Maths: Quadrilateral Angles & Perfect Tessellations

When four identical quadrilateral tiles meet at a single point on a floor, they are demonstrating a beautiful piece of geometric logic: the interior angles of any four-sided shape always sum to 360°, and the space around a point is also exactly 360°. This is no coincidence—it is the core relationship that governs tiling, tessellation, and many patterns in design and nature. The key idea is that each tile contributes exactly one of its four interior angles to the meeting point. Since the tiles are identical, those four angles are equal. Four equal angles that must fill a full turn around a point will each be 90°, and together they account for the entire 360° available. This connection between the angle sum of a polygon and the angle sum at a point is what makes perfect tiling possible—no gaps, no overlaps, just a seamless fit. Understanding this rule helps you see why some shapes tile a floor and others leave awkward holes.