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Pretend you're me and you're in math class. Actually... nevermind, I'm sick so I'm staying home today

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so pretend you are Stanislaw Ulam instead. What I am about to tell you is a true story.

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So you are Stan Ulam and you're at a meeting but there's this really boring presentation so

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of course you're doodling and, because you're Ulam and not me, you really like numbers...

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I mean <i>super</i> like them. So much that what you're doodling is numbers, just counting

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starting with one and spiralling them around. I'm not too fluent in mathematical notation so

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so i find things like numbers to be distracting, but you're a number theorist and if you love numbers

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who am I to judge? Thing is, because you know numbers so intimately,

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you can see beyond the confusing, squiggly lines you're drawing right into the heart of numbers.

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And, because you're a number theorist, and everyone knows that number theorists are

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enamoured with prime numbers( which is probably why they named them "prime numbers"),

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the primes you've doodled suddenly jump out at you like the exotic indivisible beasts they are...

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So you start drawing a heart around each prime. Well... it was actually boxes but in my version

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of the story it's hearts because you're not afraid to express your true feelings about prime numbers.

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You can probably do this instantly but it's going to take me a little longer... I'm all like -

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"Does 27 have factors besides one and itself? ... o.0 ... Oh yeah, it's 3 times 9, not prime."

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"Hmmm what about 29...? pretty sure it's prime."

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But as a number theorist, you'll be shocked to know it takes me a moment to figure these out.

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But, even though you have your primes memorised up to at least 1000 that doesn't change that

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primes, in general, are difficult to find.

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I mean if I ask you to find the highest even number, you'd say, "that's silly, just give me

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the number you think is the highest and i'll just add 2.... BAM!!"

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But guess what the highest prime number we know is? 2 to the power of 43,112,609 - 1.

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Just to give you an idea about how big a deal primes are, the guy that found this one won

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a $100,000 prize for it!

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We even sent our largest known prime number into space because scientists think

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aliens will recognise it as something important and not just some arbitrary number.

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So they will be able to figure out our alien space message...

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So if you ever think you don't care about prime numbers because they're 'not useful',

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remember that we use prime numbers to talk to aliens, I'm not even making this up!

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It makes sense, because mathematics is probably one of the only things all life has in common.

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Anyway, the point is you started doodling because you were bored but ended up

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discovering some neat patterns. See how the primes tend to line up on the diagonals?

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Why do they do that?... also this sort of skeletal structure reminds me of bones so

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lets call these diagonal runs of primes: Prime Ribs!

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But how do you predict when a Prime Rib will end? I mean, maybe this next number is prime...

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(but my head is too fuzzy for now this right now so you tell me.)

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Anyway...Congratulations, You've discovered the Ulam Spiral!

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So that's a little mathematical doodling history for you.

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Yyou can stop being Ulam now... or you can continue. Maybe you like being Ulam. (thats fine)

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However you could also be Blaise Pascal. Here's another number game you can do using

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Pascal's triangle.(I don't know why I'm so into numbers today but I have a cold so

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if you'll just indulge my sick predelections maybe I'll manage to infect you with my enthusiasm :D

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Pascal's Triangle is the one where you get the next row in the triangle by adding two adjacent

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numbers. Constructing Pascal's Triangle is, in itself a sort of number game because it's not just

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about adding, but about trying to find patterns and relationships in the numbers so you

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don't have to do all the adding.

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I don't know if this was discovered through doodling but it was discovered independantly in:

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France, Italy, Persia, China and probably other places too so it's possible someone did.

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Right... so I don't actually care about the individual numbers right now.

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So, if you still Ulam, you pick a property and highlight it(e.g. if it's even or odd)

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If you circle all the odd numbers you'll get a form which might be starting to look familiar.

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And it makes sense you'd get Sierpinski's Triangle because when you add

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an odd number and an even number, you get an odd number.

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(odd + odd) = even and (even + even) = even... So it's just like the

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crash and burn binary tree game. The best part about it is that, if you know these properties, you can

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forget about the details of the numbers

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You don't have to know that a space contains a 9 to know that it's going to be odd.

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Now, instead of two colours, let's try three. we'll colour them depending on what the remainder is

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when you divide them by three(instead of by two).

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Here's a chart! :)

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So, all the multiples of three are coloured red, remainder of one will be coloured black and

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remainder of two will be coloured green. The structure is a little different from Sierpinski's Triangle

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already but I'm tired of figuring out remainders based of individual numbers, so

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Let's figure out the rules... If you add up two multiples of three you always get

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another multiple of three( which is the sort of fact you use everday in math class)

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However, here this means (red + red) = red.

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and when you add a multiple of three to something else, it doesn't change it's remainder.

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So, (red + green) = green and (red + black) = black.

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(remainder 1 + remainder 1) = remainder 2, (remainder 2+ remainder 2) = remainder 4

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and the remainder of 4 divided by 3 is one and (1+2) = 3 remainder 0. (whew...)

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The bottom line is you're making up some rules as to what coloured dots combine to

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produce which other coloured dots and then you're following those rules to their

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mathematical and artistic conclusion...

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The numbers themselves were never necessary to get this picture.

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Anyway, those are just a couple of examples of number games that are out there but you should

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also try making up your own. For example, I have no idea what you'd get if you

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highlighted the prime numbers in Pascal's Triangle, maybe nothing interesting(who knows...)

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Or, what happens if, instead of adding to get the next row, you start with a two(and a sea of invisible ones)

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and multiple two adjacent numbers to get the next row.

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I've no idea what hapens there either or if it's already a 'thing' people do.

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(Hmmm? o.0 Powers of two...)

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I know another way to write this. Ok, that makes sense.

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Then there is also a thing called Floyd's Triangle where you put the numbers like this...

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Maybe you can do something with that as well.

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... Man, it seems like everyone has a triangle these days...

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I'm going to take a nap... ZZZzzz...