# Geometry: Transformation of the Plane II

The following are images of transformations in the plane.

## Notation Used

The notation used on this page is from Mathematica.

- A 2D vector is written as
`{x,y}`

. - A square function is written as
`Function[#1^2]`

. The`#1`

is the first argument and`#2`

indicate second argument, and so on. - For example,
`Function[#1+#2]`

is the same as`Function[{x,y},x+y]`

, and`Function[{#2, Cos[#1*#2]}]`

is the same as`Function[{x,y}, {y, Cos[x*y]}]`

or`f[x_,y_]:={y, Cos[x*y]}`

. `{a,b}*c`

means`{a*c,b*c}`

. It is automatically distributive.`{a,b}/c`

means`{a/c, b/c}`

.- A 2 by 2 square matrix is written as
`{{a,b},{c,d}}`

, with`{a,b}`

being the top row. `{{a,b},{c,d}} . {x,y}`

means matrix multiplication with the vector`{x,y}`

, resulting:`{a x + b y, c x + d y}`

.`Norm[{x,y}]`

is the length of a vector`{x,y}`

.`Normalize[{x,y}]`

is the unit vector of`{x,y}`

.

These graphics are generated by my Mathematica packages Transform2DPlot.m and PlaneTiling.m. You can get them at Mathematica Package: Geometric Transformation and Complex Function Plot and Geometry: Plane Tiling Mathematica Package.