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伟大的公式
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英国科学期刊《物理世界》曾让读者投票评选了“最伟大的公式”，最终榜上有名的十个公式既有无人不知的1+1=2，又有著名的E=mc2；既有简单的圆周公式，又有复杂的欧拉公式……
从什么时候起我们开始厌恶数学？这些东西原本如此美丽，如此精妙。这个地球上有多少伟大的智慧曾耗尽一生，才最终写下一个等号。每当你解不开方程的时候，不妨换一个角度想，暂且放下对理科的厌恶和对考试的痛恨。因为你正在见证的，是科学的美丽与人类的尊严。
No.10 圆周长公式（The
Length of the Circumference of a Circle）
$ c=2 \pi r $
No.9 傅立叶变换（The Fourier Transform）
$hat{F}(xi)=int_{-infty}^{+infty} f(x) e^{-2 pi i xi x} dx $
No.8 德布罗意关系式（The de Broglie Relations）
$ boldsymbol{p} = hbar boldsymbol{k} , E=hbar omega $
No.7 1+1=2
$ 1+1=2 $
No.6 薛定谔方程（The Schrödinger's Equation）
$ hat{H}Psi = ihbar {partial{ Psi} over partial t } $
No.5 质能方程（Mass-energy Equivalence）
$ E=mc^2 $
No.4 勾股定理/毕达哥拉斯定理（Pythagorean Theorem）
$ a^2+b^2=c^2 $
No.3 牛顿第二定律（Newton's Second Law of Motion）
$ \mathbf{F} = m \mathbf{a} $
No.2 欧拉公式（Euler's Identity）
$ e^{i\pi}+1=0 $
No.1 麦克斯韦方程组（The
Maxwell's Equations）
微分形式：
$ nabla cdot mathbf{E} = {rho over varepsilon} \ nabla cdot mathbf{B} = 0 \ nabla times mathbf{E} = -{ partial mathbf{B} over partial t} \ nabla times mathbf{B} = mu mathbf{J} + mu varepsilon {partial mathbf{E} over partial t } $
积分形式：
$ oint_{partial Omega} mathbf{E} cdot dmathbf{S} = {Q over varepsilon} \ oint_{partial Omega} mathbf{B} cdot dmathbf{S} = 0 \ oint_{partial Sigma} mathbf{E} cdot dmathbf{l} = - iint_Sigma {partial mathbf{B} over partial t} cdot dmathbf{S} \ oint_{partial Sigma} mathbf{B} cdot dmathbf{l} = mu I + muvarepsilon iint_Sigma {partial mathbf{E} over partial t} cdot dmathbf{S} $
考究起来，网上这个说法与真正的Top Ten
Greatest Equations Ever存在差距:
1. Maxwell's four equations describing how an electromagnetic field varies in space and time.
2. Euler's equation of momentum-flow and force-density in fluid dynamics.
$ {partial boldsymbol{v} over partial t } + (boldsymbol{v} cdot nabla) boldsymbol{v} = -{nabla P over rho} + boldsymbol{f} $
3. Newton's Second Law (F=ma) - 'The rate of change of momentum of a body is equal to the resultant force acting on the body and is in the same direction'.
4. Pythagoras's Theorum (a²+b²=c²) - In any right triangle, the area of the square whose side is the hypotenuse (the side of a right triangle opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.
5. Schrödinger's equation describing the time-dependence of quantum mechanical systems.
6. Boltzmann equation describing the statistical distribution of particles in a fluid.
$ {partial f over partial t} +boldsymbol{v} cdot nabla f + {boldsymbol{p} over m} cdot nabla f = ({partial f over partial t})_{coll} $
7. Principle of Least Action (or Principle of stationary action)
$ delta int_{t_1}^{t_2} L(q,dot{q},t) dt=0 $
8. De Broglie's equation - showing that the wavelength is inversely proportional to the momentum of a particle and that the frequency is directly proportional to the particle's kinetic energy.
9. Fourier Transformation - an integral transform that re-expresses a function in terms of sinusoidal basis functions.
10. Einstein's field equations for General Relativity.
$ R_{munu}-{1 over 2}g_{munu}R+g_{munu}Lambda={8pi G over c^4} T_{munu} $
也不知是不是原创者故意将几个不知名的公式替换了。
2012-07-22 16:29:14 初稿
2012-07-23 18:15:04 增加其他公式
https://blog.sciencenet.cn/blog-548663-594790.html
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