# Let's start a thread for Useful Mathematical Formulae **URL:** \ **Category:** Miscellaneous and Personal Stuff I Must Share\ **Created:** [June 11, 2008, 9:06pm UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619 "2008-06-11T21:06:37Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Sampiro](https://avatars.discourse-cdn.com/v4/letter/s/2acd7d/32.png) [@Sampiro](https://boards.straightdope.com/u/Sampiro)\ **Post date:** [June 11, 2008, 9:06pm UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/1 "2008-06-11T21:06:37Z")
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)? ---
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [June 11, 2008, 9:35pm UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/2 "2008-06-11T21:35:25Z")
Close approximation of Pi for almost all practical purposes: 355/113 Approximate weight of US gallon of water: 8 1/3 lbs. ---
**Author:** ![tomndebb](https://avatars.discourse-cdn.com/v4/letter/t/b9e5f3/32.png) [@tomndebb](https://boards.straightdope.com/u/tomndebb)\ **Post date:** [June 11, 2008, 9:59pm UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/3 "2008-06-11T21:59:40Z")
An acre is one furlong by four rods. - What?\* ---
**Author:** ![Malacandra](https://avatars.discourse-cdn.com/v4/letter/m/45deac/32.png) [@Malacandra](https://boards.straightdope.com/u/Malacandra)\ **Post date:** [June 11, 2008, 10:15pm UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/4 "2008-06-11T22:15:02Z")
To convert Celsius to Fahrenheit within typical “weather” temperature ranges, double it and add thirty. (The error becomes larger if you try to use it for cooking temperatures. It’s exact at 10C = 50F.) ---
**Author:** ![Ol\_Gaffer](https://avatars.discourse-cdn.com/v4/letter/o/8e8cbc/32.png) [@Ol\_Gaffer](https://boards.straightdope.com/u/Ol_Gaffer)\ **Post date:** [June 11, 2008, 11:11pm UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/5 "2008-06-11T23:11:53Z")
[QUOTE=tomndebb] An acre is one furlong by four rods. - What?\* [/QUOTE] to further illustrate the beauty of surveying… 1 mile = 5280 feet 1 furlong = 660 feet (1/8 mile) 1 rod = 165 feet (1/4 furlong, 1/32 mile) 1 chain = 66 feet (1/10 furlong, 1/80 mile) 10 square chains (or 4 square rods or 1 square furlong) = 1 acre. ---
**Author:** ![Duck\_Duck\_Goose](https://avatars.discourse-cdn.com/v4/letter/d/50afbb/32.png) [@Duck\_Duck\_Goose](https://boards.straightdope.com/u/Duck_Duck_Goose)\ **Post date:** [June 11, 2008, 11:20pm UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/6 "2008-06-11T23:20:00Z")
You can use “pi times the diameter” to figure out how much concrete reinforcing wire you’ll have to cut off the roll with the hacksaw to make a tomato cage. Round pi off to three, since you probably don’t have a calculator in your garden tote and it doesn’t matter anyway. ---
**Author:** ![Incensed](https://avatars.discourse-cdn.com/v4/letter/i/eb8c5e/32.png) [@Incensed](https://boards.straightdope.com/u/Incensed)\ **Post date:** [June 11, 2008, 11:55pm UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/7 "2008-06-11T23:55:05Z")
[QUOTE=Ol’Gaffer] to further illustrate the beauty of surveying… …1 rod = 165 feet (1/4 furlong, 1/32 mile)… [/QUOTE] I thought 1 rod=16.5 feet=5.5 yards=1/40 furlong=1/320 mile. That’s how it’s used on every roll of barbed/woven wire I’ve ever seen, anyway…either that or I’ve put up 10x more fence than I’d previously thought. ---
**Author:** ![Enginerd](https://avatars.discourse-cdn.com/v4/letter/e/bcef8e/32.png) [@Enginerd](https://boards.straightdope.com/u/Enginerd)\ **Post date:** [June 12, 2008, 12:53am UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/8 "2008-06-12T00:53:27Z")
Yeah, there’s a factor of ten error somewhere in there. One square mile has 640 acres - by the **ol gaffer’s** units, it would only have 64 acres. 1 mile = 8 furlongs = 80 chains = 320 rods = 1760 yards = 5280 feet. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [June 12, 2008, 12:55am UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/9 "2008-06-12T00:55:45Z")
It’s occasionally useful to know that 2[sup]10[/sup] is approximately equal to 10[sup]3[/sup]. [QUOTE=Sampiro] 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. [/QUOTE] This is the value of the [binomial coefficient](http://en.wikipedia.org/wiki/Binomial_coefficient) C(8, 2). ---
**Author:** ![Xema](https://avatars.discourse-cdn.com/v4/letter/x/9de053/32.png) [@Xema](https://boards.straightdope.com/u/Xema)\ **Post date:** [June 12, 2008, 1:07am UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/10 "2008-06-12T01:07:05Z")
I like Heron’s formula for the area of a triangle: Let a, b and c be the lengths of the sides of a triangle Let p be half the perimeter: p = (a + b + c) / 2 The area is equal to the square root of p \* (p - a) \* (p - b) \* (p - c) ---
