# What is your favorite equation? **URL:** \ **Category:** In My Humble Opinion\ **Created:** [November 21, 2006, 1:48pm UTC](https://boards.straightdope.com/t/what-is-your-favorite-equation/381280 "2006-11-21T13:48:49Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![athelas](https://avatars.discourse-cdn.com/v4/letter/a/5e9695/32.png) [@athelas](https://boards.straightdope.com/u/athelas)\ **Post date:** [November 21, 2006, 1:48pm UTC](https://boards.straightdope.com/t/what-is-your-favorite-equation/381280/1 "2006-11-21T13:48:49Z")
For the math and science Dopers, what is your favorite equation or formula? Mine has to be /\G = RTlnK, where /\G is change in free energy for a process , T is temperature, and K is the equilibrium constant. I just think it’s an incredibly elegant way to relate those three quantities. ---
**Author:** ![Baron\_Greenback](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/baron_greenback/32/48_2.png) [@Baron\_Greenback](https://boards.straightdope.com/u/Baron_Greenback)\ **Post date:** [November 21, 2006, 1:54pm UTC](https://boards.straightdope.com/t/what-is-your-favorite-equation/381280/2 "2006-11-21T13:54:50Z")
Euler’s formula e^(pi\*i)= -1. When I first saw that demonstrated my jaw dropped. It was one of those lightbulb moments. Unfortunately, being basically rubbish at maths, those moments have been few. ---
**Author:** ![athelas](https://avatars.discourse-cdn.com/v4/letter/a/5e9695/32.png) [@athelas](https://boards.straightdope.com/u/athelas)\ **Post date:** [November 21, 2006, 1:57pm UTC](https://boards.straightdope.com/t/what-is-your-favorite-equation/381280/3 "2006-11-21T13:57:08Z")
As someone who was always bothered by Euler’s formula: > **[e to the pi times i](https://xkcd.com/179/)** > > I have never been totally satisfied by the explanations for why e to the ix gives a sinusoidal wave. ---
**Author:** ![TwoTrouts](https://avatars.discourse-cdn.com/v4/letter/t/a9adbd/32.png) [@TwoTrouts](https://boards.straightdope.com/u/TwoTrouts)\ **Post date:** [November 21, 2006, 2:22pm UTC](https://boards.straightdope.com/t/what-is-your-favorite-equation/381280/4 "2006-11-21T14:22:24Z")
The angle of the dangle is proportional to the heat of the meat. 😛 ---
**Author:** ![scareyfaerie](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/scareyfaerie/32/3135_2.png) [@scareyfaerie](https://boards.straightdope.com/u/scareyfaerie)\ **Post date:** [November 21, 2006, 2:24pm UTC](https://boards.straightdope.com/t/what-is-your-favorite-equation/381280/5 "2006-11-21T14:24:18Z")
The co-efficient of expansion… ---
**Author:** ![Beware\_of\_Doug](https://avatars.discourse-cdn.com/v4/letter/b/278dde/32.png) [@Beware\_of\_Doug](https://boards.straightdope.com/u/Beware_of_Doug)\ **Post date:** [November 21, 2006, 2:29pm UTC](https://boards.straightdope.com/t/what-is-your-favorite-equation/381280/6 "2006-11-21T14:29:07Z")
[QUOTE=TwoTrouts] The angle of the dangle is proportional to the heat of the meat. 😛 [/QUOTE] Damn, beat me to it. :smack: \ Heheheheh. He said “meat”…'n I said “beat.” Heheheheh. \ ---
**Author:** ![don\_t\_ask](https://avatars.discourse-cdn.com/v4/letter/d/e68b1a/32.png) [@don\_t\_ask](https://boards.straightdope.com/u/don_t_ask)\ **Post date:** [November 21, 2006, 2:36pm UTC](https://boards.straightdope.com/t/what-is-your-favorite-equation/381280/7 "2006-11-21T14:36:51Z")
you + me = sex ---
**Author:** ![glee](https://avatars.discourse-cdn.com/v4/letter/g/b5a626/32.png) [@glee](https://boards.straightdope.com/u/glee)\ **Post date:** [November 21, 2006, 2:48pm UTC](https://boards.straightdope.com/t/what-is-your-favorite-equation/381280/8 "2006-11-21T14:48:28Z")
Struan nailed it. For goodness sake: e and Pi are irrational and i is imaginary! :eek: :eek: :eek: How you can produce a simple integer from combining these three is beyond me. ---
