# Xah's Math Blog

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

Visual Dictionary of Special Plane Curves now has side panel for easy navigation.

Algorithmic Mathematical Art, page 3 (old. repost)

### Google DeepMind AI, AlphaGo to Challenge World Champion?

you may have heard, that Google DeepMind AI, AlphaGo, is doing a human vs machine, challenge a go champion Lee Se-dol.

They said they beat European Champion 5-0, so is now challenging a champion.

I got excited, thought it happened sooner than i expected. Spent some 30 min to read about it. Turns out, that “European champion” is only ranked 2 dan. (Pros are 9 dan)

(go playing is ranked by “dan”, or “level” if you will. Rather a bad system. The chess elo system is much better. But basically, the “dan” is meant to be the number of moves a stronger player can yield to the other for a even game. That is, if you are 4 dan, and i'm 1 dan, that means, if you give me handicap 3 stones (i play 3 moves first, usually on designated spots), then we would have a “even” game. That's the ideal, anyway. In reality, there are professional ranks of dan and armature ranks of dan. Armature 9 dan is something like pro 5 dan.)

so, the AlphaGo human vs machine is rather marketing deception. Am very disappointed and annoyed by the marketing tactics.

this “news”, is rather no news. The go human champion would beat google's AI 5-0.

〔What Is Spacetime, Really? By Stephen Wolfram. @ http://blog.stephenwolfram.com/2015/12/what-is-spacetime-really/〕

see also

### the answer to life, universe and everything

got a huge laugh out of this.

and if you are mathematically inclined, see, why 42. 〔42 By John Baez. @ http://math.ucr.edu/home/baez/42.html〕

### Numbering System of Hex Grids

so, i was wondering, in writing a game on hexgonal board, whether there's a standard numbering system, as in chess and go. 〔➤ Go Board Game on Hexagonal and Triangular Grids〕

also, how do one represent the board in program. I've drawn a lot hex and triangular grids in the past, and know that, the underlying data structure, is rather ah-hoc and ugly. Have always been wondering if there's elegant way to do it. 〔➤ Geometric Tilings and Patterns Image Gallery〕

then, found this fantastic site, dedicated to this question.

〔Hexagonal Grids By Amit Patel. @ http://www.redblobgames.com/grids/hexagons/〕

http://modto.com/integral-house-by-shim-sutcliffe-architects/

〔Berkeley to fire 'love letter to learning' professor By Rory Carroll. @ http://www.theguardian.com/us-news/2015/oct/17/berkeley-math-professor-alexander-coward-campus-battle〕

〔BLOWING THE WHISTLE ON THE UC BERKELEY MATHEMATICS DEPARTMENT By Alexander Coward. @ http://alexandercoward.com/BlowingTheWhistleOnUCBerkeleyMathematics.html〕

ancient article, still relevant. Google Chrome killed MathML. The TeX Pestilence (Why TeX/LaTeX Sucks)

a great website on map projections, with interactive visualization. 〔Maps By Jason Davies. @ https://www.jasondavies.com/maps/〕

there's this book 〈Groups: A Path to Geometry〉 by R P Burn. amazon I bought in year 2000.

I never got time to read it. When i bought it, i thought, i really want to understand the subject.

today, picking it up, haha, i understand all of it.

not bad for magically reading book in 15 years.

if you are in Mountain View, CA, area, come pick it up if you like.

comment at https://plus.google.com/+XahLee/posts/7Fri5maT94T

### McGee graph

golly, each time John Baez posts something about math, 30 minutes will be gone if i just glance over to enjoy but understand nothing. And feeling terribly bad about my incompetence et al. Half a day will be gone if i tried to understand something. And feeling terribly bad about escapism. And by next month, all's forgotten.

here, have a cookie.

anyway, here's graph theory, projective geometry, affine transformation, group theory. All my favorite cookies.

- https://plus.google.com/117663015413546257905/posts/dttufb7MCk2
- http://blogs.ams.org/visualinsight/2015/09/15/mcgee-graph/
- http://mathoverflow.net/questions/215211/what-algebraic-structures-are-related-to-the-mcgee-graph
- McGee graph

comment at https://plus.google.com/+XahLee/posts/K5fEptxAa1e

the Nature of Associative Property of Algebra (minor update)

〔The reason why Involute gears turn smoothly. By Hyprodium. @ http://hyrodium.tumblr.com/post/123270340099/the-reason-why-involute-gears-turn-smoothly-fig〕

see also Involute

〔John Horton Conway: the world's most charismatic mathematician By Siobhan Roberts. @ http://www.theguardian.com/science/2015/jul/23/john-horton-conway-the-most-charismatic-mathematician-in-the-world〕

a new book. A biography of John Horton Conway

〔Genius At Play: The Curious Mind of John Horton Conway By Siobhan Roberts. @ amazon〕

Chen's theorem: every sufficiently large even number can be written as the sum of either two primes, or a prime and a semiprime (the product of two primes). Chen's theorem

〔A Guide to Plane Algebraic Curves by Keith Kending. @ amazon〕

Geometry: Requirements for a Visualization System for 2020 (repost)

### The Stanford Encyclopedia of Philosophy

The Stanford Encyclopedia of Philosophy is a great thing. It is much better than Wikipedia.

