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Number of Pythagorean triples with odd side a

Number of Pythagorean triples with odd side a
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2019-06-09 11:53
TriangleFunctionTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates how to visualize and calculate the number of Pythagorean triples (a,b,c) where side a is odd. Key math concepts include the Pythagorean theorem, factorization, and parity analysis in number theory. GeoGebra commands and objects used are DivisorsList, Factors, Element, Length, Polygon, InscribeCicle, Incentre, Intersect, Segment. Suitable for high school mathematics education, illustrating the application of number theory with geometry.

GeoGebra Commands & Parameters

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

AI Drawing Prompt Reference

Draw a right triangle with one side of odd length and display its incircle and radius. First, calculate all divisors of the square of the odd side length, then use these divisors to construct multiple right triangles with different side lengths. For each triangle, draw its incircle, find the intersection point of the incircle with one side of the triangle, and connect this point to the center of the incircle to form the radius.
The prompt above was compiled from the original drawing commands and is for reference only.