Some downloads

• Brook, T (1976–2023) Matrix Exercises
  Explanation

  Here are a few exercises inviting you to investigate some links between 3-D geometry and 3×3 matrices.

• Brook, T (2023) Matrix utilities in Python
  Explanation

  Here are a few simple Python functions for matrix algebra. They extend the standard linalg utilities from the numpy module. To use these functions, you’ll first have to download matplotlib to the appropriate folder. (A quick Web search will lead you to full instructions on how to do this.) After that, simply put from matrices import * at the top of your Python program.

  This may be a useful way to avoid tedious pencil-and-paper calculations.

• Brook, T (2023) Matrices and the RBG cube in Python
  Explanation

  Here are a few Python functions for applying matrix algebra to pixels in an image file. To use these functions, you’ll first have to download matplotlib and PIL to the appropriate folder. (A couple of quick Web searches will lead you to full instructions on how to do this.) Then you’ll need to download the matrix utilities from this page. After that, simply put from RGBcube import * at the top of your Python program.

A challenge

1. Identify all the rotational symmetries of the cube. How many axes of rotational symmetry are there?
2. Identify all the reflectional symmetries of the cube. How many planes of reflectional symmetry are there?
3. Describe the remaining symmetries.

Some links

1. Thiago Amendola Visualisation of the RGB cube [visited 25/08/2023]
   Note

   Use your pointing device to rotate the RGB cube in 3-D (drag in the image). Press the spacebar to see inside the cube.

2. Tim Brook Torn Paper [visited 23/08/2023]
   Explanation

   Torn Paper is another code art work based on the RGB cube.