment, Sphere, Intersect, Polygon, Pyramid, Centroid, OrthogonalLine, Rotate, Plane, Mirror, Line, Radius, Volume. Suitable for high school students learning solid geometry and trigonometric functions.

GeoGebra Commands & Parameters

  1. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  2. Cube(A, B, C) → a, D, caraCDHG, caraEFGH, arestaAD, arestaAB, arestaBC, arestaCD, arestaAE, arestaDH, arestaEH, arestaEF, E, arestaBF, arestaFG, arestaCG, arestaGH, F, G, H, caraABCD, caraADHE, caraABFE, caraBCGF
  3. Midpoint(arestaAE) → L
  4. Segment(E, L) → f
  5. Point(f) → I
  6. Sphere(E, I) → b
  7. Intersect(arestaEF, b) → J, P
  8. Intersect(arestaEH, b) → K, Q
  9. Polygon(I, J, K) → tri1, k, i, j
  10. Pyramid(tri1, E) → p1, caraEIJ, caraEJK, caraEIK, arestaEI, arestaEJ, arestaEK
  11. Centroid(caraABCD) → M
  12. OrthogonalLine(M, caraABCD) → g
  13. Rotate(p1, π / 2, g) → p2
  14. Rotate(p1, π, g) → p3
  15. Rotate(p1, (3 * π / 2), g) → p4
  16. Plane(L, caraABCD) → d
  17. Mirror(p1, d) → p1'
  18. Mirror(p2, d) → p2'
  19. Mirror(p3, d) → p3'
  20. Mirror(p4, d) → p4'
  21. Midpoint(B, H) → N
  22. Line(E, C) → h
  23. Intersect(h, tri1) → O
  24. Sphere(N, O) → c
  25. Radius(c) → RE
  26. Segment(O, N) → l
  27. Volume(c) → e