Euclidean plane

Geometric ideas are still understood as objects in the Euclidean plane.

A ball in the Euclidean plane, for example, is the same thing as a disk, the area bounded by a circle.

Assume the setting is the Euclidean plane and a group of different points are given.

Consider a group of different points in the Euclidean plane.

After removing a single point from the 2-sphere, what remains is homeomorphic to the Euclidean plane.

There are 4 symmetry classes of reflection on the sphere, and two in the Euclidean plane.

One can consider similar minimal surface problems on other quadrilaterals in the Euclidean plane.

But notice that the flat Euclidean plane is given by taking .

This system has all the symmetries of the Euclidean plane.

In the Euclidean plane, we have the following possibilities.