Exercise 1: Why Correct Triples Aren't the Same as a Proof — Possible Solution
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Plimpton 322 lists 15 real, correct numerical examples that satisfy the
Pythagorean relationship (a^2 + b^2 = c^2 for the three sides of a right
triangle). Each row is genuinely a valid instance of the pattern - the
Babylonian scribes clearly knew HOW to generate numbers that fit this
relationship, likely using a systematic method involving reciprocal
number pairs.

But knowing 15 correct examples, however impressive the underlying
generation method, only tells you the relationship holds for THOSE 15
specific triples. It says nothing about whether it holds for every
possible right triangle that could ever exist - including triangles
with irrational, non-integer side lengths that could never appear as
neat rows on a tablet at all.

A general proof of the Pythagorean theorem (the kind Greek geometry
would later supply) would need to show, through pure logical
deduction from agreed starting principles, that a^2 + b^2 = c^2 holds
for EVERY right triangle, without exception, regardless of whether
anyone has ever written down or checked that specific triangle's
numbers. Plimpton 322 provides real instances; it does not provide
that universal, exception-proof guarantee.

ANSWER: Plimpton 322 demonstrates real, working numerical INSTANCES of
the Pythagorean relationship, generated through some systematic
method - but a proof requires a general, logically necessary argument
showing the relationship holds for every possible right triangle, not
just the specific triples someone happened to compute and record.

WHY THIS WORKS AS AN ANSWER
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This correctly identifies the real gap between "known correct
examples" and "a universal guarantee," which is exactly the
distinction Chapter 1 draws between the tablet's real content and what
a general proof would actually require.