Twenty-some years ago, I started teaching an advanced high school geometry elective class called Space. I offered it every other year until I retired last year. Most of the course was about transformational geometry and symmetry. (That turned out to be excellent preparation for Common Core geometry. I will be presenting and co-presenting four workshops for teachers on this subject this summer.)
Another part of the course was a discussion of dimension, including reading Flatland and building polyhedra and polytope models with Zometool. Inspired by this work (and by Doctor Demento,) I created a “Doctor Dimension” skit for a school talent show. Later, Doctor Dimension showed up in Algebra: Themes, Tools, Concepts where his two-dimensional impersonation poured 2-D liquids into 2-D containers:
As the height of the liquid increases, how does the amount of liquid change? When is the growth linear? When does the rate of change increase? decrease?
Later yet, Doctor Dimension made an appearance in my precalculus and calculus classes, where he raised questions about concavity, continuity, and differentiability. And finally, yesterday, he set up his lab on my Web site, to share his collected works, plus four new interactive animations.
He awaits your visit!
PS: I played the part of the Doctor in the school talent show, so it’s a “he”. However a student who didn’t see my performance pointed out that there was no reason for Dr. Dimension to be male, and of course she was right. I have removed any gender identification on the website.
Read about a fifth interactive animation, and more on Doctor Dimension here!