Daily Archives: April 4, 2019

April 4, 2019

Sideband #65: 4D Rotation

This is a Sideband to the previous post, The 4th Dimension. It’s for those who want to know more about the rotation discussed in that post, specifically with regard to axes involved with rotation versus axes about which rotation occurs.

The latter, rotation about (or around) an axis, is what we usually mean when we refer to a rotation axis. A key characteristic of such an axis is that coordinate values on that axis don’t change during rotation. Rotating about (or on or around) the Y axis means that the Y coordinate values never change.

In contrast, an axis involved with rotation changes its associated coordinate values according to the angle of rotation. The difference is starkly apparent when we look at rotation matrices.

5 Comments | tags: 2D, 3D, 4D, column vector, matrix math, matrix transform, rotation, rotation matrix, unit vector, vectors | posted in Math, Sideband

April 4, 2019

The 4th Dimension

By Wyrd Smythe

Here on the 4^th day of the 4^th month, I feel I really should be writing about the 4^th dimension. I did say that I would during March Mathness, and I tried to set the math foundation here and here.

But two problems: Firstly, I’m kinda burned out. Those three posts were a bit of work, diagrams & models & math (oh, my!), and then trying to explain them clearly. Secondly, obviously no one finds this interesting except me, so not much motivation for the effort involved. Which was expected (kinda the story of my life). I also said these posts were as much recording my notes as attempts to share.

But it is 4/4 (and no Twins game today), so I thought I’d try winging it anyway.

16 Comments | tags: 2D, 3D, 3D space, 4D, coordinates, cube, dimensions, square, tesseract | posted in Science