A regular hexagon with three diagonals and two line segments at right angles. What is the proportion green : yellow : blue : orange?
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The seesaw
Author: Rik D. Tangerman
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The consonant squares
Four squares and a rectangle. What’s the angle α?
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The Zamani suggestion
Two regular hexagons share a vertex. What’s the area proportion red : yellow hexagon?
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The forward lean
A square with a diagonal and an isosceles triangle. What fraction is brown?
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The purple square
A regular octagon of side length 2 with two diagonals and a square. What is the purple area?
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Ruyles squares
There are four possible squares with a vertex at distance a from the centre and two vertices on the circle of radius r. Find their areas in terms of a and r.
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Pushing the boundary
Two equilateral triangles are placed side by side. What’s the proportion green : red?
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The Pyramid of Austerlitz
An equilateral triangle and a parabola that is tangent to two of its sides in two vertices. Proof that the triangle centre coincides with the parabola focus.
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The skewed tree
A triangle with a line segment through its centroid and parallel to a side. What faction is dark green?
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A deep connection
Two squares inside a circle. What is the circle area in terms of length a?