Prime numbers
What are they and why should we care about them? Well, they are the fundamental building blocks of all other numbers.
Brent Yorgey found what I think is perhaps the best way of displaying prime numbers: factor diagrams. Now we all know a prime number is a number that is only divisible by itself and one, but what does this really mean? It's really not all that intuitive.
A better way to think about prime numbers is that they are the numbers which can't be grouped into groups of the same size. Let's take a non-prime number, 12, as an example. This can be grouped into 2 groups of the same size, each group being of size 6. This can be done recursively, 6 can be grouped into 2 groups of size 3. So 12 can be grouped into 2 groups of 2 groups of size 3.
The animated gif above shows the factor diagrams for the numbers 10 through 20. Notice that the prime numbers all form rings. This is because these are the numbers that cannot be grouped into subgroups that have the same size!
In my spare time a few years ago I made a little program which smoothly animates the factor diagrams for all numbers. Here is the link for your viewing pleasure. Careful! You may end up hypnotising yourself.
you're not kidding about getting hypnotized
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Thoroughly enjoyed that, I'd be interested in reading your code too. :)
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I'll do a follow up post on how it's done. It's some really nice recursive code.
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Sweet.
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A very graphic way of showing it. Easy and clear.
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This is amazing.
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Wow i bet the patterns even have intrinsic meaning!!! upvoted
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you are going in my top 5 honorable mentions of steemit with this post. I just loved it.
the visualization is dope... keep it up mate.
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That was such a kind thing to say. It really made my day.
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Always cool to see math stuff being made accessible to everybody :-)
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Beautiful. What about even and odd bases in finite (all numbers consists of N or less digits in base B) arithmetic. Is the sign always defined? What about other operations, can we define absolute value or division or multiplication cleanly?
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