Hi,
I am not so intelligent to think so much. One of my friend forwareded this to me. I find it interesting and thought of sharing with you guys. Maths has many wonders this way. If you have any such things post them here. Lets explore the world of maths.
Beauty of Maths!
1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321
1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 +10= 1111111111
9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888
Brilliant, isn't it?
And finally, take a look at this symmetry:
1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111=12345678987654321
Here's some material to keep number fans happy.
Huge list of numbers and interesting facts about them
There is much interesting stuff arising from the Pythagorean school in ancient Greece. Numbers were seen by the Pythagoreans as divine insomuch as they represented the world in numeric ratios so that philosophers could contemplate the beauty of creation without having to muck around with tape measures and other crude measuring devices. The pythagoreans believed that certain number ratios were divine and each number had a significance which was intrinsic to the number, so for example :
The number one : the number of reason.
The number two: the first even or female number, the number of opinion.
The number three: the first true male number, the number of harmony.
The number four: the number of justice or retribution.
The number five: marriage.
The number six: creation
The school thought that any physical quentity could be reduced to a simple ratio which would correspong to the harmonic geometric or arithmetic ratio as follows:
Allowing A , G, and H denote the arithmetic, geometric and harmonic means, the Pythagoreans called the proportion A:G=G:H the perfect proportion.
The major blow to the school came with the discovery of irrational or incommensurable numbers. This was a fundamental blow to the whole system of pythagoras and was reputed to have been the cause of at least one murder (Hippasos) - because he leaked the secret of the demonic irrationals which were almost blasphemous to the school.
An irrational number is one which cannot be expressed as the ratio of two integers. They are also odd and even at the same time. The pythagoreans called them 'arrhetos' meaning unspeakable.
The most elegant proof that I know of for demonstrating irrationals is one I read in Koestler's masterly book 'The Sleepwalkers' many years ago and goes as follows:
http://camres.frih.net/resources/math/irrational.htm
Regards
Chris Hello Chris,
Thanks for the information and the excellent links.
Hope more poeple will share many thing like this here.
regards
Justin
Fundamental Theorem of Interesting Numbers:
There are no natural numbers which are not interesting.
Proof:
Let x be the smallest uninteresting number. Since being the smallest uninteresting number is an interesting property for x to have, we must conclude that indeed x IS interesting. Since this assumption leads to a contradiction, we can conclude that no natural number is uninteresting and thus, all natural numbers ARE interesting.
My favourite math phenomenon is the golden ratio and the fibonacci sequence. It is infinately interesting and you can find out more about it here: http://en.wikipedia.org/wiki/Divine_proportion By far the most amazing and beautiful thing in all of mathematics is the Euler identity:
It links some of the most fundamental constants in all of mathematics all in one. e and π are two of the most famous and most commonly used irrational numbers. i is the basis for complex (imaginary) numbers. And 1 and 0 are the two most important numbers.
One each of the basic arithmetic operations is present, representing the basis operations for all of arithmetic - addition (subtraction is just addition by a negative number), multiplication (division is just multiplication with one number raised to the power -1) and exponentiation.
It also links several conceptual fields. π is fundamental to geometry and trigonometry. e is the natural base, and occurs a lot in limits, number theory, infinite series and so on. i is the imaginary base unit (√(-1)) and occurs a lot in calculus and the analysis of periodic functions and allows for the closure of algebra by allowing solutions for all polynomial functions.
And it does all this in a formula that on the surface is so simple that anyone with basic math skills can understand it, but is conceptually so difficult that you're never quite sure whether or not you really understand it. | Indi wrote: |
By far the most amazing and beautiful thing in all of mathematics is the Euler identity:
|
Difficult to argue with that, particularly since one of my heros in science - Feynman - would have agreed I think.
Others worthy of consideration (IMHO, would be :
Archimedes recurrance:
The Riemann hypothesis:
and 
implies 
Gaussian Interval
Mandlebrot recursion:
