Point in a Polygon
For any point inside a square, the sum of the distances from this point to the four sides is half of the perimeter.
Squares in Squares
Let’s draw a smaller square inside a unit square by dividing out a fixed fraction of each side and connecting the dividing point to an opposite angle.
Triangles in a Square
This problem is inspired by this geometry puzzle on Twitter. The original problem asks to find the ratio between two equilateral triangles fitted into a square. Let’s generalize it.
Perimeters of Polynominoes
If we separate all tetrominoes according to their perimeters, we would have two groups.
Square in Lattice
Consider drawing squares using the lattice points in a grid as vertices.
Flattening Cubes
We want to flatten the outer shell of a cube without tearing or stretching the surface.
Triangle Average Divider
Let’s say instead of “bisecting” the triangle, we draw a line from the top vertex to the base with a length that is the average of the remaining two sides...
Triangle Bisectors
Let’s start with a right triangle with a height of 1 unit and consider two ways of dividing it into two triangles.
Curve Stitching
Starting with a square, choose two points on the perimeter of the square to make a line, and then move both end points incrementally in the same direction (clockwise or counterclockwise) and the same distance along the perimeter of the square to make subsequent lines.
Cross Sections of Polyhedra
Cutting three dimensional shapes and looking at the possible shapes of the cross section.