**Author:** ![Cub\_Mistress](https://avatars.discourse-cdn.com/v4/letter/c/ea666f/32.png) [@Cub\_Mistress](https://boards.straightdope.com/u/Cub_Mistress)\ **Post date:** [June 12, 2008, 1:28am UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/11 "2008-06-12T01:28:04Z")
Mine is really simple, especially next to some of the others that have been posted. I used to teach this as an emergency math lesson plan for 7th grade and up. figuring a tip: 10% tip: take the total of the food price and move the decimal one place to the left. 27.88 becomes $2.78 . Feel free to go to $2.75 or $3.00, close enough. 15% tip: divide the answer you got in step one in half and add to the answer in step one $27.88=2.75 plus 1.40 (close enough)= $4.15 20% tip: double the answer in step one $27.88= 2.75 plus 2.75= $5.50 ---
**Author:** ![TokyoBayer](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tokyobayer/32/13989_2.png) [@TokyoBayer](https://boards.straightdope.com/u/TokyoBayer)\ **Post date:** [June 12, 2008, 1:46am UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/12 "2008-06-12T01:46:56Z")
Always carry a cell phone with a calculator funtion. Helps when figuring out tips for lots of drinks. ---
**Author:** ![chacoguy](https://avatars.discourse-cdn.com/v4/letter/c/50afbb/32.png) [@chacoguy](https://boards.straightdope.com/u/chacoguy)\ **Post date:** [June 12, 2008, 2:06am UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/13 "2008-06-12T02:06:03Z")
The true speed limit can be calculated by adding 4mph to the posted speed for speeds posted less than 50mph or by adding 8mph to speeds posted greater than 50mph. So, where the posted speed limit is 45, the real speed limit is 49mph. I’ve been driving 83 on the interstates for year and never even turned a cops head. ---
**Author:** ![Yumblie](https://avatars.discourse-cdn.com/v4/letter/y/76d3ee/32.png) [@Yumblie](https://boards.straightdope.com/u/Yumblie)\ **Post date:** [June 12, 2008, 2:12am UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/14 "2008-06-12T02:12:23Z")
One year is about pi\*10^7 seconds. ---
**Author:** ![John\_Carter\_of\_Mars](https://avatars.discourse-cdn.com/v4/letter/j/2bfe46/32.png) [@John\_Carter\_of\_Mars](https://boards.straightdope.com/u/John_Carter_of_Mars)\ **Post date:** [June 12, 2008, 2:17am UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/15 "2008-06-12T02:17:34Z")
Lay out a 3,4,5 triangle to make a square corner. Useful in building anything rectangular. ---
**Author:** ![Ignatz](https://avatars.discourse-cdn.com/v4/letter/i/3be4f8/32.png) [@Ignatz](https://boards.straightdope.com/u/Ignatz)\ **Post date:** [June 12, 2008, 2:26am UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/16 "2008-06-12T02:26:21Z")
[QUOTE=Malacandra] To convert Celsius to Fahrenheit within typical “weather” temperature ranges, double it and add thirty. (The error becomes larger if you try to use it for cooking temperatures. It’s exact at 10C = 50F.) [/QUOTE] And to be more exact: C = 5/9 (F-32) and conversely, F = 9/5 F + 32 The sum of the squares of the two perpendicular sides of a right (90-degree) triangle equals the square of the long side (hypotenuse). If one of the perp sides is 3 units long and the other is 4 units long, then the hypo is 5 units long (3x3) + (4x4) = 5x5. 9+16=25. Thank Pythagoras for that theorem. ---
**Author:** ![Ol\_Gaffer](https://avatars.discourse-cdn.com/v4/letter/o/8e8cbc/32.png) [@Ol\_Gaffer](https://boards.straightdope.com/u/Ol_Gaffer)\ **Post date:** [June 12, 2008, 3:27am UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/17 "2008-06-12T03:27:44Z")
Well shoot… it appears that; although my mile, furlong, and chain are of normal size; my rod is significantly larger than standard. Thanks for the clarification \*_Enginerd_ and _Incensed_ - my cheat sheet has been revised. ---
**Author:** ![Ol\_Gaffer](https://avatars.discourse-cdn.com/v4/letter/o/8e8cbc/32.png) [@Ol\_Gaffer](https://boards.straightdope.com/u/Ol_Gaffer)\ **Post date:** [June 12, 2008, 3:29am UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/18 "2008-06-12T03:29:45Z")
Well shoot… it appears that; although my mile, furlong, and chain are of normal size; my rod is significantly larger than standard. Thanks for the clarification **Enginerd** and **Incensed** - my cheat sheet has been revised. ---
**Author:** ![NinetyWt](https://avatars.discourse-cdn.com/v4/letter/n/cc9497/32.png) [@NinetyWt](https://boards.straightdope.com/u/NinetyWt)\ **Post date:** [June 12, 2008, 4:07am UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/19 "2008-06-12T04:07:56Z")
[QUOTE=Ol’Gaffer] my rod is significantly larger than standard. [/QUOTE] How _you_ doin? 😛 ---
**Author:** ![Autolycus](https://avatars.discourse-cdn.com/v4/letter/a/22d042/32.png) [@Autolycus](https://boards.straightdope.com/u/Autolycus)\ **Post date:** [June 12, 2008, 4:26am UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/20 "2008-06-12T04:26:52Z")
F = MA. Force = Mass x Acceleration. I grant that it doesn’t come up too often in daily life for the average person, but it’s such a fundamental physics formula that I think it deserves mention. Also, the acceleration of gravity is 9.8 meter per second squared. [Next page](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619.md?page=2)