In case anyone wants a copy, here’s Numerical Mathematics and Computing, 6th ed. as a free pdf.
Series of posters created for the love of math, nature, art, and education.
Prints available: http://meganemoore.storenvy.com/
Views of the Tesseract Poster by theFOUNDRY. A tesseract is the four-dimensional analog of the cube; the tesseract is to the cube as the cube is to the square. Just as the surface of the cube consists of 6 square faces, the hypersurface of the tesseract consists of 8 cubical cells.
This is the largest prime number ever discovered.
2^57,885,161 - 1 is the exact number. Like all primes, 2^57,885,161 - 1 is divisible only by itself and 1. But this prime is special. It’s a Mersenne prime—so called because it can be written in the form 2^p - 1, where p is also prime. Prime numbers of this form are named after French monk/mathematician Marin Mersenne, who studied them at the beginning of the 17th century.
Dots are used to represent the adjacency between digits. Each digit 0-9 is represented by a colored segment. Dots assigned to a segment represent digits that follow the digit represented by the segment. The position of the dot is roughly the position within the number that the digit appears.
Art by by Cristian Ilies Vasile.
Hope you like it :)
Ok so suppose we have ourselves a map and we want to colour it in. The only rule is that two neighboring countries can’t be the same colour (obviously because then we couldn’t tell them apart!). Sounds easy enough right? But buying new colours of paint is expensive business and so we want do it in the smallest number of colours possible. Here’s the question then: how many colours do we need to get? More than this, what’s the minimum number we need to colour in any general map?
Ok so let’s start simple. Let’s get ourselves two colours: red and blue. Is this enough to colour our map following the rule? No! Why not? Well look in the very simple map below - we can’t colour the “?” box; it neighbours the blue one so it can’t be blue and it neighbours the red one so it can’t be red. Uh oh!
Looks like we need to get ourselves a new colour then, so let’s get a green involved. We can now colour the “?” green and we’re done! But are these 3 colours enough? Well actually no again! Why not? Well look at the map below, once more we’ve got a problem here. What colour can this new “?” box be?
Seems we’re going to have to get ourselves another colour; let’s get a nice pretty purple. We can now colour this “?” box purple and wahey, we’re done.
We’ve now got 4 colours in our arsenal. Is this enough to colour in our map? Well, four colours is certainly enough to colour even really complicated maps like the one in the picture below - but is it enough to colour any map?
There’s a really key mathematical concept floating around here: we want to see if every single possible map can be coloured in with just 4 colours. Showing that it’s true for one example (like the one we’ve done above) isn’t enough - we somehow have to prove that it’s true for any map. Can you see the difference here?
So how do we do it?