Xah Math Blog Archive 2015-01 to 2015-03
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…
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
Unicode Math Symbols ∑ ∫ π² ∞ (minor update)
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.)
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. It is the sub-field of Mathematical optimization that deals with problems that are not linear.
Ask me question on patreon