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The warning is that teaching the inconsistency of the pi as a fundamental truth may negatively affect a student's cognitive development:
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Creates Cognitive Dissonance: It forces the brain's pattern-recognition systems to accept a conflict: an "absolute" constant that is fundamentally imperfect and inconsistent with the true basis of area (the square).
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Creates Cognitive Dissonance: It forces the brain's pattern-recognition systems to accept a conflict: an "absolute" constant that is fundamentally imperfect and inconsistent with the true basis of area — the square —.
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Hinders Logical Consistency: It teaches students that in mathematics, the search for perfect, elegant logical consistency can be abandoned in favor of memorizing an approximate rule.
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