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The Impossible Trisection

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60° TRISECTION MADE POSSIBLE.  The chasm between 60° and 20° angles was thought to be so wide that after two millennia of failing to bridge it, euclidean angle trisection was finally written off by mathematical theory back in the 1830s. The claim was that trisection had been solved by proving it was mathematically impossible. But many trisection diehards soldiered on, and those who assailed mathematicians with drawings were routinely dismissed out-of-hand. Despite its deep influence on mathematics, no one would take the question of trisection seriously again.  I became one of those diehards. I couldn't agree that even the most rigorous mathematics could account for all the variables or prove impossibility. So I toiled on the problem and thought I'd nailed it a few years ago, but was off by a few hundredths of a degree after testing with better software. Through the process, I'd grown to appreciate geometry and persisted, this time using GeoGebra's interactive geometry s...