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Quanta Magazine

Quanta Magazine
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Guide to 'scissors congruence': An ancient geometric idea that's still fueling cutting-edge mathematical research

Ancient Greek mathematicians, such as Euclid, thought of area as something geometric, not algebraic, a perspective that has inspired research programs across centuries.

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A brief illustrated guide to 'scissors congruence' − an ancient geometric idea that's still fueling cutting-edge mathematical research

While scissors congruence accurately captures the modern algebraic notion of 2D area, things get more complicated in higher dimensions. Maxine Calle, CC BY-NDIn math class, you probably learned how to compute the area of lots of different shapes by memorizing algebraic formulas. Remember “base x height” for rectangles and “½ base x height” for triangles? Or “𝜋 x radius²” for circles? But if you were in math class in ancient Greece, you might have learned something very different. Ancient Greek m

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'Scissors congruence,' an ancient geometric idea that's still fueling cutting-edge mathematical research

'Scissors congruence,' an ancient geometric idea that's still fueling cutting-edge mathematical research
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Quanta Magazine

Two monumental works have led many mathematicians to avoid the equal sign. The process has not always gone smoothly.

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The mathematic mind of Emily Riehl

Mathematician Emily Riehl finds deep and useful connections among objects that don't exist yet are everywhere.

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