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Mondriaan in maths

Two squares with areas of 1 and 3 are inscribed in a square frame. What’s the angle?

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Solution

The angle is 30°.

Solution by Ben Akkus.

From the areas we can infer the lengths as shown. It is also straightforward from comparing angles that the right triangles in the top are similar. Therefore we can say x/√3=1/(x+√3-1). This gives x=1, so in fact the triangles are congruent. Finally, tan(α)=1/√3, so α=30°.

Poem

Mondrian’s work
Lights, lines effects
Painting with signs and symbolic
Empty painting, like a mosaïc
Shrill red, grey blue, lemon yellow
A cosmic world so geometric
A general beauty neoplastic
Duality from man and woman
An esoteric creation and so mystic

Bella

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