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Plane Geometry is about flat shapes like lines, circles and triangles , shapes that can be drawn on a piece of paper

19 votes
Accepted

Planar sets where any line through the center of mass divides the set into two regions of eq...

Assume that $A$ is compact and convex. If there is a point $P$ such that any line through it is a bisector of $A$ then $A$ has to be centrally symmetric. In fact a stronger result is known (see the pa …
Andrey Rekalo's user avatar
29 votes
Accepted

Parabolic envelope of fireworks

E. Torricelli, who was the last Galileo's secretary, suggested a purely geometrical method to find the envelope in his De motu Proiectorum. He also coined the term `parabola of safety'. Apparently i …
Andrey Rekalo's user avatar