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Simplifying Radicals

Simplifying Radicals
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2013-08-01 08:12
TrigonometryCoordinate GeometryGeometric Construction
In collections Regular Polygons
This example demonstrates how radicals can be simplified when points appear on the diagonal. It involves core math concepts like radical simplification, geometric construction, and analytical geometry. GeoGebra commands/objects used include Intersect, Circle, OrthogonalLine, Polygon, Segment, Midpoint, and Point. Suitable for high school students and teachers to understand the relationship between radical simplification and geometric figures.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, height) → c
  3. Circle(A, base) → d
  4. OrthogonalLine(A, xAxis) → e
  5. OrthogonalLine(A, e) → f
  6. Intersect(d, f, 1) → B
  7. OrthogonalLine(B, f) → g
  8. Circle(B, height) → h
  9. Intersect(h, g) → C, D
  10. OrthogonalLine(C, g) → i
  11. Intersect(c, i) → E,
  12. Polygon(A, B, C, E) → poly1, a_1, b_1, c_1, e_1
  13. Segment(A, C) → j
  14. Midpoint(j) → F
  15. Intersect(a, j) → K
  16. Intersect(b, j) → L
  17. Intersect(j, k) → M
  18. Intersect(l, j) → N
  19. Intersect(j, m) → O
  20. Intersect(n, j) → P
  21. Intersect(p, j) → Q
  22. Intersect(q, j) → R
  23. Intersect(r, j) → S
  24. Polygon(T, U, V, W) → poly2, t_1, u, v, w
  25. Polygon(Z, A_1, B_1, C_1) → poly3, z, a_2, b_2, c_2
  26. Polygon(D_1, E_1, F_1, G_1) → poly4, d_1, e_2, f_1, g_1
  27. Polygon(H_1, I_1, J_1, K_1) → poly5, h_1, i_1, j_1, k_1
  28. Point(xAxis) → N_1
  29. Polygon(O_1, P_1, Q_1, R_1) → poly6, o_1, p_1, q_1, r_1
  30. Intersect(c_2, z) → S_1
  31. Intersect(b_2, a_2) → T_1
  32. Segment(S_1, T_1) → l_1
  33. Intersect(g_1, f_1) → U_1
  34. Intersect(e_2, d_1) → V_1
  35. Segment(U_1, V_1) → m_1
  36. Intersect(i_1, h_1) → W_1
  37. Intersect(k_1, j_1) → Z_1
  38. Segment(W_1, Z_1) → n_1
  39. Intersect(p_1, o_1) → A_2
  40. Point(r_1) → B_2
  41. Segment(A_2, B_2) → s_1

AI Drawing Prompt Reference

Draw a coordinate system with two perpendicular lines as axes. Create two circles centered at the origin with different radii, intersecting the axes. Draw tangents from the origin to these circles, and connect the intersection points to form a quadrilateral. Then, find the midpoints of the diagonals and connect them to the vertices, creating smaller quadrilaterals and triangles. Finally, connect some vertices to form pentagons and hexagons.
The prompt above was compiled from the original drawing commands and is for reference only.