Whenever you move something like a teapot from the cupboard to the table, you have just unwittingly performed a mathematical operation called an isometry. In this collection of 5 Minute Seminars, you can find out more about isometries, their connection to geometry, and their application to computer animation. ...

Isometries of the Euclidian Plane Introduction Wallpaper groups consist of isometries of the Euclidian plane. I'll just refer to them as isometries or for simplicity, symmetries. A symmetry of an object is a transformation that takes the object onto a copy of the object. Symmetries preserve dimensions, but not always orientations. There are two general classes of symmetries of the plane, order ...