Xah's Math Blog

2013-04-04

Math Tiling Automata Morph

2013-04-02

recursion yesterday reading todays paper — «Woman spotted yesterday reading today's paper»

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?

2013-02-07

linear algebra comics

linear algebra anime — linear algebra tutorial, in the form of comics, in Japan. How wonderful.

thx to weizhoupan

2013-02-04

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

2013-02-03

Doyle spiral + Mobius transformation

math art marbles spirals-2 — “Doyle spiral + Mobius transform” by fdecomite img src on 2008-04-04. 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).

2013-01-14

recursion bonanza. moved to Teacup Recursion Animation

2013-01-09

5-Point Conics (needs Java installed.)

2013-01-08

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.

logic; linguistics

2013-01-07

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. ⁖ when you give something you no longer want to someone, a value is created “out of nothing”.

2012-12-03

Mathematician Robert J Vanderbei made a comment at Geometry: Gallery of Surfaces. He wrote a surface viewer using latest tech WebGL. It's excellent. Check it out at 〔 http://www.princeton.edu/~rvdb/WebGL/minsurf.html 〕 . You will need to use a broweser that supports WebGL, such as Google Chrome.

2012-11-20

I can never remember what “xor” do. But now i got a easy way to remember it. xor returns true if the values of two sides differ.

2012-11-18

update: Math Font, Unicode, Gothic Letters, Double Struck, 𝔄 𝔅 ℭ

2012-11-10

updated links: Great software for Tilings, Patterns, Symmetry

2012-11-09

Great Software for Plane Geometry

2012-10-24

Intro to Public-key Cryptography for Sys Admin; What's HTTPS, SSH, SSL, TLS, AES, SHA-1, MD5, …

2012-10-16

bug eyed monster Hop David — BEM - Bug Eyed Monster, by Hop David.

Math Art of Hop David

2012-09-17

this tweet is going around:

Dear math, i'm sick and tired of finding your x, just accept the fact that she is gone.

It needs a prelude:

dear girls, i had a fight with my x, but i think she loves me still. help me find x^2+1=5. —Math

2012-09-16

3 wonderful articles on cycloids. By mathematician physicist John C. Baez.

Rolling Circles and Balls (Part 1) 2012-08-31 By John Baez. @ johncarlosbaez.wordpress.com…
Rolling Circles and Balls (Part 2) 2012-09-03 By John Baez. @ johncarlosbaez.wordpress.com…
Rolling Circles and Balls (Part 3) 2012-09-11 By John Baez. @ johncarlosbaez.wordpress.com…

It mentioned my site a lot. Thanks John.

2012-08-23

William Thurston died. (1946 〜 2012). Of skin cancer.

I think i first heard of him thru Jeff Week's book 《The Shapes of Space》. 〔☛ Reading Notes on 《The Shapes of Space》〕 I realized that he's one of the world's top mathematician. Though, his work is beyond my understanding.

2012-08-20

anti-calculus toothpaste — Anti-Calculus, but is it anti-derivative?

2012-01-13

What Voting Systems are There?

2012-08-01

Memories of Kurt Gödel 2012-08-01 By Rudy Rucker. @ www.rudyrucker.com…

2012-07-30

“what i saw”. Source thepunsultancy.blogspot.com

2012-07-25

Discovered a Unicode Character ℇ (EULER CONSTANT)

Discovered a Unicode char ℇ

character: ℇ (codepoint 8455, #o20407, #x2107)
name: EULER CONSTANT
old-name: EULERS

This is a bit strange. It's not clear whether it meant the base of the natural logarithm or Euler–Mascheroni constant.

The symbol for the base of the natural logarithm is traditionally ℯ (SCRIPT SMALL E), while the symbol for Euler–Mascheroni constant is γ (GREEK SMALL LETTER GAMMA).

The Unicode ℇ has name EULER CONSTANT. It's a bit ambiguous, but i suppose it means ℯ. However, i tried several Unicode fonts, all of them has the appearance of mirrored 3, none showed it as ℯ.