Any four consecutive terms of a Fibonacci-style sequence form a Pythagorean Triple
Created by Inder J. Taneja
For four consecutive terms Gₙ, Gₙ₊₁, Gₙ₊₂, Gₙ₊₃ of any sequence obeying Gₙ₊₂ = Gₙ₊₁ + Gₙ, the following triple is constructed:a = Gₙ·Gₙ₊₃, b = 2·Gₙ₊₁·Gₙ₊₂, c = Gₙ₊₁² + Gₙ₊₂², and it always satisfies a² + b² = c².
Sequence:
Fibonacci Sequence Values
The raw terms of the sequence itself — independent of whichever n the Pythagorean triple below uses
Relations with Pythagorean Triples
Single n
Interval
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Fibonacci sequence windowMove n—the four values and graph change together
Fibonacci spiral · caracolThe same four values travel through the golden spiral
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Corresponding Pythagorean triangleThe triangle is redrawn from a, b and c
Uses exact big-integer arithmetic, so this stays exact even for large n (terms grow fast — by n≈300 they have 60+ digits).
Every n in the range yields exactly one triple, and no two values of n ever produce the same triple — so the count below is exact.
Builds a plain-text file listing the Fibonacci quadruple and the verified equation for every n in the range.