Bezier Curve (minor update)
in this video, interview of John Conway, Conway talked about this problem and his experience with Wu-Yi Hsiang and also Thomas Hales
starting on 6:40 to 25:00 or so.
John Baez the other day, when reading about your hyperreal article, i find myself more interested in another topic the surreal numbers and end up watching this interview of John Conway. In this Conway video he rather rambled on many his life's tales, but i actually got a very good intro to surreal numbers. (which made following up on Wikipedia fruitful). again, thank you John.
#math When an attractive girl flips her wet hair, the water stream forms a Fibonacci spiral. Math Mysticism: is Hurricane Shape a Fibonaci Spiral?
“Distress not yourself if you cannot at first understand the deeper mysteries of Spaceland”
FLATLAND: A Romance of Many Dimensions. The best book to understand higher dimensions.
reading math is just immense pure pleasure. Some people like video games, some movies, some drink bars… these are considered pleasure. But really, nothing beats reading just math. The purity, the beauty, the depth, and the austerity.
O, math, my true love, but how i have alienated thee, and you being quite difficult.
2 decades ago, i know about gamma function, which is a extention of the factorial to all positive real numbers (to say the least). i didn't understand how it is done. i just knew it's something advanced. but today, reading about it, i can understand it! Gamma function must be thanks to, my study of complex analysis sometimes in 2006!
my old rival beats me!
added a hyperbolic tiling interactive software to Great software for Tilings, Patterns, Symmetry
William Thurston on Tiling ＆ Automata
Found this on math overflow, a pure hogwash http://mathoverflow.net/questions/43690/whats-a-mathematician-to-do/44213#44213 YOU know? the kinda pleasing and meaningless things to say, that everyone loves to hear. Which id wrote that? Then i noticed, the name Bill Thurston. Bill Thurston? The William Thurston, geometry god of the century who died few years ago? Indeed.
〔Groups, Tilings, and Finite State Automata By William P Thurston. @ http://timo.jolivet.free.fr/docs/ThurstonLectNotes.pdf〕
learning math, and math idiom “motivation”
a story of looking up math. so today, i want to lookup ultra-filter. “…an ultrafilter on a poset P is a maximal filter on P, …” so, i have to lookup filter: “filter is a special subset of a partially ordered set.” but don't remember what's “partially ordered set” so, lookup it is: “A poset consists of a set together with a binary relation that indicates that, for certain pairs of elements in the set, one of the elements precedes the other.” ok, but i want to lookup “total order” to see if that's something i recall: “a linear order, total order, simple order, or (non-strict) ordering is a binary relation (here denoted by infix ≤) on some set X which is transitive, antisymmetric, and total.”
great, i remember having worked out this. That's total satisfaction. (actually, i discovered the properties of the Equivalence relation. When around 1997 i was writing code to decide if 2 polygons in 3d are equivalent, and discovered inconsistancies in my code, namely a==b, b==c, yet my code a≠c. And, i discovered, to great happiness, that to define equivalence is equivalent to partition of a set.)
well, that's a bit excursion. But i was writing about my typical trip to math these days. When trying to understand one thing, involves some 10 or 20 other Wikipedia articles.
by the way, also, some'd suggest math books instead. But no, i prefer dictionary style learning, esp for math. I prefer, the cold, logical, senseless, definition. The human touch of “motivation”, i want after the fact. (side note: sometimes, the human touch are often mis-leading, and there are many different takes, depending on the author. The human touch is often necessary though. But, i've been thinking, it is possible to do without entirely, because, math (defined as the essence of something), is how things are. And, to some degree (perhaps 100%), you really just need to know that gist, anything else is fluff, and possibly even harmful. But why do we have the need for the human touch? i gather possibly it's pure habit. As in, new thinking usually happens with newer generation (as is, only older generation have problems with imaginary number, whereas newer generation who are taught its definitions directly never have this problem and moves on)) (the gist of this thought is that, what happens, when people learned math ONLY by their logical definitions and never the story behind it.)
