Yes, 3D

Below are pages on various topics that use 3-dimensional visualization, or on 3D visualization itself. Pages on 3D solids themselves (such as the octahedron) are under 3D Solids.  Click and Enjoy!

Staircases and Matchsticks

Counting Squares in a Staircase and Triangles Made of Matchsticks A beautiful relationship Background This all started with a tweet from @KiranABacche: https://twitter.com/KiranABacche/status/1340575537845002276?s=20 I worked on it for half an hour and couldn’t make sense of it. So I tweeted that it seemed to have problems. Clarification tweets came in. In particular, that one needs …

Triangular Numbers

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, … Triangular numbers are a beautiful thing. It is a visual pattern, a numeric pattern, and there is a nice algebraic function. The is the mathematical trifecta we love. Videos My introduction to triangular numbers (at the 1:12 minute mark, …

Draw in 3d app

The Draw in 3d app (by Steffan Poulsen) is really great. Link: appsto.re/us/lJCX2.i  There is a built-in Tutorial.  The app is quite intuitive. I have made a (PDF) slideshow (<<click) of screen shots of the tutorial for reference. One early drawing is shown. Much, much more can be done.

Explosion/Squash Book

Here is a neat art project that involves geometry and the result is a 3D book.  Photos and art can be put inside this Explosion/Squash Book.