# 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:** 3
**Author:** ![BMalion](https://avatars.discourse-cdn.com/v4/letter/b/e274bd/32.png) [@BMalion](https://boards.straightdope.com/u/BMalion)\ **Post date:** [June 13, 2008, 12:15pm UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/41 "2008-06-13T12:15:49Z")
What’s the tonic, subdominant and the dominant? 1,4 and 5 _duh!_ ---
**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 13, 2008, 1:37pm UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/42 "2008-06-13T13:37:42Z")
[QUOTE=Malacandra] And “Minus forty” is the temperature for which you don’t need to give the scale (use either formula above and substitute F=C). [/QUOTE] Plus, it’s almost exactly the temperature mercury freezes at. ---
**Author:** ![NinetyWt](https://avatars.discourse-cdn.com/v4/letter/n/cc9497/32.png) [@NinetyWt](https://boards.straightdope.com/u/NinetyWt)\ **Post date:** [June 13, 2008, 2:02pm UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/43 "2008-06-13T14:02:07Z")
[QUOTE=HeadNinja] if you take someone’s hourly rate of pay and multiply it by 2000 you have a decent approximation of their annual wage. (this obviously works in the other direction as well) [/QUOTE] I thought that was 2080? 52 work-weeks times 40 hours. ---
**Author:** ![Leaffan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leaffan/32/299_2.png) [@Leaffan](https://boards.straightdope.com/u/Leaffan)\ **Post date:** [June 13, 2008, 2:23pm UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/44 "2008-06-13T14:23:45Z")
[QUOTE=NinetyWt] I thought that was 2080? 52 work-weeks times 40 hours. [/QUOTE] Some people only get paid for a 37.5 hour work week, so it evens out. Multiplying by 5 is the same as taking half and moving the decimal place. 5 X 422 = 2110, for example. You can approximate easily for other numbers too. Multiplying by 3 approximates to taking a third and moving the decimal, etc. ---
**Author:** ![NinetyWt](https://avatars.discourse-cdn.com/v4/letter/n/cc9497/32.png) [@NinetyWt](https://boards.straightdope.com/u/NinetyWt)\ **Post date:** [June 13, 2008, 2:28pm UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/45 "2008-06-13T14:28:04Z")
[QUOTE=Leaffan] Some people only get paid for a 37.5 hour work week, so it evens out. [/QUOTE] Color me surprised. Pour quoi? Are they not getting a paid lunch? ---
**Author:** ![Malacandra](https://avatars.discourse-cdn.com/v4/letter/m/45deac/32.png) [@Malacandra](https://boards.straightdope.com/u/Malacandra)\ **Post date:** [June 13, 2008, 2:47pm UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/46 "2008-06-13T14:47:36Z")
[QUOTE=NinetyWt] I thought that was 2080? 52 work-weeks times 40 hours. [/QUOTE] That’d be why he said “decent approximation”, then - 4% out ain’t bad. [QUOTE=NinetyWt] Color me surprised. Pour quoi? Are they not getting a paid lunch? [/QUOTE] May differ from country to country, but I’ve worked 37.5 (or 37) hour weeks many times. ---
**Author:** ![Leaffan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leaffan/32/299_2.png) [@Leaffan](https://boards.straightdope.com/u/Leaffan)\ **Post date:** [June 13, 2008, 2:56pm UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/47 "2008-06-13T14:56:20Z")
[QUOTE=NinetyWt] Color me surprised. Pour quoi? Are they not getting a paid lunch? [/QUOTE] Correct. We don’t get paid for lunch here. I am paid for 8 hours a day; I’m expected to be here for 8.5 hours. ---
**Author:** ![NinetyWt](https://avatars.discourse-cdn.com/v4/letter/n/cc9497/32.png) [@NinetyWt](https://boards.straightdope.com/u/NinetyWt)\ **Post date:** [June 13, 2008, 2:57pm UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/48 "2008-06-13T14:57:11Z")
[QUOTE=Malacandra] That’d be why he said “decent approximation”, then - 4% out ain’t bad. [/quote] Agreed, but my brain piped up and sez “why not use the exact number?”. Here 40 hours is standard - it’s very ingrained. > [@](#): > > May differ from country to country, but I’ve worked 37.5 (or 37) hour weeks many times. I learn more stuff on the Dope! 🙂 ETA: I see, **Leaffan**. Thanks. ---