**Author:** ![Squink](https://avatars.discourse-cdn.com/v4/letter/s/b5e925/32.png) [@Squink](https://boards.straightdope.com/u/Squink)\ **Post date:** [November 21, 2006, 3:03pm UTC](https://boards.straightdope.com/t/what-is-your-favorite-equation/381280/9 "2006-11-21T15:03:57Z")
[QUOTE=athelas] Mine has to be /\G = RTlnK [/QUOTE] Nice, but I find S = kLn Omega more evocative of the microscopic chaos and disarray which underlie our apparently continuous macroscopic experience. Still, it’s hard to beat the tiny rhyme of PV = nRT. It simply _rolls_ off the tongue. ---
**Author:** ![RealityChuck](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/realitychuck/32/195_2.png) [@RealityChuck](https://boards.straightdope.com/u/RealityChuck)\ **Post date:** [November 21, 2006, 3:27pm UTC](https://boards.straightdope.com/t/what-is-your-favorite-equation/381280/10 "2006-11-21T15:27:02Z")
I’ve always been partial to E=MC^2 ---
**Author:** ![carnivorousplant](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/carnivorousplant/32/3563_2.png) [@carnivorousplant](https://boards.straightdope.com/u/carnivorousplant)\ **Post date:** [November 21, 2006, 3:42pm UTC](https://boards.straightdope.com/t/what-is-your-favorite-equation/381280/11 "2006-11-21T15:42:40Z")
[QUOTE=athelas] As someone who was always bothered by Euler’s formula: > **[e to the pi times i](https://www.xkcd.com/179/)** [/QUOTE] I bet that’s got the joke “What do you get when you cross a mouse with an elephant” in there somewhere. 🙂 ---
**Author:** ![scr4](https://avatars.discourse-cdn.com/v4/letter/s/59ef9b/32.png) [@scr4](https://boards.straightdope.com/u/scr4)\ **Post date:** [November 21, 2006, 4:13pm UTC](https://boards.straightdope.com/t/what-is-your-favorite-equation/381280/12 "2006-11-21T16:13:39Z")
[QUOTE=Struan] Euler’s formula e^(pi\*i)= -1. [/QUOTE] I prefer this form: e[sup] _pi_ i[/sup] + 1 = 0 That way you incorporate the 5 most important numbers in the world. ---
**Author:** ![gotpasswords](https://avatars.discourse-cdn.com/v4/letter/g/c57346/32.png) [@gotpasswords](https://boards.straightdope.com/u/gotpasswords)\ **Post date:** [November 21, 2006, 5:41pm UTC](https://boards.straightdope.com/t/what-is-your-favorite-equation/381280/13 "2006-11-21T17:41:21Z")
I work with [this one](http://www.cs.virginia.edu/cs200/lectures/rsa.jpg) all day long. Or course, what they left off the shirt is that P and Q are not just primes, but really, really, really big primes\* The RSA encryption algorithm is simple - its strength is in that simplicity, meaning it’s easy for mathematicians to beat up on it and try to find faults. So far, they’ve not found anything significant. - A typical number used may be 8,000+ digits long. And you all thought the quest for big prime numbers was just to keep supercomputers busy - we use 'em for cryptography. ---
**Author:** ![gotpasswords](https://avatars.discourse-cdn.com/v4/letter/g/c57346/32.png) [@gotpasswords](https://boards.straightdope.com/u/gotpasswords)\ **Post date:** [November 21, 2006, 5:41pm UTC](https://boards.straightdope.com/t/what-is-your-favorite-equation/381280/14 "2006-11-21T17:41:20Z")
I work with [this one](http://www.cs.virginia.edu/cs200/lectures/rsa.jpg) all day long. Or course, what they left off the shirt is that P and Q are not just primes, but really, really, really big primes\* The RSA encryption algorithm is simple - its strength is in that simplicity, meaning it’s easy for mathematicians to beat up on it and try to find faults. So far, they’ve not found anything significant. - A typical number used may be 8,000+ digits long. And you all thought the quest for big prime numbers was just to keep supercomputers busy - we use 'em for cryptography. ---
