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

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6
votes
2answers
112 views
+50

Task “Inversion” (geometry with many circles)

Incircle $\omega$ of triangle $ABC$ with center in point $I$ touches $AB, BC, CA$ in points $C_{1}, A_{1}, B_{1}$. –°ircumcircle of triangle $AB_{1}C_{1}$ intersects second time circumcircle of $ABC$ ...
1
vote
1answer
59 views
+50

Maximal intersection of slabs in $\mathbb{R}^n$ with a compact convex centrally symmetric set

Let $K \in \mathbb{R}^n$ be a compact convex set containing the origin and symmetric with respect to the origin. Let $S_i(t_i)$ be a finite set of slabs of various widths and orientations, translated ...
0
votes
1answer
32 views
+150

Defining ellipse using points and normal vectors from them

There is an article on how to detect circles in images using pairs of gradient vectors (assuming the circle is dark and background is bright). The thing is that gradient of image intensity at each ...
6
votes
0answers
40 views
+50

Largest $n$-vertex polyhedron that fits into a unit sphere

In two dimensions, it is not hard to see that the $n$-vertex polygon of maximum area that fits into a unit circle is the regular $n$-gon whose vertices lie on the circle: For any other vertex ...