Can anyone please tell me something very interesting about maths. It could be an amazing or unbelievable thing, some good shortcut trick or anything which I will like very much. I will also tell you some if you tell me.:)
Practice makes a man perfect.
There is no substitute to hard work
All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam
This might be interesting to you. I certainly find it interesting.
Start with the Fibonacci sequence:
1, 1, 2, 3, 5, 8, 13, 21, 34, .....
Divide each term by the one before:
1/1 = 1
2/1 = 2
3/2 = 1.5
5/3 = 1.6666
8/5 = 1.6
The numbers converge on the golden ratio (phi) ; oscillating either side of that number.
If you compute 1/1, 1/2, 2/3, 3/5, 5/8, .......
the numbers converge to phi - 1, which is also 1/phi
Apparently, the sequence (of rationals converging on an irrational) has a special property (which I've forgotten for the moment) which means that a plant (such as a sunflower), growing a seed head from the centre, and with angular separation atan(phi), will be least likely to form cleavage planes which might cause the seed head to fall apart. So nature discovered the property first!
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Perhaps the most interesting thing that I ever saw was the Monty Hall problem. Not only does it have mind boggling probability, EM, the worlds highest IQ, tons of differing opinions, it has one more thing...goats! Yes, math ain't nothing without a couple of stinky goats thrown in.
The most amazing things about it, were all personal. I became further convinced that EM was the only way to go if one desired to get the right answer an infuriating amount of times. Also, we were 2 of only 4 people in the world who knew that those Stanford and Duke university guys were not arguing with Marilyn. That would have been difficult enough, they were arguing with their own methods and colleagues who had hashed this problem to death in a statistics journal, many years before. RIPOSTP.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.