Find the minimal natural number
Prove that one can tile the whole plane without spaces and overlaps, using any non self-intersecting quadrilaterals of the same shape. Note: quadrilaterals might not be convex.
It is impossible to completely tile the plane using only regular pentagons. However, can you identify at least three different types of pentagons (each with at least two different corresponding sides AND angles) that can be used to tile the plane in three distinct ways? Here essentially different means the tilings have different patterns.
Draw how to tile the whole plane with figures, made from squares
Consider a line segment of length
Twelve lines are drawn on the plane, passing through a point
Inside a square of area
A Wimbledon doubles court is
There are
We have an infinitely large chessboard, consisting of white and black squares. We would like to place a stain of a specific shape on this chessboard. The stain is a bounded and connected shape with an area strictly less than the area of one square of the chessboard. Show that it is always possible to place the stain in such a way that it does not cover a vertex of any square.