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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 …
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 …