Mr Bear Posted October 20, 2015 Share Posted October 20, 2015 Ahh, takes me back to the days of fractint on DOS. An entirely integer based fractal generator designed for high speed. You could have lots of fun adjusting the numbers to get new fractals. https://en.wikipedia.org/wiki/Fractint Link to comment Share on other sites More sharing options...
Merkin Posted October 20, 2015 Share Posted October 20, 2015 I once had so much fun doing this that I shat myself. Good times. Ahh, takes me back to the days of fractint on DOS. An entirely integer based fractal generator designed for high speed. You could have lots of fun adjusting the numbers to get new fractals. https://en.wikipedia.org/wiki/Fractint Link to comment Share on other sites More sharing options...
thebees Posted October 20, 2015 Author Share Posted October 20, 2015 Perhaps it's about time I changed it. How about to this: Maybe get a bit more maths discussion going on here. For me this is a thing of beauty. An elegant equation that connects arguably the 5 most important numbers in the whole of maths. Zero and one, when combined with the operation of addition and its inverse define the integers, and the use of division gives you all rational numbers. Combine these numbers into polynomial equations and some of them will have solutions that need algebraic irrational numbers, and imaginary numbers. i is defined as one of the solutions to x^2 = -1. That leaves pi and e, which are the 2 most important transcendental numbers, that turn up naturally in maths as the circumference:diameter ratio in a circle, and the base of natural logarithms respectively. Proving that pi is irrational is awkward. e is easier, but proving e's transcendental nature is more difficult. Once you have that last point however Euler's equation implies pi's transcendental quality. Plenty more for you to go on there thebees if you're so inclined. I'll have to wait until MrBees gets home from work Link to comment Share on other sites More sharing options...
wrighty Posted October 20, 2015 Share Posted October 20, 2015 I can produce reams of this stuff if anyone's interested. Next topic, I reckon, should be a proof of the existence of irrational numbers. Something the Pythagoreans found abhorrent. After that I'd do Cantor's diagonal argument proving the infinity of natural numbers is not as big as the infinity of real numbers. From there we're not too far from the Banach-Tarski paradox. Link to comment Share on other sites More sharing options...
paswt Posted October 21, 2015 Share Posted October 21, 2015 Don't tell Merkin ! Link to comment Share on other sites More sharing options...
squelch Posted October 21, 2015 Share Posted October 21, 2015 Perhaps it's about time I changed it. How about to this: Maybe get a bit more maths discussion going on here. For me this is a thing of beauty. An elegant equation that connects arguably the 5 most important numbers in the whole of maths. Zero and one, when combined with the operation of addition and its inverse define the integers, and the use of division gives you all rational numbers. Combine these numbers into polynomial equations and some of them will have solutions that need algebraic irrational numbers, and imaginary numbers. i is defined as one of the solutions to x^2 = -1. That leaves pi and e, which are the 2 most important transcendental numbers, that turn up naturally in maths as the circumference:diameter ratio in a circle, and the base of natural logarithms respectively. Proving that pi is irrational is awkward. e is easier, but proving e's transcendental nature is more difficult. Once you have that last point however Euler's equation implies pi's transcendental quality. Plenty more for you to go on there thebees if you're so inclined. I'll have to wait until MrBees gets home from work Don't worry thebees. It is only a formula wrighty uses to make sure his patients legs are the same size after he operates. Link to comment Share on other sites More sharing options...
thebees Posted October 22, 2015 Author Share Posted October 22, 2015 No it's not, it's to with imaginary numbers and something else I don't really understand Mrbees explained it when he came home from work, I declined to comment on the thread further... I understood it all but not well enough to remember it or be able to retell, bit like most things really, yes yes I understand all of that but I don't understand it in the way you want me to Link to comment Share on other sites More sharing options...
wrighty Posted October 22, 2015 Share Posted October 22, 2015 No it's not, it's to with imaginary numbers and something else I don't really understand Mrbees explained it when he came home from work, I declined to comment on the thread further... I understood it all but not well enough to remember it or be able to retell, bit like most things really, yes yes I understand all of that but I don't understand it in the way you want me to Euler's equation is great, but to fully understand it I think you need a good grasp of Taylor series expansions, complex numbers and trigonometry! Try this one instead Bees. The Pythagoreans liked everything to be harmonious, including numbers. They liked whole numbers, and rational numbers - fractions basically, numbers that can be expressed as a ratio of two others. This worked for musical intervals - in the Pythagorean scale a perfect fifth (in rock and metal that's your basic power chord!) had a frequency ratio of 3:2, a perfect fourth was 4:3 and so on. Then they came across a problem - what's the distance from corner to opposite corner of a square with side length of 1? Everybody knows Pythagoras' formula for a right angled triangle (a2+b2=c2), so the problem was to find a number (and for these guys it had to be rational) such that when multiplied by itself gave 2 - 12+12=?2. Trouble is it's impossible, and here's why. Assume such a number exists, a fraction p/q, such that (p/q)2=2. Moreover, the fraction p/q is fully cancelled, so p and q have no factors in common. Therefore p2/q2=2 and so p2=2q2. This means that p2 must be an even number which means p must be an even number. You could then write p as being equal to 2r for some other whole number r. Therefore (2r)2=2q2 which simplifies to q2=2r2 which means that q must be an even number also. So p and q are both even, which means that p/q was NOT fully cancelled as stated in the assumption. The only conclusion of all this is that a number p/q that when squared is equal to 2 cannot exist. So the Pythagoreans had come across a simple geometrical quantity - the diagonal of a square - that couldn't be written as a ratio of 2 numbers. This is probably the first demonstration of a so-called irrational number - one that cannot be written down as either or a fraction or a terminating/recurring decimal. The square root of 2 is 1.41421356237309...... and the numbers could literally go on for ever. This blew the Pythagoreans' minds. More stuff here. Link to comment Share on other sites More sharing options...
Neil Down Posted October 26, 2015 Share Posted October 26, 2015 Numberphile explains: Watching that video, for some reason I keep thinking of this one: What the hell did she just say (or not say)? Link to comment Share on other sites More sharing options...
Bobbie Bobster Posted October 26, 2015 Share Posted October 26, 2015 That's Numberwang! Link to comment Share on other sites More sharing options...
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