For questions about geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, angles.

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14
votes
0answers
122 views
+50

Does there exist regular planar pentagon?

How to prove or disprove that the boundary of any convex body in $\mathbb{R}^3$ (treated as a surface) includes 5 points which form a regular planar pentagon?
0
votes
1answer
142 views
+50

Viviani's theorem using Pythagoras

Did anyone find the proof of Viviani's Theorem just by using Pythagoras' relations in the triangles? Thanks.
4
votes
0answers
55 views
+100

Law of sines: uniform proof of Euclidean, spherical & hyperbolic cases

There is a unified formulation of law of sines which is true in all 3 constant curvature geometries (Euclidean, spherical, hyperbolic): $$ \frac{l(a)}{\sin\alpha}= \frac{l(b)}{\sin\beta}= ...