**Author:** ![Bosstone](https://avatars.discourse-cdn.com/v4/letter/b/22d042/32.png) [@Bosstone](https://boards.straightdope.com/u/Bosstone)\ **Post date:** [June 13, 2008, 3:09pm UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/49 "2008-06-13T15:09:55Z")
[QUOTE=NinetyWt] Agreed, but my brain piped up and sez “why not use the exact number?”. Here 40 hours is standard - it’s very ingrained. [/QUOTE] Sure, but if you’re doing a quick in-your-head calculation, x2000 is just doubling the number and moving the decimal over three places. x2080 requires more thought or a calculator. ---
**Author:** ![NinetyWt](https://avatars.discourse-cdn.com/v4/letter/n/cc9497/32.png) [@NinetyWt](https://boards.straightdope.com/u/NinetyWt)\ **Post date:** [June 13, 2008, 3:25pm UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/50 "2008-06-13T15:25:56Z")
[QUOTE=Bosstone] Sure, but if you’re doing a quick in-your-head calculation, x2000 is just doubling the number and moving the decimal over three places. x2080 requires more thought or a calculator. [/QUOTE] What? Your calculator is not within arm’s reach 24/7 ??? 😛 ---
**Author:** ![Santo\_Rugger](https://avatars.discourse-cdn.com/v4/letter/s/e95f7d/32.png) [@Santo\_Rugger](https://boards.straightdope.com/u/Santo_Rugger)\ **Post date:** [June 13, 2008, 6:24pm UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/51 "2008-06-13T18:24:24Z")
[QUOTE=Pseudocode] Sorry, I saw what he did and misremembered summation as 7(6)/2, or n(n-1)/2, instead of n(n+1)/2. [/QUOTE] You had the summation formula right, you just misread the problem as having 7 people, when there are really 8. ---
**Author:** ![HeadNinja](https://avatars.discourse-cdn.com/v4/letter/h/b4bc9f/32.png) [@HeadNinja](https://boards.straightdope.com/u/HeadNinja)\ **Post date:** [June 14, 2008, 12:52am UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/52 "2008-06-14T00:52:23Z")
[QUOTE=NinetyWt] What? Your calculator is not within arm’s reach 24/7 ??? 😛 [/QUOTE] Mine takes the weekends off. The main reason the trick is useful is for spot math. if someone tells you they make 20$ an hour knowing they make about 40K is about as useful as knowing they make 41600. Unless you are approving a loan application. for tip math you can multiply the dollar figure by two and slide a decimal place. 7.40 tab? 1.40. Round as you see fit. ---
**Author:** ![Jeeves](https://avatars.discourse-cdn.com/v4/letter/j/73ab20/32.png) [@Jeeves](https://boards.straightdope.com/u/Jeeves)\ **Post date:** [June 14, 2008, 6:38am UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/53 "2008-06-14T06:38:00Z")
To convert PSI to head (ft of water) multiply by 2.3 . i.e. 14.7 PSI = 33.81 ft of water ---
**Author:** ![Derleth](https://avatars.discourse-cdn.com/v4/letter/d/b9e5f3/32.png) [@Derleth](https://boards.straightdope.com/u/Derleth)\ **Post date:** [June 14, 2008, 6:38am UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/54 "2008-06-14T06:38:02Z")
From the fortune files: ```auto How many seconds are there in a year? If I tell you there are 3.155 x 10^7, you won't even try to remember it. On the other hand, who could forget that, to within half a percent, pi seconds is a nanocentury. -- Tom Duff, Bell Labs ``` ---
**Author:** ![NinetyWt](https://avatars.discourse-cdn.com/v4/letter/n/cc9497/32.png) [@NinetyWt](https://boards.straightdope.com/u/NinetyWt)\ **Post date:** [June 14, 2008, 5:33pm UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/55 "2008-06-14T17:33:36Z")
[QUOTE=HeadNinja] The main reason the trick is useful is for spot math. [/QUOTE] Yes, yes I got that (finally). Sometimes I forget that most people don’t enjoy multiplying in their head and/or that estimating is faster and more useful than figuring out the ‘real’ number. Usually I can refrain from posting idiot replies but I that one snuck through the filter. 🙂 ---
