Modular Multiplication Wheel Constructs Curves

Modular Multiplication Wheel Constructs Curves
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2016-01-15 04:26
This example demonstrates how a modular multiplication wheel mysteriously constructs curves like the cardioid and nephroid. It involves core math concepts: modular multiplication, equations, logarithms, translation, random variables, and similarity transformations. The construction uses GeoGebra commands like Sequence with objects n, list1, a, speed, list2, c. Suitable for high school and above, exploring parametric equations and locus generation dynamically.

GeoGebra Commands & Parameters

  1. Sequence((cos(((k * 2) * π / n)), sin(((k * 2) * π / n))), k, 0, n - 1) → list1
  2. Sequence(Segment[Element[list1, k], Element[list1, Mod[(a * k) - 1, n] + 1]], k, 1, n) → list2