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Results tagged with plane-geometry
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user 13093
Plane Geometry is about flat shapes like lines, circles and triangles , shapes that can be drawn on a piece of paper
1
vote
Visual proof of convergence for Steiner's symmetrization
Consider $\omega$ a convex shape and $B$ a ball having the same volume centered at a point in $\omega$ (for example the centroid). Define a coordinate system in $\Bbb{R}^d$ and make a Steiner symmetri …
- 2,222
1
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Strengthened version of Isoperimetric inequality with n-polygon
The keyword you are looking for is "quantitative isoperimetric inequalities". The case of polygons was solved in the following paper: https://arxiv.org/abs/1402.4460
The "quantitative" term in the pap …
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0
votes
A generalization of Napoleon's theorem
Notice that triangles $ACD, AEB, FCB$ are similar. Working out the ratios of the sides and the angles one can see that:
Triangles $AI_1I_3$ and $ACE$ are similar. Rotating $I_1I_3$ around $A$ with an …
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2
votes
Dissecting a square
I think there are very few such solutions. The pieces must be identical, and they must touch the center. Consider the segment joining the center with one of the vertices. Then all small figures (in wh …
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