A new proof breaks a decades-long drought of progress on the problem of estimating the size of triangles created by cramming points into a square. Consider a square with a bunch of points inside. Take ...

The area of one triangle is equivalent to half of the area of the rectangle. The area of the rectangle is the length multiplied by the width. The length and width of the rectangle are the base and ...

The same number of arcs means the angles are the same size. A square marked at a vertex shows an angle that is exactly 90°. Image caption, The longest side of a triangle is opposite the largest ...

In fact, any shape of constant width would do, and there are infinitely many such shapes. The simplest example is the Reuleaux triangle, named after distinguished mechanical engineer Franz ...

In two dimensions, the Reuleaux triangle has the smallest area of constant-width shapes. You can draw this shape yourself using a sort of three-way Venn diagram. First, draw an equilateral ...