The study of geometric forms that remain the same after continuous (smooth) transformations.

The forms can be stretched, twisted, bent or crumpled. But not torn or stuck together.

Things studied include: how they are connected, how tightly they are connected, how many "holes", etc.

Examples:

• a circle is topologically equivalent to an ellipse (just needs some stretching)

• a sphere is topologically equivalent to a spheroid

• a donut is topologically equivalent to a coffee cup (each has one hole, the coffee cup's is in the handle)

The forms can be stretched, twisted, bent or crumpled. But not torn or stuck together.

Things studied include: how they are connected, how tightly they are connected, how many "holes", etc.

Examples:

• a circle is topologically equivalent to an ellipse (just needs some stretching)

• a sphere is topologically equivalent to a spheroid

• a donut is topologically equivalent to a coffee cup (each has one hole, the coffee cup's is in the handle)

Copyright © 2018 MathsIsFun.com