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Complete the Triples

Complete the Triples
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2022-01-24 20:47
TriangleCalculusMatrix
This example demonstrates how to generate and verify Pythagorean triples (a, b, c) using GeoGebra, involving core concepts like the Pythagorean Theorem, right triangles, real numbers, matrix operations, curve sketching, interest calculation, and secant lines. Key GeoGebra commands and objects used in the construction include Sequence, Join, RandomElement, Sort, Remove, IndexOf, Point, and Textfield, making it suitable for high school and above mathematics learners exploring geometric and algebraic applications.

GeoGebra Commands & Parameters

  1. Sequence(Sort[{m^(2) - 1^(2), ((2 * m) * 1), m^(2) + 1^(2)}], m, 2, 7) → m1, {{3, 4, 5}, {6, 8, 10}, {8, 15, 17}, {10, 24, 26}, {12, 35, 37}, {14, 48, 50}}
  2. Sequence(Sort[{m^(2) - 2^(2), ((2 * m) * 2), m^(2) + 2^(2)}], m, 3, 6) → m2, {{5, 12, 13}, {12, 16, 20}, {20, 21, 29}, {24, 32, 40}}
  3. Sequence(Sort[{m^(2) - 3^(2), ((2 * m) * 3), m^(2) + 3^(2)}], m, 4, 6) → m3, {{7, 24, 25}, {16, 30, 34}, {27, 36, 45}}
  4. Join({m1, m2, m3}) → m4
  5. RandomElement(m1) → l1, {3, 4, 5}
  6. Sort(Sample[l1, 2]) → l2
  7. Remove(l1, l2) → l3
  8. IndexOf(Element[l3, 1], l1) → a
  9. Point(yAxis) → A
  10. Textfield(ans) → InputBox1

AI Drawing Prompt Reference

Draw a series of Pythagorean triples triangles, including right triangles with sides 3-4-5, 5-12-13, etc. First, generate a sequence with side lengths m^2-1^2, 2*m*1, m^2+1^2, then repeat this process to generate other sequences, merge these sequences, randomly select one Pythagorean triple, then randomly select two numbers from it, remove these two numbers, find the position of the remaining numbers in the original sequence, and finally create a point on the y-axis.
The prompt above was compiled from the original drawing commands and is for reference only.