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Number of Pythagorean triples with even side a

Number of Pythagorean triples with even side a
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2019-06-09 12:09
TriangleFunctionCoordinate GeometryGeometric ConstructionSlider Animation
This example demonstrates the number of Pythagorean triples (a,b,c) where side a is even, exploring patterns and properties. Key math concepts include Pythagorean Theorem, integer properties, factorization, and number theory. GeoGebra commands used are DivisorsList, Factors, Length, Element, Intersect, Polygon, InscribeCircle, Incentre, and Segment. Suitable for high school mathematics education, focusing on the intersection of geometry and number theory.

GeoGebra Commands & Parameters

  1. DivisorsList((a / 2)^(2)) → dl
  2. Factors((a / 2)^(2)) →
  3. Length(dl) → N_d
  4. Element(dl, i) → d_i
  5. Intersect(xAxis, yAxis) → C
  6. Polygon(A, B, C) → t1, c_1, a_1, b_1
  7. InscribeCicle(A, C, B) → e
  8. Incentre(A, C, B) → D
  9. Intersect(e, b_1, 1) → E
  10. Segment(E, D) → r