### magic polyhedron

the Rubik cube of today have advanced. Now, there's stickerless versions, and better mechanical design.

see updated Magic Polyhedrons

### ℭ = Cardinality of the continuum.

ℚ = be rational, ℝ = get real.

ℭ = Cardinality of the continuum.

Math Font, Unicode, Gothic Letters, Double Struck, ℤ ℚ ℝ ℂ ℍ ℜ ℑ ⅇ ⅈ

### Tiling ＆ Patterns, Classic Text Now in Print Again

just discovered, this classic, definitive, book on tilings ＆ patterns is in print again, now reprinted by Dover.

see also: Reading Notes on Tilings and Patterns

### tiling the plane with 5-fold symmetry tiles

John Baez, gave a intro on the problem of tiling the plane with 5-fold symmetry tiles @ https://plus.google.com/117663015413546257905/posts/5CHdeLRckRm

see also 〔The trouble with five By Craig Kaplan. @ https://plus.maths.org/content/trouble-five〕

sample of tiling ＆ patterns, see:

See also: Discontinuous Groups of Rotation and Translation in the Plane

### Skew But Fair Dice

it supposed to be fair dice. Am thinking there's a major difference from the cube. This one, has 2 different sides, like a coin. In a sense, when you throw this dice, it decides which of the side will fall first, then, decide which of the 3 faces will land.

So, one can actually make a 3-sided pyramid, and have 2 of them and glue the bottom together. So, we could make a infinite shape of 6 faced dice that's still fair. Then, if we wiggle the cutting plane like a saw tooth, we could create quite a lot strange looking and still fair 6-faced dice.

comment at https://plus.google.com/+XahLee/posts/L9FP178N6eq

Cycloid (animation update)

### Unicode Char for Logarithm?

apparently there's a Unicode char for log. ㏒. The Unicode name is “U+33D2: SQUARE LOG”. It's Japanese origin.

There's also a ㏑ “U+33D1: SQUARE LN”

for many more, see http://www.unicode.org/charts/PDF/U3300.pdf

See also: Unicode: Math Symbols ∑ ∞ ∫ π ∈ ℝ² (use the search box there to find Unicode)

(thanks to https://twitter.com/Ryuutei)

English/Chinese Math Terminology 中/英 数学术语 (minor update)

LimaconOfPascal (updated gif animation)

Trochoid (updated gif animation)

Tractrix (updated gif animation)

Conchoid (minor update)

Notes on A New Kind of Science (photo of the book added)

### How to Lose Interest at Go Board Game Fast

in early 1990s i spend 2 years playing go. At the time i bought the best go program called Nemesis for the Mac. Was able to beat it with 5 stone handicap for the computer. (the software is rated 13 kyu, which means, i'm i think 9kyu at the time)

some said that playing with computers gets you bad habits…

sometimes in 2009 or so, i suddenly find go to be not interesting at all, after i read Stephen Wolfram's “A New Kind of Science”.

the essence is that it's a kinda a cellular automata, and as such, there's no intrinsic math in it, and there are infinite cellular automata. And go players are simply those with great memory and specialized talent and seen lots of cellular automata of the go kind…

see Go Board Game as Cellular Automata

the other thing that has been interesting for me to explore is go on triangular grid or other tiling. Though, it's disappointing that i haven't seen much literature about it at all.

how to lose all interest in go. Go Board Game as Cellular Automata

What is Technical Drawing, Descriptive Geometry, Projective Geometry, Linear Algebra (minor update)

Extending the Euclidean Plane: Riemann Sphere and Real Projective Plane

Unicode: Math Symbols ∑ ∞ ∫ π ∈ ℝ² (minor update)

Schmidt Arrangement, Algebra Integer, Gaussian integer, Eisenstein Integer

### Stereographic Projection and Geometric Inversion

Stereographic projection is a special case of sphere inversion.

consider a sphere of diameter d, and plane at bottom. The inversion circle is centered on North pole, with diameter 2*d.

also:

Stereographic Projection (minor update Mathematica notebook. If you have a problem running it, let me know, i'll fix.)

Table of mathematical symbols by introduction date

In mathematics, nonlinear programming (NLP) is the process of solving an optimization problem defined by a system of equalities and inequalities, collectively termed constraints, over a set of unknown real variables, along with an objective function to be maximized or minimized, where some of the constraints or the objective function are nonlinear.[1] It is the sub-field of Mathematical optimization that deals with problems that are not linear.