We dissect the Wizard of Oz diploma moment where the scarecrow declares a formula for an isosceles triangle that fails on three counts: wrong shape (not necessarily a right triangle), wrong operation (square roots vs squares), and the wrong relation between sides. We explain why Pythagoras only applies to right triangles, why the 'any two sides' setup collapses under the triangle inequality, and how the gag echoed in pop culture (The Simpsons). It's a meditation on confidence versus real understanding and why rigorous math matters in the real world. Sponsored by Ember Silk to help you find where AI truly adds value.

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