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mrtaurho
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A few decades ago Sherman Stein asked whether a trapezoid whose parallel sides are in the ratio 1:root 2 can$1:\sqrt2$ can be dissected into triangles, all of the same area. This remains open--it's a mystery which trapezoids admit such dissections./

A few decades ago Sherman Stein asked whether a trapezoid whose parallel sides are in the ratio 1:root 2 can be dissected into triangles, all of the same area. This remains open--it's a mystery which trapezoids admit such dissections./

A few decades ago Sherman Stein asked whether a trapezoid whose parallel sides are in the ratio $1:\sqrt2$ can be dissected into triangles, all of the same area. This remains open--it's a mystery which trapezoids admit such dissections.

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paul Monsky
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A few decades ago Sherman Stein asked whether a trapezoid whose parallel sides are in the ratio 1:root 2 can be dissected into triangles, all of the same area. This remains open--it's a mystery which trapezoids admit such dissections./