**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:** [November 21, 2006, 5:49pm UTC](https://boards.straightdope.com/t/what-is-your-favorite-equation/381280/15 "2006-11-21T17:49:45Z")
[QUOTE=scr4] I prefer this form: e[sup] _pi_ i[/sup] + 1 = 0 That way you incorporate the 5 most important numbers in the world. [/QUOTE] Damnit, you beat me to it. Yeah, Euler’s Identity is pure beauty in the form of mathematics, and gives you all the numbers you need to do any mathematical operation (provided you’re prepared to deal with transforms from binary to natural number base arithmetic). And more generally, [Euler’s formula](http://en.wikipedia.org/wiki/Euler%27s_formula) underpins all of plane trigonometry, and allows us to cope in linear fashion with the otherwise nonlinear phenomena of circular and periodic motion via complex analysis. The [Golden Ratio](http://en.wikipedia.org/wiki/Golden_ratio)–(a+b)/a = a/b–is pretty keen as well. The [Lorentz transformations](http://en.wikipedia.org/wiki/Lorentz_transformation) are a wonderfully simple way of expressing the effects of relativity between intertial reference frames without yacking on about twin brothers and clocks in orbit. Simple, elegant mathematics that makes it all clear. [Maxwell’s Equations](http://en.wikipedia.org/wiki/Maxwell's_equations) look hideous to the unenlightened, but they bring together all of classical electrodynamics into an (almost) symmetric system. Similarly, the [Navier-Stokes](http://en.wikipedia.org/wiki/Navier-Stokes_equations) equations are lovely in their simplicity of describing fluid motion. Stranger ---
**Author:** ![ralph124c](https://avatars.discourse-cdn.com/v4/letter/r/8797f3/32.png) [@ralph124c](https://boards.straightdope.com/u/ralph124c)\ **Post date:** [November 21, 2006, 6:10pm UTC](https://boards.straightdope.com/t/what-is-your-favorite-equation/381280/16 "2006-11-21T18:10:09Z")
The best one! 1 X 1 = 1! ALL of western mathematics is bound up in this one! ---
**Author:** ![Jelymag](https://avatars.discourse-cdn.com/v4/letter/j/d2c977/32.png) [@Jelymag](https://boards.straightdope.com/u/Jelymag)\ **Post date:** [November 21, 2006, 7:26pm UTC](https://boards.straightdope.com/t/what-is-your-favorite-equation/381280/17 "2006-11-21T19:26:45Z")
[hijack] Hmmm, since there seem to be so many other geeks here at once… I’m having trouble with an equation. The answer book (and my students) insist the answer to problem below is 53.1 L… but I believe them to be wrong… As a system increases in volume, it releases 52.5 J of energy in the form of heat to its surroundings. It is working against a pressure of 10.25 atm. The final volume of the system is 58.0 L. What was the initial volume of the system if the total internal energy of the system decreased by 102.5 J? I used E=q+w to get work, and w=-P delta V but am I wrong in thinking that the work must first be converted from J to L\*atm before using it in the second equation??? ---
**Author:** ![GargoyleWB](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/gargoylewb/32/199_2.png) [@GargoyleWB](https://boards.straightdope.com/u/GargoyleWB)\ **Post date:** [November 21, 2006, 7:40pm UTC](https://boards.straightdope.com/t/what-is-your-favorite-equation/381280/18 "2006-11-21T19:40:08Z")
I like **F=ma**. You could derive any physical equation or concept from that starting point. At least until that meddlesome Einstein came along… ---
**Author:** ![NinjaChick](https://avatars.discourse-cdn.com/v4/letter/n/71c47a/32.png) [@NinjaChick](https://boards.straightdope.com/u/NinjaChick)\ **Post date:** [November 21, 2006, 8:19pm UTC](https://boards.straightdope.com/t/what-is-your-favorite-equation/381280/19 "2006-11-21T20:19:16Z")
A^2 + B^2 = C^2. ---
**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:** [November 21, 2006, 8:21pm UTC](https://boards.straightdope.com/t/what-is-your-favorite-equation/381280/20 "2006-11-21T20:21:33Z")
[QUOTE=GargoyleWB] I like **F=ma**. You could derive any physical equation or concept from that starting point. At least until that meddlesome Einstein came along… [/QUOTE] Yeah, seems like no matter how complicated the problem is, F=ma is always a good starting point! I wouldn’t say I have a favorite, but one I think is pretty cool for shaft design is: d=[16n/(pi_Sy)_(4M^2+3T^2)^(1/2)]^(1/3) It is used to find the minimum diameter for a shaft in quasi-static loading, given the loads and yield strength. It utilizes Von Mises theory of failure, and also Pythagorean’s theorem, amongst other things. [Next page](https://boards.straightdope.com/t/what-is-your-favorite-equation/381280.md?page=2)