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Defining Multi-Colored Regions with Inequalities

Defining Multi-Colored Regions with Inequalities
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2013-07-23 00:06
Coordinate GeometryInequalityGraphing
This example demonstrates how to define multi-colored regions using inequalities. It involves core math concepts like inequalities, region partitioning, and coordinate geometry. The construction utilizes GeoGebra commands/objects such as a, b, c, d, f, e, g, h, i, j, k, l, m, n, o, p, z, q, r, s, t, u, b_1, c_1, d_1, g_1, v, pulsante1, pulsante2, pulsante3, a_1, f_1, h_1, i_1, l_1, m_1, p_1, q_1, j_1, k_1. Suitable for high school mathematics education to understand the relationship between inequalities and graphical regions.

GeoGebra Commands & Parameters

  1. a(x, y) = (x > 0) ∧ (y > 0)
  2. b(x, y) = (x < 0) ∧ (y > 0)
  3. c(x, y) = (x < 0) ∧ (y < 0)
  4. d(x, y) = (x > 0) ∧ (y < 0)
  5. f(x, y) = x - y > 0
  6. e(x, y) = x + y > 0
  7. g(x, y) = x - y < 0
  8. h(x, y) = x + y < 0
  9. a(x, y) ∧ f(x, y)
  10. b(x, y) ∧ h(x, y)
  11. a(x, y) ∧ g(x, y)
  12. e(x, y) ∧ b(x, y)
  13. c(x, y) ∧ g(x, y)
  14. c(x, y) ∧ f(x, y)
  15. d(x, y) ∧ h(x, y)
  16. d(x, y) ∧ e(x, y)
  17. Numeric z(40.0)
  18. q: x > 3
  19. r: x < -3
  20. s: y > 3
  21. t: y < -3
  22. u(x, y) = (-3 < x) ∧ (x < 3) ∧ (-3 < y) ∧ (y < 3)
  23. b_1(x, y) = 2 * x + 5 + y > 0
  24. c_1(x, y) = 3 * x - 5 - y < 0
  25. d_1(x, y) = 1 / 2 * x + 5 - y > 0
  26. g_1(x, y) = (2 * x + 5 + y > 0) ∧ (3 * x - 5 - y < 0) ∧ (1 / 2 * x + 5 - y > 0)
  27. a(x, y) ∧ b(x, y) ∧ c(x, y) ∧ d(x, y)
  28. a_1: -4 < x < -2
  29. f_1: -8 < x < -6
  30. h_1: 2 < y < 4
  31. i_1: 6 < y < 8
  32. l_1(x, y) = (-8 < x) ∧ (x < -6) ∧ (6 < y) ∧ (y < 8)
  33. m_1(x, y) = (-4 < x) ∧ (x < -2) ∧ (6 < y) ∧ (y < 8)
  34. p_1(x, y) = (-8 < x) ∧ (x < -6) ∧ (2 < y) ∧ (y < 4)
  35. q_1(x, y) = (-4 < x) ∧ (x < -2) ∧ (2 < y) ∧ (y < 4)
  36. j_1: -2 < y < 0
  37. k_1: -6 < y < -4
  38. t_1(x, y) = (-8 < x) ∧ (x < -6) ∧ (-2 < y) ∧ (y < 0)
  39. w: 0 < x < 2
  40. e_1: 4 < x < 6
  41. n_1(x, y) = (6 < y) ∧ (y < 8) ∧ (0 < x) ∧ (x < 2)
  42. o_1(x, y) = (6 < y) ∧ (y < 8) ∧ (4 < x) ∧ (x < 6)
  43. r_1(x, y) = (2 < y) ∧ (y < 4) ∧ (0 < x) ∧ (x < 2)
  44. s_1(x, y) = (2 < y) ∧ (y < 4) ∧ (4 < x) ∧ (x < 6)
  45. u_1(x, y) = (-4 < x) ∧ (x < -2) ∧ (-2 < y) ∧ (y < 0)
  46. v_1(x, y) = (-2 < y) ∧ (y < 0) ∧ (0 < x) ∧ (x < 2)
  47. w_1(x, y) = (-2 < y) ∧ (y < 0) ∧ (4 < x) ∧ (x < 6)
  48. z_1(x, y) = (-8 < x) ∧ (x < -6) ∧ (-6 < y) ∧ (y < -4)
  49. a_2(x, y) = (-4 < x) ∧ (x < -2) ∧ (-6 < y) ∧ (y < -4)
  50. b_2(x, y) = (-6 < y) ∧ (y < -4) ∧ (0 < x) ∧ (x < 2)
  51. c_2(x, y) = (-6 < y) ∧ (y < -4) ∧ (4 < x) ∧ (x < 6)
  52. Point A(1.7805908446546472, 1.2820737971730134)
  53. Point B(-3.219409155345355, 1.2820737971730134)
  54. Point C(-3.219409155345355, 5.2820737971730125)
  55. d_2(x, y) = x + 5 - y < 0
  56. e_2(x, y) = x - 5 - y > 0
  57. f_2(x, y) = (x + 5 - y > 0) ∧ (x - 5 - y < 0)