**Author:** ![RTFirefly](https://avatars.discourse-cdn.com/v4/letter/r/c77e96/32.png) [@RTFirefly](https://boards.straightdope.com/u/RTFirefly)\ **Post date:** [June 14, 2008, 8:42pm UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/56 "2008-06-14T20:42:35Z")
[QUOTE=Inner Stickler] And the derivative of a real number is xn^x-1. So the derivative of x^4 is 4x^3 [/quote] Actually, the derivative of a _number_ - real, imaginary, complex, or whatever - is zero. Numbers being constants and all, and the rate of change of a constant being zero. Now if _x_ is a real _variable_, then the derivative of _x[sup]n[/sup]_ is _nx[sup]n-1[/sup]_. Sorry to be a stickler 😃 about that, but I couldn’t help myself. ---
**Author:** ![Stranger\_On\_A\_Train](https://avatars.discourse-cdn.com/v4/letter/s/13edae/32.png) [@Stranger\_On\_A\_Train](https://boards.straightdope.com/u/Stranger_On_A_Train)\ **Post date:** [June 15, 2008, 5:23am UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/57 "2008-06-15T05:23:41Z")
I get a surprising amount of traction out of the [Euler formula](http://en.wikipedia.org/wiki/Euler's_formula). It is especially nice when you need to so some trig transformations and don’t have a table handy. I may also be the only living engineer who still uses decadic logarithms for calculation, which allows me to save a few microseconds per calculation in a totally meaningless exercise in computational efficiency. The natural logarithm, on the other hand, is eminently useful, and I’ll know that I’ve found my one true love in a woman who appreciates the Laplace transform as much as I do. Beyond that, Pythagoras’ Theorem and the Golden Ratio have served me pretty well. As for units, I just convert everything into Planck units, which doesn’t make it easier but confuses the hell out of everyone. Stranger ---
**Author:** ![Ignatz](https://avatars.discourse-cdn.com/v4/letter/i/3be4f8/32.png) [@Ignatz](https://boards.straightdope.com/u/Ignatz)\ **Post date:** [June 15, 2008, 8:52pm UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/58 "2008-06-15T20:52:28Z")
12345679 x 9 x (your favorite single digit number) = a string of your favorite digit number. Ex., if your favorite digit is 6, then multiple 12345679 x 54 to get 666666666. ---
**Author:** ![Bravo\_Romeo](https://avatars.discourse-cdn.com/v4/letter/b/e8c25b/32.png) [@Bravo\_Romeo](https://boards.straightdope.com/u/Bravo_Romeo)\ **Post date:** [June 16, 2008, 9:57am UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/59 "2008-06-16T09:57:22Z")
I’m going to make some error here, so bear with me: I remember from one of my maths textbooks in high school something like: If you have a cylinder, a cone and a sphere of height h and the diameter of the sphere (or circular face) is also equal to h then the ratio of their volumes will be 3:2:1. Someone correct me… please. ---
**Author:** ![Stranger\_On\_A\_Train](https://avatars.discourse-cdn.com/v4/letter/s/13edae/32.png) [@Stranger\_On\_A\_Train](https://boards.straightdope.com/u/Stranger_On_A_Train)\ **Post date:** [June 16, 2008, 6:06pm UTC](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619/60 "2008-06-16T18:06:52Z")
[QUOTE=Hyper Aware] I’m going to make some error here, so bear with me: I remember from one of my maths textbooks in high school something like: If you have a cylinder, a cone and a sphere of height h and the diameter of the sphere (or circular face) is also equal to h then the ratio of their volumes will be 3:2:1. Someone correct me… please. [/QUOTE] The ratio between a cylinder:cone:sphere of height h and radius = h/2 is 3:1:2. Stranger [Previous page](https://boards.straightdope.com/t/lets-start-a-thread-for-useful-mathematical-formulae/452619.md?page=2)