# Xah Math Blog

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

### omg, how boring is topology?

you'd think you gonna see how coffee cup turns into a donut.

instead, you got a fiat “open set”. From there on, its set of sets, subset, empty set, union of set, intersection of set, complementary set, power set, super set, finer set, coarser set, and it's set all the way!

The Method of Fluxions by Issac Newton https://archive.org/stream/methodoffluxions00newt#page/n3/mode/2up

Hilbert's 16th problem. the relative positions of the branches of real algebraic curves of degree n. Hilbert's sixteenth problem

Comprehensive Introduction to Differential Geometry By Michael Splvak. Classic. Comprehensive Introduction Differential Geometry

that's 5 volumes heavy expensive book. and, is graduate level.

you wonder, why's such book named “introduction”. It's actually graduate text, at 5 thick heavy volumes. Mathematicians not specialized in differential geometry have lots to learn from it, i assume.

but, “introduction” implies, this 5 volumes book only touches the surface. But then, its got the word “comprehensive” in it?

so, the proper interpretation seems to be, that the topic of differential geometry really is deep, and tied with lots other advanced math. Therefore, even at 5 volumes, and being a comprehensive tome, is, still just a intro.

On several occasions, most prominently in Volume 2, Spivak “translates” the classical language that Gauss or Riemann would be familiar with to the abstract language that a modern differential geometer might use.

2017-10-08 Wikipedia Michael Spivak

that'd be interesting to read.

http://3d-xplormath.org/ for Mac

### software for plotting math surfaces: Surfer

software for plotting math surfaces, especially algebraic surfaces. (Microsoft Windows, MacOS, Linux) https://imaginary.org/program/surfer

For some example of plots, see a friend Jean Constant's blog at https://jcdigitaljournal.wordpress.com/category/01-january-the-surfer-program/page/2/

### Vladimir Voevodsky, Fields Medalist, Dies at 51

### notation for recursion, what about notation for reduce?

been wanting a notation for recursion. Found it. In math, it's called iteration of a function, written as f^(°n). However, that doesn't cover reduce.

the term polytope is from mathematician Alicia Boole Stott. Alicia Boole Stott

### understand the “expansion” operation on polyhedron

understand the “expansion” process on polyhedron. http://VirtualMathMuseum.org/Polyhedra/Icosahedron/index.html

[• How real are real numbers? By Gregory Chaitin. At https://arxiv.org/pdf/math/0411418.pdf , Accessed on 2017-04-14 ] (local copy How_real_are_real_numbers_By_Gregory_Chaitin_f76de.pdf)

### gyroscopic precession

Learned about gyroscopic precession. Not intuitive. Don't know how the physics works out. But this video is amazing

### Visualize Math with 3D Printing

Visualizing Mathematics with 3D Printing. one expensive book Buy at amazon

### euler's disk

#physics euler's disk. haven't seen this before.

Euler's Disk Buy at amazon

### rattleback

this thing, your spin it, and it spins in reverse direction. Due to built up of instability, the rocking.

rattle back on amazon. Buy at amazon

Math: Density Plots of Trig Expressions. old. repost.

Valentine's Day Gift for a Platonic Relationship: Regular Polyhedrons Chocolates

### Kolam pattern

Kolam (Tamil-கோலம்) is a form of drawing that is drawn by using rice flour/chalk/chalk powder/white rock powder often using naturally/synthetically colored powders in Tamil Nadu, Karnataka, Andhra Pradhesh, Kerala and some parts of Goa, Maharashtra, Indonesia, Malaysia, Thailand and a few other Asian countries. A Kolam is a geometrical line drawing composed of curved loops, drawn around a grid pattern of dots. In South India, it is widely practised by female Hindu family members in front of their houses.[1] Kolams are regionally known by different names in India, Raangolee in Maharashtra, Aripan in Mithila , Hase and Raongoli in Kannada in Karnataka, Muggulu in Andhra Pradhesh, Golam in Kerala etc.,[2] More complex Kolams are drawn and colors are often added during holiday occasions and special events.

[2017-01-12 Kolam]

many more, see https://twitter.com/mariawirth1/status/810098967761616897

logician Raymond Smullyan is 97 now. ☹

Raymond Smullyan is famous among armature mathematicians for his many books on logic, presented as intriguing logic puzzles.

## Knights and Knaves

On a island, all inhabitants are either knights, who always tell the truth, or knaves, who always lie.

John and Bill are residents of the island.

John says: We are both knaves.

Who is what?

here's his books Raymond Smullyan books

### Truly Amazing Euler, Greatest Mathematician. A Intro.

truly amazing Euler, greatest mathematician. Here's his story told by William Dunham, 2008. Save 1 hour to watch.

### Best Introduction to Graph Theory

the best introduction to graph theory is this one.

if you don't know the basics, get it, read it in a week, 1 hour a day. Once you start reading, you can't put it down.

Henry Segerman has been doing amazing things lately.

The story of SageMath. http://wstein.org/papers/talks/2016-06-sage-bp/bp.pdf

excellent story, if you want to know about math software, open source, academia.

here's video version.

### Why is Mandelbrot Set Cardioid Shaped?

more about cardioid here: Cardioid