For example, on a flat surface, the angles of a triangle ... and it would imply a universe shaped like the surface of a sphere. In a sphere, two parallel lines would not remain parallel forever ...

A sphere is completely curved, a ball shape. Image caption ... This is shown in the formula \(E\) = \(V\) + \(F\) – 2 The flat surface of a cube is a face. Each face of a cube is a square.

Most trigonometry students look at triangles on a flat surface. However, people from ancient astronomers to modern navigators calculated the arc lengths and angles of triangles on a sphere. They used ...

Cosmologists explore whether the universe is flat, closed, or open. New data challenges long-held beliefs, but the true shape ...