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Sankagu13 Math Example

Sankagu13 Math Example
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2019-08-12 14:42
TrigonometrySequenceSolid GeometryOptimizationParametric Equation
This example demonstrates how to construct complex geometric figures and mathematical objects using GeoGebra. The core math concepts involved include sequences, solid geometry, linear programming, parametric equations, and trigonometry. Key construction points involve commands like CurveCartesian, Join, Sort, Circle, Sequence, and objects such as a, f, g, M_n, b, T_n, N, n, O_{1} to O_{7}, Numel, modulo13, L, PIE, shift, c, d, l1, l2. Suitable for high school and above mathematics learning and exploration.

GeoGebra Commands & Parameters

  1. CurveCartesian(M_n(t) + t, (-1 / f'(t) * M_n(t)) + f(t), t, 0, π / 2) → b
  2. Join({{0, 0, 0, 0, 0, 0, 0}, Sequence[Element[L, modulo13(t)], t, 1, n]}) → PIE
  3. Sort(Join[{Sequence[g(t), t, 1, n], Sequence[g(t), t, 1, n], Sequence[g(t), t, 1, n], Sequence[g(t), t, 1, n], Sequence[g(t), t, 1, n], Sequence[g(t), t, 1, n], Sequence[floor(n / 2)], {0, 0, 0, 0, 0, 0, 0}}]) → shift
  4. Circle(((Element[shift, n] * π) + (((-1)^(Element[PIE, n]), 0) * Element[O_n, Element[Numel, modulo13(n)]]), (Element[O_n, Element[Numel, modulo13(n)]] * (0, (-1)^(Element[shift, n])))), (Element[O_n, Element[Numel, modulo13(n)]] * (0, 1))) → c
  5. Circle(((Element[shift, n] * π) + (((-1)^(Element[PIE, n]), 0) * Element[O_n, Element[Numel, modulo13(n)]]), (Element[O_n, Element[Numel, modulo13(n)]] * (0, (-1)^(Element[shift, n])))), (Element[O_n, Element[Numel, modulo13(n)]] * (0, 1))) → d
  6. Sequence(Circle[O_n(t), (O_n(t) * (0, 1))], t, 1, n) → l1
  7. Sequence(Circle[((Element[shift, t] * π) + (((-1)^(Element[PIE, t]), 0) * Element[O_n, Element[Numel, modulo13(t)]]), (Element[O_n, Element[Numel, modulo13(t)]] * (0, (-1)^(Element[shift, t])))), (Element[O_n, Element[Numel, modulo13(t)]] * (0, 1))], t, 1, n) → l2