Pythagorean Theorem

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What this is? A self‑contained, browser‑only rendition of the Pythagorean Theorem proof by triangle similarity (altitude to hypotenuse). It mirrors the structure of the reference case and includes a silent numeric harness.

  • Answer: states the theorem for legs a,b and hypotenuse c.
  • Reason why: uses similarity to show p=b²/c, q=a²/c, p+q=c and concludes a²+b²=c². Also notes h=(ab)/c and h²=pq.
  • Check: runs many triangles across scales to verify all identities within a tight tolerance.

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Deterministic run (no inputs). Auto‑runs on load.

ARC Output

Answer
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Colored SVG illustrating the Pythagorean theorem A 3–4–5 right triangle with colored squares on each side: red on the vertical leg a (length 3×), blue on the horizontal leg b (length 4×), and green on the hypotenuse c (length 5×). It shows that the combined area of the two small squares equals the big one. b a c b² a² c² a² + b² = c² (Areas add: red + blue = green)
Pythagorean theorem visual: squares on the legs (a, b) match the square on the hypotenuse (c).
Reason why
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Check (harness)
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