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Pythagorean Hyperbola

Pythagorean Hyperbola
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2016-08-18 07:46
Coordinate GeometryParametric Equation
This example demonstrates the geometric properties of the Pythagorean hyperbola. Key mathematical concepts include the definition and properties of hyperbolas. Using the Translate command to move polygons, the construction process of the hyperbola is illustrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Translate(Polygon[(0, 0), (1, 0), (0, 1)], Vector[(3, 3)]) → poly1
  2. Translate(Polygon[(0, 0), (0, 1), (-1, 1), (-1, 0)], Vector[(3, 3)]) → poly3
  3. Translate(Rotate[Polygon[(1, 0), (1 + sqrt(2), 0), (1 + sqrt(2), sqrt(2)), (1, sqrt(2))], π / 4, (1, 0)], Vector[(3, 3)]) → poly4
  4. Translate(Polygon[(0, 0), (1, 0), (1, -1), (0, -1)], Vector[(3, 3)]) → poly2
  5. Polygon((0, 0), (1, 0), (1, 1), (0, 1)) → poly5, s, t, a, b
  6. Polygon((1, 0), (2, 0), (2, 1), (1, 1)) → poly6, c, d, e, f_1
  7. Polygon((0, 0), (sqrt(2), 0), (sqrt(2), sqrt(2)), (0, sqrt(2))) → poly7, g_1, h_1, i_1, j_1