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

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4
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1answer
38 views
+50

What series of 'hyperpolyhedrons' do exist? Is there an effective way to derive their cross-sections by 3-d subspace?

There are two obvious series of 'hyperpolyhedrons'. 'Hyperoctahedron' with vertices $(\pm1,0...0), (0,\pm1,0,...0)...(0,...0,\pm1)$ and each vertex connected by an edge with each other vertex ...
11
votes
1answer
192 views
+50

How fat is a triangle?

The slimness factor of a geometric shape in 2 dimensions is the ratio between the side-length of its smallest containing square and its largest contained square. This is an important factor in ...
6
votes
0answers
104 views
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Hands of the clock, Revisited.

It has already been answered (here) that it is impossible for the (continuously moving) hands of a clock to trisect the face of said clock. Even ideally the hour, minute, and second hand can never ...
2
votes
2answers
78 views
+100

Which statements are equivalent to the parallel postulate?

I would like to have a long-ish list of statements that are equivalent to the parallel postulate. If a line segment intersects two straight lines forming two interior angles on the same side that ...
21
votes
2answers
303 views
+100

What is the Coxeter diagram for?

I understand that Coxeter diagrams are supposed to communicate something about the structure of symmetry groups of polyhedra, but I am baffled about what that something is, or why the Coxeter ...
3
votes
0answers
73 views
+50

Area of ​​the intersection of two discs : Integral solution?

Here is the problem : We consider two cirlces that intersect in exactly two points. There $O_1$ the center of the first and $r_1$ its radius. There $O_2$ the center of the second and $r_2$ its ...