Xah Math Blog Archive 2015-01

[What Is Spacetime, Really? By Stephen Wolfram. At http://blog.stephenwolfram.com/2015/12/what-is-spacetime-really/ , accessed on 2015-12-03 ]

see also

the answer to life, universe and everything

got a huge laugh out of this.

the answer to life, universe and everything

and if you are mathematically inclined, see, why 42. [42 By John Baez. At http://math.ucr.edu/home/baez/42.html , accessed on 2015-12-02 ]

Numbering System of Hex Grids

Comprehensive Hexagonal Grids programing tutorial. added to

Great software for Tilings, Patterns, Symmetry

Integral House

James Stewart (mathematician)



[Berkeley to fire 'love letter to learning' professor By Rory Carroll. At http://www.theguardian.com/us-news/2015/oct/17/berkeley-math-professor-alexander-coward-campus-battle , accessed on 2015-10-17 ]

[BLOWING THE WHISTLE ON THE UC BERKELEY MATHEMATICS DEPARTMENT By Alexander Coward. At http://alexandercoward.com/BlowingTheWhistleOnUCBerkeleyMathematics.html , accessed on 2015-10-17 ]

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

xah math books 20150919 181118-s
Math and Geometry Books

Groups: A Path to Geometry

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.

McGee graph 37662
McGee graph

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

the Nature of Associative Property of Algebra (minor update)

Seashell Gallery

[The reason why Involute gears turn smoothly. By Hyprodium. At http://hyrodium.tumblr.com/post/123270340099/the-reason-why-involute-gears-turn-smoothly-fig , accessed on 2015-08-15 ]

see also Involute

[John Horton Conway: the world's most charismatic mathematician By Siobhan Roberts. At http://www.theguardian.com/science/2015/jul/23/john-horton-conway-the-most-charismatic-mathematician-in-the-world , accessed on 2015-08-15 ]

abacus pink rabbit 1


a new book. A biography of John Horton Conway

[Genius At Play: The Curious Mind of John Horton Conway By Siobhan Roberts. At Buy at 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. At Buy at amazon ]

Requirements for a Visualization System (repost)

The Stanford Encyclopedia of Philosophy

The Stanford Encyclopedia of Philosophy is a great thing. A different take than Wikipedia.

magic polyhedron

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

Kawai MP9000 piano dodecahedron
magic dodecahedron.

see updated Magic Polyhedrons

ℭ = Cardinality of the continuum.

ℚ = be rational, ℝ = get real.

ℭ = Cardinality of the continuum.

Math Font ℤ

Tiling and Patterns, Classic Text Now in Print Again

tiling and patterns
[Tiling and Patterns By Branko Grunbaüm, G C Shaphard. Buy at amazon ]

just discovered, this classic, definitive, book on tilings and 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 At https://plus.google.com/117663015413546257905/posts/5CHdeLRckRm

see also [The trouble with five By Craig Kaplan. At https://plus.maths.org/content/trouble-five , accessed on 2015-05-11 ]

sample of tiling and patterns, see:

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

Skew But Fair Dice

skew 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 ∑ ∫ π² ∞

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

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

archimedes spiral
Archimedean Spiral (updated animation)
ball shadow
Conic Sections (updated animation)
hypotrochoid spiralgraph
Hypotrochoid (updated animation)

LimaconOfPascal (updated gif animation)

Regular Polyhedron Domes (Geodesic Dome) Photo Gallery

Involute of a circle.

Trochoid (updated gif animation)

Tractrix (updated gif animation)

Conchoid (minor update)

Seashell Gallery: Misc Seashells, Cut-in-Half View

Giant Parabolic-dish Photo Gallery


Epi and Hypotrochoid Animation Gallery

Mathematics of Seashell Shapes

The TeX Pestilence: Why TeX/LaTeX Sucks (repost)

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.

tri game2
Go Board Game on Hexagonal and Triangular Grids

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

Go Board Game on Hexagonal and Triangular Grids (repost)

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 ∑ ∫ π² ∞ (minor update)

Visual Complex Functions: by Elias Wegert

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.


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

the Nature of Associative Property of Algebra

Go Board Game as Cellular Automata

Table of mathematical symbols by introduction date

History of mathematical notation


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.

Nonlinear programming