As opposed to tiling the plane, here’s knitting the plane. Or, the fence.
As you can see, they’ve still got a ways to go!
And this isn’t the first example of mathematical knitting I’ve seen: check out this knitted Klein bottle!
Application Geometry
Math and Art: Math and Computer Animation
This is a clear, concise, and fascinating overview of how some very advanced mathematical ideas are making their way into 3-D animation.
http://www1.ams.org/samplings/feature-column/fcarc-harmonic
Here’s the basic setup. In order to efficiently model a character, you approximate it with a frame that is built around a few important points. To move the character, you focus on moving just those points that define the frame. Thus, moving the character from point A to point B boils down to understanding where those handful of crucial points go.
The tricky part is figuring out a way to smoothly bring all those in-between points along for the ride, and that’s where the math comes in. The secret is to think of those in-between points as averages of the points that define the frame. The article explains how barycentric coordinates, harmonic functions. and a surprising amount of calculus are being used to pull off this movie magic!
Appreciation Geometry Photography
Math and Art: Shadows and Triangles
The sun sometimes turns rectangles into triangles. A nice Sunday morning image.
Appreciation Art Representation
Math and Art: Dancing Bubble Sort
This is a fun and whimsical demonstration of bubble sorting through dance!
http://www.youtube.com/watch?v=lyZQPjUT5B4
The dancers arrange themselves in numerical order in the same manner one would bubble sort an unordered list. One by one, each number “compares” himself with the number on his left; if they are out of order, they switch places. Make you’re way down the list, and start again at the front. Repeat until no one switches places and voila! everyone’s in order!
And just to be thorough, the troupe does dance-representations of Insert-Sort, Shell-Sort, and Select-Sort algorithms as well!
Appreciation Art Challenge
Math and Art: Custom Pi Necklace
My contribution to Pi Day Celebrations: a student-made necklace that encodes the first 80 or so digits of pi in beads!
Starting with the pendant as 3, the student carefully strung the beads in a circle (clockwise) according to the following mapping:
Thus, you can read off 3.14159265358, and so on. A truly thoughtful, creative, and inspired work! I think the student’s original inspiration might have been this other pi-themed necklace.
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