Question

Anyone know any clever math tricks?

Answer 1

Clever math tricks regarding what topic in mathematics? I know a few but they do not apply to the same subject area...

Answer 2

For what ?? Calculation , geometry etc ???

Answer 3

Doesn't matter, all math.

Answer 4

Preferably calculus or differential equations, but really anything. Trigonometry, even something really simple. Doesn't matter, as long as you think it's clever.

Answer 5

Hmmm.... there's one that has to do with calculating numbers from 1-100 (function-wise) but I forgot how to do it...

Answer 6

@Kainui
When multiplying a two digit number by 11, the result is always first digit of the number, sum of the two numbers, last digit. Example: 11 x 18 is 198. 11 x 32 is 352. If the sum of the digits comes out greater than nine, add one to the first digit. 11 x 78 is 858.

Haha, I find it useful sometimes..

Answer 7

Ahh, so like you want to add up all the numbers:\[S=1+2+...+99+100\]so you can say it this way too:\[S=100+99+...+2+1\]

So you add up each one to get:

\[2S=101+101+...+101+101\]

And since we're counting to 100, there are 100 of those 101's.\[2S=101*100\]

So divide both sides by 2 to get your answer:
\[S=\frac{ 100*101 }{ ? }\]

Answer 8

Are you talking to me? o_o

Answer 9

@kittiwitti1 Yeah!

@liliegirl That's a pretty good trick actually thanks. =)

Answer 10

@Kainui Generalize the trick you just used.

Answer 11

Come up with the most general form it could have.

Answer 12

Ah, okay o.o

Answer 13

Here are a few threads of mine:

http://openstudy.com/users/aravindg#/updates/506fb24ae4b060a360ffce23
http://openstudy.com/users/aravindg#/updates/506da7f0e4b088f3c14d687d
http://openstudy.com/study#/updates/50ed4e29e4b0d4a537cd1595

Also you can refer to this one by ryan:

http://openstudy.com/study#/updates/515de89be4b02fd2c0ce28a2

Answer 14

@wio how general is most general? For instance, I believe there's some sort of weird way it generalizes to sums of numbers to non integer powers with bernoulli numbers.

Answer 15

Here is a pretty good one and not too well known
http://www.1728.org/fibonacci.htm
Yes, that is my website.

Answer 16

I like that, why is this true though?

Answer 17

It's just the way the Fibonacci sequence works. If you start with the first number being x, even that will obey the 7th number rule.
Still that does not make it a mathematical proof does it? No.

Answer 18

I've never even heard of the 7th number rule. But I suppose as long as you know the sequence it's not too hard to look at it.

Answer 19

A trick remains clever as long as it is a black-box. Once you get to know how it works; it becomes obvious. So I don't know which trick should I put here. Still glad this feed came up :)