# symmetry-function-translation-shape.mp4

Chapter section: Translations and Function Representation

Caption (verbatim):

Translation of functions preserves their shape

Image description (verbatim):

Translation preserving a function shape

## Before the animation

Chapter lines 561–561:

This makes sense. Translational symmetry needs an object to translate, just as $D_3$ symmetry needs a triangly thing to translate. We can think of the function as a shape. If a system possesses translational symmetry, that shape is preserved.

Chapter lines 563–563:

This describes how the function transforms. Whether the physical system it describes behaves the same way after translation is a separate question.

## After the animation

Chapter lines 571–571:

Indeed, this representation is completely analogous to our 3 dimensional representation of $D_3$. There a vertex contained a component value, here an input value does. Indeed, the $D_3$ representation is itself a function representation, with a domain that contains only three members and is cyclic.