Poincaré separation theorem

Poincaré Separation Theorem is a mathematical principle about two different types of shapes. The theorem says that two shapes can be separated by drawing a line between them, so that one shape is completely surrounded by the other shape. For example, imagine two circles: you could draw a line between them, so that one circle is completely on the left side of the line and the other is completely on the right side. That's a good example of the Poincaré Separation Theorem.