Page shows one of nineteen trillion simple maps of the United States, will show a different map the next time loaded.

A well-known theorem proves that with only four colors, any simple map of can be drawn so that no color touches itself. The next step is to ask how many ways there are to accomplish this simple task. For the contiguous United States, there are over nineteen trillion different maps that use only four colors. Even the tightest constraints can yield near-infinite variety.

NumPy is the fundamental package needed for scientific computing with Python. It contains among other things:

a powerful N-dimensional array object
sophisticated (broadcasting) functions
tools for integrating C/C++ and Fortran code
useful linear algebra, Fourier transform, and random number capabilities.
Besides its obvious scientific uses, NumPy can also be used as an efficient multi-dimensional container of generic data. Arbitrary data-types can be defined. This allows NumPy to seamlessly and speedily integrate with a wide variety of databases.

Cellular Automata rule 30 in hole punch and paper tape.

map is not the territory, but it captures a bunch of useful information about it.

'Graph theory captures this idea of things being "adjacent" to one another in abstract, mathematical terms, and studies it without the hindrances of useless specifics.'

Information on a simplified proof the four color theorem, with links to 633 unavoidable configurations.

"This page gives a brief summary of a new proof of the Four Color Theorem and a four-coloring algorithm found by Neil Robertson, Daniel P. Sanders, Paul Seymour and Robin Thomas."

First great American mathematician, despite being English. Coined the term 'graph.'

"I am a recreational mathemusician currently living on Long Island, NY." (Awesome mathematical doodling videos)

Read's chromatic polynomial algorithm shown to have worst-case time-complexity of O(n2B(n)), where B(n) is the nth Bell Number. Fun fact: c^n < B(n) < n! for any c, sufficiently large n.

Bell numbers

If only I'd known graph coloring was so cool!

"It is much more fun to put cream cheese on these bagels than on an ordinary bagel. In additional to the intellectual stimulation, you get more cream cheese, because there is slightly more surface area."

probably the classiest map

basic physics sim for processing. I was looking for something like this about 18 months ago, I wish I could remember what for.

mathematical instructions for some azimuthal projections

perfect gift for your favorite science nerd.

'Just as “plastics” was the catchword in the 1967 movie “The Graduate,” the catchword for math teachers today should be “fractions,”'

not the best or most complete resource, but a start.

"Two consecutive integers (eg 714 & 715) for which the sums of the prime factors of each are equal. Named for Babe Ruth and Hank Aaron bc. Ruth's career regular-season home run total was 714, a record which Aaron eclipsed"

Using a phase space to group economic outputs.

Checkers has been solved. Play the machine they built with that information.

Hungarians using quantum physics to serve true random numbers! rad. thx 18b.

Euler's 300th birthday was in April! Genius is too small a word for Euler: first user of functions, discoverer of e^iπ+1=0, and on and on. Respect, Euler.

averaged baking process. tasty & hilarious.

"Nicolas Bourbaki is the collective allonym under which a group of (mainly French) 20th-century mathematicians wrote a series of books presenting an exposition of modern advanced mathematics, beginning in 1935"

Whoa: "This terminology was originally coined by the Bourbaki group."

"The Institute For Figuring is an organization dedicated to the poetic and aesthetic dimensions of science, mathematics and the technical arts." [read: these guys are the best.]

one-line prime tester? (no way?) np-hard

Some cities are likfe fractals, some aren't. Author is Krier-ist and ♡'s Prince Charles, but makes good points about node homogeneity & etc.

We demand an architecture of quasi-crystals!

Paper giving overview of the properties of the gomoboc. The math isn't too hard, the first & last pages are most interesting to the non-mathematician

"There is only one thing which is more unreasonable than the unreasonable effectiveness of mathematics in physics, and this is the unreasonable ineffectiveness of mathematics in biology." and economics, history, etc

"The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research a

"In lists of numbers from many real-life sources of data, the leading digit is 1 almost one-third of the time, & larger numbers occur as the leading digit with less & less frequency ... Based on the plausible assumption that people who make up figures ten

Analogous to 'almost always.' The dart explanation illustrates the concept nicely.

Topologically transitive: given f:X->X, open sets A & B in X: ∃ n so that fⁿ(A) ∩ B ≠ ∅. In other words, you're breathing Caesar's last breath, & given an arbitrary X & enough time, X is the new Y for all Y.

"Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere" -Bertrand Russell. "I know numbers are beautiful. If they aren't beautiful, nothing is." -Paul Erdos

Fibonacci '1-55' by Mario Merzi (thx kio)

At 17 "he began to study what he thought was a new class of numbers, but instead he had independently developed and investigated the Bernoulli numbers". Hate it when that happens. Superhuman genius.

using the power of multiplication to generate "31,000,000,000 different shapes" composed of 6 sections, each of which has 144 or 12 different options. Handwaving connects it to world population size. History => demographics?

Negative zero does not, strictly speaking, exist. But it turns out that it's a useful thing to have lying around.

About 30,000 photos tagged with the empty set.

In 2D; the polygon of points closer to x than any other point. "John Snow used a Voronoi diagram in [uberfamous] 1854 [map] to illustrate how ... the Soho cholera epidemic [clusted around] the infected Broad Street pump"

"the Erdös Number Project studies research collaboration among mathematicians."

"free software environment for statistical computing and graphics"

Technically a wild sphere. The outer complement is not simply connected (!) (via Cabinet 20).

"Researchers ... have found that isolated indigenous peoples deep in the Amazon readily grasp basic concepts of geometry ... The results suggest that geometry is a core set of intuitions present in all humans ... Many of the references in our paper are fr

electronic edition of graph theory textbook

The waste dump event Emscherblick, briefly tetrahedrons in Bottrop is of the architect Wolfgang Christian in form of a three-lateral pyramid more sketched in the year 1995 more delighted and a freely accessible observation tower on the waste dump

way dumber than Tatlin

a drunk bird might forever wander around, never finding its nest

based on the following criteria: "the place the theorem holds in the literature, the quality of the proof, and the unexpectedness of the result."

Valuable structures' components are selected from such diverse springs as digital logic, conservation, rock and roll, telecommunications, obsolete consumer products, industrial design, grassroots democracy, number theory, composition theory, differential

this page uses uncredited wikipedia txt (or vice versa)

drilling square holes

three card monte hall!

summary of the Unabomber's dissertation @ UM

daily fractals

the convex polyhedra having regular faces and equal edge lengths (with the exception of the completely regular Platonic solids, the Archimedean solids, and the two infinite families of prisms & antiprisms). There exist exactly 92 Johnson solids.

notebooks of Indian math prodigy