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# Beauty of Maths!

just-in
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
Bikerman
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
just-in
Hello Chris,

Thanks for the information and the excellent links.

Hope more poeple will share many thing like this here.

regards

Justin
Tac-Tics
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.
mephisto73
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
Indi
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.
Bikerman
 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:
asnani04
great man! great observation!
codersfriend
whoah I like the patterns.. I wonder how do they get discovered.. what's behind all of these findings?
mukesh
great trick
_AVG_
I agree that Euler's equation is the most beautiful mathematical formula (in fact, a lot of Euler's stuff: including the Euler polyhedron formula, the Euler circle, etc. are very elegant)
Besides Euler, I also find Cauchy's work in Complex Analysis very elegant. Otherwise, there's Gauss and Riemann whose work is also "beautiful" in a mathematical sense. And of course, Georg Cantor's Transfinite numbers are also quite a treat and perhaps the most extraordinary feat of mathematics and reason over intuition till date.
therimalaya
Very amazing facts. I've never noticed them.
orangbaik
how bout fibonacci, is it considered math or myth ?
PlasticCard8
 just-in wrote: 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

Great tricks, amazing ideas
likeabreeze
yeah, good post.
It's really difficult for people to appreciate the beauty of Maths when they don't do well in Maths Exams.
setfirework
This is a funny interesting part of maths. Enjoy the beauty of mathematics in sequential numbers.
Btw,Math can be so useful in many ways, without it, I don't know how I'd survive .
hspb
It is very interesting
spinout
I think the biggest math discorevy for mankind was... tataaa!!: 0

And today that number, zero, is so natural. But once upon a time it was not!!!

Well, as a former teacher, the math teaching was different that other classes... If you did wrong, then you are no more than wrong - and there is no escape. Hehe, bite the bullet!!! So if you want to be a math teacher have this in mind. OK, there are some math that are a bit vague in its form so you might survive an error but mostly you bite the bullet. I still remember some cases by heart actually... Cool stunt on a party... or errrhhh too nerdish

Hm, all those math studies and little use... i had an idea once of an invention using math to signals thru a sound system for copyin sound - had it worked out but... 2 things stopped me. Laws n my heart - why bother to steal other persons creations? This was 20 years ago and still no product is close, I have seen an attempt from an guitaramp company, yoiu use cables and must have access to the amp you want to copy... My solution was just better with just a microphone. anyhow, have a gr8 friday night!
SonLight
 orangbaik wrote: how bout fibonacci, is it considered math or myth ?

The Fibonacci sequence, A[n] = A[n-1] + A[n-2], 1, 1, 2, 3, 5, 8, 13, ... and the Fibonacci ratio, 1.618:1 has a number of mathematical applications. The Greeks called the ratio, phi = 1.618:1 the "golden ratio", because it is visually pleasing when an object has length = phi * width, for example. Fibonacci numbers show up many places in nature.

On the other hand, some push the power and beauty of the ratio to great lengths and wind up spouting mystical nonsense. I would recommend reading about it on a math site before trying to evaluate artistic and supposedly beneficial applications of the ratio.
spinout
Fibonacci is math, and ununderstood math by many!
The key to understand music is Phi - the octave is double wave length but you can't explain the tones between exactly (temperation) if you don't have phi!
mshafiq
Interesting informations
playfungames
Quote interesting indeed. Not sure how it would serve us in real life maths but I find it great to impress someone, mathematically.
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