From time to time there really are occasions when I need to know a mathematical formula, and it can sometimes be a pain to google when I don’t know what the term is. My goal in this is to make a thread I can search for when I need one, so- please add any formulas and tell how they apply. Thankee.
I’ve seen this called "The “Number of Handshakes” Formula but the first word problem I heard that used it involved pictures, so I’ll go with that.
There are eight siblings. They’ve had group shots and individual shots made, but now they want to have a series of pictures made in which each sibling will be pictured with exactly one sibling until ultimately each sibling will have a picture of himself/herself one-on-one with each other sibling (i.e. A will have 7 pictures, one showing him standing with B, then with C, with D, with E, with F, with G, with H, and with I, and B will have a picture made with A, C, D, E, F, G, H, and I, etc.). Each sibling will have 7 pictures of themself in all. How many pictures will need to be made (not including copies for each sibling to have a picture)?
The handshake version is “8 people are in a room. If every person shakes hands with every other person one time, how many handshakes will occur?” A surprising number of people will instantly answer “64”, incidentally.
Since I’m not sure how to write it the way I would in a word processor it may seem clumsy, but the formula for this one is:
In the below X is the number of pictures needed, N = the number of siblings.
X = half the sum of N (N - 1) (I know that’s clumsy looking)
X = half the sum of 8 (7), or half of 56. There will need to be 28 pictures in order to have a shot of each sibling with each sibling.
The Rule of 72
Useful to know. The Rule of 72 tells you how long it will take money, if left alone, to double if the interest is compounded annually.
If you invest $1,000 at 4% interest, it will be $2,000 in 18 years ( 72/4 = 18).
What are some other useful formulas (not theoretical or things used in quantum physics but things that have everyday life uses)?