For any rectangle, the sum of the squares of the distances from any point P to two opposite corners is equal to the sum of the squares of the distances from that point to the two other corners (so, above, a² + c² = b² + d²). This remains true whether the point is inside or outside the rectangle, on a side or a corner, or even outside the plane.

Pushkin wrote, “Inspiration is needed in geometry, just as much as in poetry.”