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Get you best paper, cut a circle and fold it so that the circumference falls on a fixed point inside. Repeat, using random folds. Now see the creases. This is how you paper-fold an ellipse.
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As one vertex in a triangle slides along the horizontal axis, another vertex slides along the other axis. The third vertex then retraces an ellipse. Leonardo da Vinci discovered this.
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A √5-by-√5 square polygon is being fully covered on both sides with 5-by-2 wrapping paper. This is an optimal solution to the problem from the previous post as the polygon total area equals the area of the paper’s colored face.
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Golden Ratio Decagon Spiral
Another beauty from Ghee Bom Kim in the Mathematical Tiling FB group. Pentagons cutting the golden obtuse triangles into two golden acute triangles is egregiously clever. Then he adds...
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Epidauros



https://commons.wikimedia.org/wiki/Category:Epidaure,_restauration_%26_description_des_principaux_monuments_du_sanctuaire_d%27Ascl%C3%A9pios
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Karl Weichardt, Rekonstruktion der Villa Jovis auf Capri
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St. Ulrich und Afra, Augsburg
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Lange Seite / kurze Seite = Wurzel aus 3.
Kurze Seite = Radius.
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The truncated icosahedron is the only polyhedron my son is interested in.
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