Xah Math Blog Archive 2013-01 to 2013-02

a blog by Glenn Wilcox with lots beautiful math-related pictures generated in Rhinoceros 3D @ http://www.generativedesigncomputing.net/

Teacup Recursion Animation

O, math, my true love, but how i have alienated thee, and you being quite difficult.

true false ambigram
“the right way to answer true and false questions”
math rubiks cube tattoo 170353
math rubiks cube tattoo

Microwave Arithmetic

on a microwave, you press 2 0 0 for 120 seconds, but 1 2 0 for 80 seconds, yet 9 0 for 90 seconds.

can you establish the rules for microwave number system or microwave arithmetic?

linear algebra comics

linear algebra anime
“线性代数”. Linear algebra tutorial, in the form of comics, in Japan. How wonderful.

thx to weizhoupan

math comics x2 x3 higher power 2008-06-04
by C. Burke (used with permission)

Doyle spiral + Mobius transformation

math art marbles spirals-2
“Doyle spiral + Mobius transform” by fdecomite image source on . 2800×2100 ©cc

can you identify what function is this?

it looks like a Mobius Transformation. But what's the exact parameters and what's the input image? (assume each ball is just a dot.)

Mobius Transformation is a function of the form f[z] = (a z + b) / (c z + d) and a d − b c ≠ 0. The variables are all complex numbers.

For a simple geometric explanation of complex numbers, see: Isometries: Translation, Rotation, Reflection and Mandelbrot Set Explained (no complex number needed).

recursion bonanza: Teacup Recursion Animation

5-Point Conics (needs Java installed.)

Logic Based Human Language: Lojban

lojban translated
xkcd comics on lojban. (http://xkcd.com/191/)

Lojban is a constructed language, design based on predicate logic. Some tutorial here, with voice recording: Xah's lojban Tutorial.

Alice in Wonderland, Zero-sum game

“The more there is of mine, the less there is of yours.”

from Wonderland: Chapter 9: The Mock Turtle's Story

That's the concept of Zero-sum game. However, in real world, most things isn't zero-sum game. Both parties actually benefit. For example, when you give something you no longer want to someone, a value is created “out of nothing”.