Xah Math Blog

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

Visual Complex Analysis  Tristan Needham 83391
Visual Complex Analysis

How real are real numbers? By Gregory Chaitin. At https://arxiv.org/pdf/math/0411418.pdf〕 (local copy How_real_are_real_numbers_By_Gregory_Chaitin_f76de.pdf)

gyroscopic precession

Helicopter Physics Series - #4 They're Gyroscopes - Smarter Every Day 48

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

Visualize Math with 3D Printing

math 3d printing  Sofie M Langdon 2017 03 04
“Home schooler presents the math she's studied via @henryseg's book and some 3D printing. @maanow Golden section art exhibit” 〔image source https://twitter.com/timchartier/status/838147872323330049

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

euler's disk

Euler's Disk - Longest Spin Ever

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

Euler's Disk Buy at amazon


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

20 rattlebacks.

rattle back on amazon. Buy at amazon

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

curly dragon curve 02902
Curly dragon curve. 〔 All Plane-Filling Curves By Jeffrey Ventrella. At http://fractalcurves.com/all_curves/

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

Google AlphaGo Beats World Champions, 60 to 0

tire print snow pattern
tire print in snow. 〔image source https://plus.google.com/+KazimirMajorinc/posts/7SrScNqV3wp by Kazimir Majorinc, 2017-01-17〕

Kolam pattern

800px Kolam Indigo Dyed Cloth
3x3 symmetry 9 goddesses swastika Kolam with a single cycle by Nagata S, each of which corresponds to one of the nine Devi (Goddess) of the Vedic system 〔image source

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

Visualizing the Riemann zeta function and analytic continuation
Missing square puzzle
Missing square puzzle

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.

A Tribute to Euler, by William Dunham, 2008. Talk starts at 1:20.
truncated octahedra chc airport 2016-s
Truncated Octahedrons, Rhombic Triacontahedron, Dodecahedron in Real Life

Best Introduction to Graph Theory

the best introduction to graph theory is this one.

Introduction to Graph Theory  Trudeau
Introduction to Graph Theory By Richard J Trudeau. @ Buy at amazon

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.

Adaptive Sampling, Plotting Math Curve

The maths of spherical video

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.

the origins of SageMath; I am leaving academia to build a company.

Abuse of Math Notation

Why is Mandelbrot Set Cardioid Shaped?

Times Tables, Mandelbrot and the Heart of Mathematics

more about cardioid here: Cardioid

Peg solitaire

solitaire puzzle marbles set
buy! Authentic Models Solitaire Di Venezia 20mm Semi-Precious Marbles


in my youth, i studied this game and lots similar ones. You can search wikipedia for math and books. The name is peg solitaire. Here: Peg solitaire.

You begin with a configuration where there's a hole in the center, while all other are filled with marbles (or called pegs). You can remove a peg by jumping one over it. The goal is to leave just 1 peg on the board.

The Involute of a Cubical Parabola By John Baez. At https://johncarlosbaez.wordpress.com/2016/03/22/the-involute-of-a-cubical-parabola/

The Capricornoid By John Baez. At https://johncarlosbaez.wordpress.com/2016/03/06/the-capricornoid/

Free Calculus Textbooks

Why Are Text Book So Expensive?

Geometer's Sketchpad Closed Shop? Now, Free Download!

Interactive Geometry of Plane Curves

real rose

Plane Curves: GeoGebra Files Index

update complete. There are 60 of them. Enjoy!

Interactive Geometry of Plane Curves

following are interactive geometry of plane curves.

They are GeoGebra software. Google no longer supports Java Applets. I'm updating them to html5 so they run in your browser. There are about 50 more to do, i'll be posting them in next few days. Hope you like them.

plane tiling mathematica 2016-05-04 35001
Plane Tiling Mathematica package.

been working on Geometry: Plane Tiling Mathematica Package

for illustration at the Nature of Associative Property of Algebra

barth sextic mapped to sphere-s

beautiful images of Barth Sextic

The Symmetries of Things by John H. Conway (Author), Heidi Burgiel (Author), Chaim Goodman-Strauss (Author) Buy at amazon

John H Conway's new old book

math art: islamic pattern metal sphere

cubical two point pattern metal sphere Craig S Kaplan
“cubical two point pattern metal sphere” by Craig S Kaplan. Buy at http://www.shapeways.com/product/Y26YZRL3Y/cubical-two-point-pattern
islamic geometry pattern z
islamic geometry pattern 〈Tending toward the convex〉 〔 Tending toward the convex By Craig S Kaplan.. At http://isohedral.ca/tending-toward-the-convex/

Craig S Kaplan is a expert at mathematical decorative patterns. You can find more of his work on his site at http://isohedral.ca/

Computer Generated Islamic Star Patterns By Craig S Kaplan. At http://vismath4.tripod.com/kaplan/index.html

visual proofs is such that we have to artfully distribute the errors all over, so that in the limit, the error disappears!

Rectified Truncated Icosahedron and Elongated Square Gyrobicupola

John Baez again, from which i learned about the term “rectification” (of regular polyhedron), and also read what's archimedean solid, and learned about this strange beast Elongated square gyrobicupola.

the Elongated square gyrobicupola is interesting, besides the name, because

It is sometimes considered to be an Archimedean solid, because its faces consist of regular polygons that meet in the same pattern at each of its vertices. However, unlike the rest of the Archimedean solids, it lacks a set of global symmetries that take every vertex to every other vertex.

see Baez's article here: 〔 Rectified Truncated Icosahedron By John Baez. At http://blogs.ams.org/visualinsight/2016/04/01/rectified_truncated_icosahedron/

by the way, i highly recommend this software KaleidoTile. See Great Math Software: Polyhedrons and Polytopes

Find Intersections of Lines. Bentley–Ottmann Algorithm

In computational geometry, the Bentley–Ottmann algorithm is a sweep line algorithm for listing all crossings in a set of line segments. Wikipedia Bentley–Ottmann algorithm

beautiful internactive demo (JavaScript) by Adam Pearce http://bl.ocks.org/1wheel/464141fe9b940153e636

Prime Number's Ending Digit, Probability

Soundararajan was drawn to study consecutive primes after hearing a lecture at Stanford by the mathematician Tadashi Tokieda, of the University of Cambridge, in which he mentioned a counterintuitive property of coin-tossing: If Alice tosses a coin until she sees a head followed by a tail, and Bob tosses a coin until he sees two heads in a row, then on average, Alice will require four tosses while Bob will require six tosses (try this at home!), even though head-tail and head-head have an equal chance of appearing after two coin tosses.

Mathematicians Discover Prime Conspiracy. A previously unnoticed property of prime numbers seems to violate a longstanding assumption about how they behave. By Erica Klarreich. At https://www.quantamagazine.org/20160313-mathematicians-discover-prime-conspiracy/

see also

Free Good Category Theory Book

Mathematician John Baez, and expert of category theory (and quantum mechanics), has a blog about it his course of category theory, at http://math.ucr.edu/home/baez/qg-winter2016/

in particular, he highly recommend this free book on category theory.

Emily Riehl, Category Theory in Context, 2014. Emily_Riehl__Category_Theory_in_Context_2014.pdf

Google AI AlphaGo vs Lee Sedol

Combinatorics, Algorithm, and Humanity