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Golden Mean, Music Scale, Quadratic Equation

Golden Mean, Music Scale, Quadratic Equation
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2018-10-26 12:06
Coordinate Geometry
This example demonstrates the manifestation of the Golden Mean in music scales and quadratic equations, revealing the intrinsic connection between mathematics and art. Core concepts include the Golden Mean, mathematical expressions of music scales, and geometric solutions of quadratic equations. GeoGebra commands and objects used in construction include Intersect, Point, Segment, Rotate, Circle, Polygon, and Line. Suitable for high school students and above, as well as enthusiasts and researchers in music theory, exploring the application of mathematics in artistic fields.

GeoGebra Commands & Parameters

  1. Intersect(f, xAxis, 2) → E
  2. Intersect(f, xAxis, 1) → D
  3. Point(xAxis) → A
  4. Intersect(xAxis, yAxis) → G
  5. Point(xAxis) → J
  6. Segment(A, E) → a
  7. Intersect(f, j, 1) → H_1
  8. Rotate(E, 45°, A) → P
  9. Circle(A, E) → c
  10. Polygon(E, P, 8) → poly2, h, H, O, Q, R, U, k, t, d, e, f_1, g_1, h_1, F
  11. Intersect(g, k_1, 1) → B
  12. Circle(N, 1) → p
  13. Point(p) → C
  14. Line(C, xAxis) → s
  15. Circle(C, 1) → c_1
  16. Intersect(c_1, s, 2) → I
  17. Polygon(I, E, 5) → poly1, l, m, n, q, r, K, L, M
  18. Segment(N, E) → g_2
  19. Segment(E, B) → i_1
  20. Intersect(i, l_1) → S
  21. Segment(S, B) → m_1
  22. Segment(N, S) → n_1