(side note: xah's edu corner: linguistics: by the way, in math lingo, often you'll encounter the phrase “Motivation” as a section title. It is a idiom among math texts. The context is that, math becomes so abstract, that just definining something seems out of the blue. So, one needs to provide a context, so that readers can see how the definition came to be. And that, is often called “Motivation”, which is kinda a math idiom. I can't help but finding it funny, when reading math papers (the “formal” type), you encounter a section titled “Motivation” pro forma)
after writing all these, i haven't understood ultra-filter yet. Now, back to procrastination…
POV-Ray ashtray, cubic spline POV-Ray: Surface of Revolution and Prisms
Math Prizes and Nobel Ignobility (repost)
math of Maryam Mirzakhani, hyperbolic geometry
Maryam Mirzakhani (a beautiful girl) won the Fields medal yesterday. Read this post by John Baez on the math she did. https://plus.google.com/117663015413546257905/posts/UTt2WeAcPEY
Geometry: How to Order the Edges of a Cube?. see the g+ link for discussion.
Logical Operators, Truth Table, Unicode (minor update)
quite amazing. This is when seemingly useless math becomes useful. ⁖ folding solar panels in spaceship.
Math Valentines Heart = Cardioid
every Valentines Day ♥ ♥ ♥ is the day to post the cardioid curve, because cardioid means heart-shaped.
more about Cardioid at Cardioid
if you search the web, you'll find 3D equations for 3D heart ♥ (that is a polynomial of 3rd degree who's level set is like a heart-shaped foil balloon)
What Does Bagua, Taichi Mean? Bagua, the Trigrams, as Binary System
what does bagua, taichi mean? Bagua, the trigrams, as binary system ☰ ☱ ☲ ☳ ☴ ☵ ☶ ☷
this is Chinese metaphysics.
exercise: look at South Korean flag. It has 4 of the 8 trigrams. Find a description of why those 4.
co-inventor of calculus, Gottfried Leibniz, also as the father of computer, said that “hexagrams a base for claiming the universality of the binary numeral system.”. Why?
Great Math Software (old collection)
Graphing Software for Microsoft Windows (update on plotting software for Microsoft Windows)
ugh, another idiocy of TeX legacy
see http://mathquill.com/. It's cool and all, but note the syntax. Quote:
MathQuill renders LaTeX math … try \sqrt x, try \sin\theta
when you want square root or sin etc, why cannot we simply write
Sqrt[x^2+y^2] and let that be the syntax? why the backslash syntax soup?
the damage of TeX, like unix, is deep and pervasive. It's free, like cig given to children, washed people's brain. It's so rooted that people are now saying the web should abolish MathML and let TeX be the standard.
on a separate note, learned this: Manuel de Codage «The Manuel de Codage (abbr. MdC) is a standard system for the computer-encoding of transliterations of Egyptian hieroglyphic texts.»〔➤ Unicode: Egyptian Hieroglyph Characters〕
9 Tools to Display Math on Web (updated)
Math Typesetting, Mathematica, MathML (updated)
How Mathematica does Unicode? (updated)
The Geometric Significance of Complex Conjugate (oldie but goodie)
Vectors and Complex Numbers
complex numbers, or complex analysis, is one of the most beautiful math. If you don't know complex numbers, and you love geometry, it is essential you get to know it.
If you want to understand Einstein's theory of relativity, you must understand mobius transformation. To understand mobius transformation, you must first understand Riemann sphere, complex numbers, geometric inversion. Video and explanation at Stereographic Projection 3D-Printed Physical Model
Astroid as Catacaustic of Deltoid
yay, my site made it to AMS blog. 〔Astroid as Catacaustic of Deltoid By John Baez. @ blogs.ams.org…〕
it's written by the redoubtable mathematician John Baez. Baez is great, in that he writes serious math for any math undergraduate to appreciate, as opposed to many math popularizing authors who write for the laymen.
i did my curves project Visual Dictionary of Special Plane Curves mostly in 1994 〜 1997, almost 2 decades ago, while i was a college student. I never seen the proof of how Deltoid's Catacaustic is a Astroid. I recall trying to, but it was too difficult for me back then. I haven't done much math since.
Do you know a proof of how Deltoid's Catacaustic is a Astroid? Post to John's g+ post. Thanks.