was waiting that someone will ask it. Was sick of same question about computer guys, and programmers. Let me tell you some- \pi \neq 22/7 0.999999.......=1 The Largest known prime number til this date is 2^{57885161}-1 . It has 17,425,170 digits. It is a Mersenne prime Balls can be square too. Everything you can do with ruler and compass, you can do with compass alone. For more info read this- Geometric construction with the compass alone The most famous theorem of mathematics- Pythagorean theorem- whose NCERT proof troubles school kids most, has more than 500 proofs, may be more than 1000s. Eli Maor wrote a book in which he showed 367 proofs that were distinct enough to bother writing about separately. (The Pythagorean Theorem) Yes, 1>0 needs a proof. 0 can be equal to 2 , if you work in field of characterstic 2 i.e. \mathbb{Z}_2 . Jordan Curve Theorem- It is a very tough theorem to prove that every simple closed curve divides a region into two parts, interior and exterior. A mathematician Kurt Godel has actually proved that God exist!! The Proof- Gödels ontological proof A shape with finite volume must have finite surface area- False Gabriels Horn is an example. There are more rational numbers than there are integers- False i^i is real number. The Fibonacci sequence is encoded in the number 1/89- ( 1/89 = 0.01 + 0.001 + 0.0002 + 0.00003 + 0.000005 + 0.0000008 + 0.00000013 + 0.000000021 + 0.0000000034 ...) Too much beauty in one pic.. 1+1/2+1/4+1/8+ \ldots \ldots =2 Joke based on this- Infinitely many mathematicians walk into a bar. The first says, Ill have a beer. The second says, Ill have half a beer. The third says, Ill have a quarter of a beer. The barman pulls out just two beers. The mathematicians are all like, Thats all youre giving us? How drunk do you expect us to get on that? The bartender says, Come on guys. Know your limits. 1+1/2+1/3+1/4+ \ldots \ldots =\infty Joke base on this- An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third orders a third of a beer. The bartender bellows, Get the hell out of here, are you trying to ruin me? A pizza that has radius “z” and height “a” has volume Pi × z × z × a. If you shuffle a pack of cards properly, chances are that exact order has never been seen before in the whole history of the universe. Explanation- A deck of 52 cards can be ordered in 52! = 52 \times 51 \times 50 \times...\times 2 \times 1 ways. But 52! is a very large number: larger than 8 \times 10^{67} . How big is this number? Well, someone shuffling a deck of cards once per second since the beginning of the universe (believed to be about 14 billion years ago) would not have shuffled the deck more than 10^{18} times. Zero is even number. Three Interesting Theorems- The four-color theorem states that any map in a plane can be colored using four-colors in such a way that regions sharing a common boundary (other than a single point) do not share the same color. Brouwer’s Fixed Point Theorem (implication) says that if you take two sheets of paper, one lying directly above the other. If you crumple the top sheet (do not rip or tear the sheet), and place it on top of the other sheet, then there must be at least one point on the top sheet that is directly above the corresponding point on the bottom sheet! Do you believe that? Hairy Ball Theorem (Real life implication)- It states that given a ball with hairs all over it, it is impossible to comb the hairs continuously and have all the hairs lay flat. Some hair must be sticking straight up! It took Russell and Whitehead several hundred pages to prove that 1+1=2 in Principia Mathematica. Divisibility by 7- Remove the last digit, double it, subtract it from the truncated original number and if the result is a multiple of seven, then so is the original number, keep repeating till number is small enough. Random walk theory- A result by Polya states that in one or two dimension, a random walker returns to the origin infinitely many times but only a finite number of times in dimension 3 (or greater). Thus they say- A drunk ant or a drunk man will always reach home but a drunk bird might not! Mathematician exclusive jokes- The B in Benoît B. Mandelbrot stand for Benoît B. Mandelbrot. (If you know a little about Fractals) My Favourite- A comathematician is a device for turning cotheorems into ffee. (Hint look up Paul Erdos quotes). I went to visit him while he was lying ill at the hospital. I had come in taxi cab number 14 and remarked that it was a rather dull number. No he replied, it is a very interesting number. Its the smallest number expressible as the product of 7 and 2 in two different ways.- Hint- Ramanujans most famous story. Prof: Give an example of a vector space. Student: V Why did the mathematician name his dog Cauchy? Because he left a residue at every pole. :P The primary reason Bourbaki stopped writing books was the realization that Lang was one single person. Let epsilon
Posted on: Tue, 30 Dec 2014 18:06:20 +0000
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