Greatest Equations Ever

sgant writes "What is your favorite equation? This was the question asked by Physics World in a recent poll. This is also covered in a New York Times article about the same poll. Some of the equations mentioned were the simplistic 1+1=2 and Euler's equation, eⁱ + 1 = 0. What are some of your favorite equations?"

Comments

correction

[schematix]

Euler's equation is actually Exp[i*Pi] + 1 = 0 not Exp[i*n] +1 = 0 (unless they say n = Pi, which they don't). I'd have to say this is the most elegant equation of all time. It combines the 5 most important numbers in all of mathematics into a single formula. This formula also has tremendous applications in many fields of engineering and other areas of applied mathematics. If it wasn't for this equation, your cell phone wouldn't work.

Re:correction

[niks42]

Actually, isn't Euler's formula Exp[i*theta] = cos[theta] + i*sin[theta] ? and then substitute in the value of pi into theta, and the more famous result appears.

H = F ^ 3

[Rob_Warwick]

Happiness = Food x Friends x Fun
From Woz.

It's the most important and beautiful equation I've ever seen.

(Generalized) Stokes equation

[Ibag]

The integral of a differential form on the boundry of a manifold is equal to the integral of the exterior derivative on the manifold itself.

S_{dM)w=S_(M)dw

An important special case is the fundamental theorem of calculus. Not only is this a beautiful looking theorem, but important too.

Other special cases are the classical forms of green's theorem, stoke's theorem, and the divergence theorem.

I dunno if its my favorite equation, but its up there.

Actually...

[yoshi_mon]

If it wasn't for this equation, your cell phone wouldn't work.

If it wasn't for the laws of nature things wouldn't work. The mathematical formulas are our way of expressing them.

Re:Actually...

[Phekko]

Mathematical formulas indicate an understanding of such laws, so without that understanding, your cell phone wouldn't work.

I believe there are quite a few inventions that have been stumbled upon without any understanding about mathematical formulas whatsoever. Amazing what can be accomplished with the old trial and error method =)

Re:Actually...

[Rich0]

e^i*pi=-1 isn't a law of nature.

It is a mathematical relationship which is completely abstract - none of those values are physical quantities, although all of them are used in other physical equations.

In theory an alien in a completely different universe could come up with the same formula.

Think about it - e is related to the integral of 1/x on a flat plane - which doesn't exist in real life. i is the square root of -1, which is about as abstract a concept as you'll ever come up with - it certainly doesn't correspond to any physical quantity (unless you define a physical system using complex coordinates for the sake of convenience). Pi is a number which is very useful in practical measurements, but which can be described completely in the abstract.

In any case, an equation like Euler's formula reflects our understanding of mathematics in general more than it reflects our knowledge of any particular physical process.

Re:What about

[crull]

0.999999... is just another way of symbolising the value 1. Its the same value, just two ways to write it.

The Pythagorean Theorem

[syntap]

I use this in day-to-day life probably more than anything else. Helpful for calculating my home theater projector screen sizes when I need to one-up friedns that get new televisions.

Re:one of the more famous misquotes there

[Zak3056]

A classic misquote. The verse actually runs, "The love of money is the root of all evil," but this joke wouldn't be as funny that way.

It's still funny--you just have to change the punchline to "The love of money is the root of all women."

A^2+B^2=C^2

[Shotgun]

A^2+B^2=C^2

This is the only equation that will give you the quickest way from here to there in an airplane.