(Mathhombre) Miscellanea turned 3 today. I’ve really come to appreciate what Tumblr can do for a kind of cultural development of mathematics, but don’t know how to use it with my university students productively. Any ideas?

Image:

@mpershan pointed out this classic, available on the TERC website. Battista and Clements explaining Piaget and Van Hiele on the idea of proof.

"Ironically, the most effective path to engendering meaningful use of proof in secondary school geometry is to avoid formal proof for much of students’ work. By focusing instead on justifying ideas while helping students build the visual and empirical foundations for higher levels of geometric thought, we can lead students to appreciate the need for formal proof. Only then will they be able to use it meaningfully as a mechanism for justifying ideas."

Originally: Battista, M. T. & Clements, D. H. (1995). Geometry and proof. *Mathematics Teacher*, 88(1), 48-54. ©1995 by the National Council of Teachers of Mathematics.

Image: Building Blocks grant page (NSF)

Bubbles.

2 dimensional patterns, translation…

Pretty?

No idea why anyone else would be interested in this. Just got distracted in GeoGebra… so it’s on the Tube.

This is the magic hexagon. The numbers add up to 38 along each diagonal/vertical line.

It can be called it

themagic hexagon rather thanamagic hexagon because there are no other hexagons numbered 1,2…n with this property, no matter how many layers the arrangement has.(well, except for the one which is just one hexagon with ‘1’ written in it, and that’s hardly magical…)

(credit:

Mathematical Gems Iby Ross Honsberger)

3 Piece Hexagonal TessellationI was looking at the standard (yet beautiful) isometric rhombus tessellation in tile on some floor, and got wondering about how it would look for non-isometric parallelapipeds. Started to make it in GeoGebra and realized that of course I wanted to be able to make Escher style edge alterations.

Hope you can make something pretty! On GeoGebraTube.

Polygon Portal.

Thinking about ways to make a nice polygon spiral. This one is created by rotating and dilating the point that determines the first rotated polygon. (Using matrix exponentiation to rotate around the origin.) I love the spiral and 3-D effect of the transformation.

On GeoGebraTube.