Saturday, January 15, 2011

Divisors of Integers

Divisibility and primes

What properties can integers ( 0, 1, 2, ….) have?

One property is divisibility: We say that integer a divides integer b, notation a∣b, if there is an integer c so that a*c=b. If such an integer does not exist a∤b.

We can plot b horizontally and a vertically we can put a∎ in when a∣b:

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This starts showing some patterns: the lines like the diagonal originating
On this page I show a plot on 'millimeter paper' of numbers and their divisors.
X and Y pairs are like:


The X axis shows an integer, and the Y axis too. The square is black when y divides x. alt : It seems your browser does not support SVG. Consider using Google Chrome or another SVG enabled browser, I don'know why this fails in IE.... This shows both patterns and a kind of chaos: for me it is like a bubble chamber revealing the tracks of subatomic particles and cosmic mysteries. There is a beautifull site devoted to these patterns: divisorplot.com.
This version allows you to travel alang the number line at varying speed (the graphics are not yet optimal) clicking < or > you can increase or decrease speed. Watch the stroboscopic effects!

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