17 équations qui ont changé le monde

Cet article est uniquement disponible en anglais pour l’instant.

I just finished the excellent book Seventeen Equations That Changed The World by Ian Stewart!

From the title, you might think that this book will describe a few equations. It’s actually a lot more. Each equation is actually just a pretext to present a period of time and / or a field of mathematics related the equation.

Don’t expect any important calculus in this book, it’s all about historical scientific context and usage. And it was actually a good thing for me. I knew and had used almost all the equations equations presented in this book, but there is actually not a lot of things that I knew from this book.

The equations presented in the book are:

Title Formula Author & Date
Pythagoras Theorem $a^2+b^2=c^2$ Pythagoras (530 BC)
Logarithms $\log xy=\log x+\log y$ John Napier (1610)
Calculus $\frac{df}{dt}=\lim\limits_{h \to 0} \frac{f(t+h)-f(t)}{h}$ Newton (1668)
Law of Gravity $F=G\frac{m_1 m_2}{d^2}$ Newton (1687)
Imaginary Number $i^2=-1$ Euler (1750)
Euler’s Formula for Polyhedra $V-E+F=2$ Euler (1751)
Normal Distribution $\Phi(x) = \frac{1}{{\sigma \sqrt {2\pi } }}e^\frac {( x – \mu)^2 } {2\sigma ^2 }$ C.F. Gauss (1810)
Wave Equation $\frac{\partial ^2 u}{\partial t^2}=c^2\frac{\partial ^2 u}{\partial x^2}$ J. d’Alembert (1746)
Fourier Transform $f(\omega )=\int_{-\infty }^{+\infty }f(x) e^{-2\pi ix\omega }dx$ J. Fourier (1822)
Navier-Stokes Equation $\rho \left(\frac{\partial v}{\partial t}+v\cdot\triangledown v \right) = -\triangledown p + \triangledown\cdot T+f$ C. Navier, G. Stoker (1845)
Maxwell’s Equations $\triangledown\cdot E=0$
$\triangledown\cdot H=0$
$\triangledown \times E=-\frac{1}{c} \frac{\partial H}{\partial t}$
$\triangledown \times H=\frac{1}{c}\frac{\partial E}{\partial t}$
James Clerk Maxwell (1865)
Second Law of
Thermodynamics
$dS\geq 0$ Ludwig Boltzmann (1874)
Relativity $E=mc^2$ Albert Einstein (1905)
Schrödinger’s Equation $i\hslash \frac{\partial }{\partial t} \psi=H\psi$ Erwin Schrödinger (1927)
Information Theory $H=-\sum p(x)\log p(x)$ Claude Shannon (1949)
Chaos Theory $x_{t+1}=kx_t(1-x_t)$ Robert May (1975)
Black-Scholes Equation $\frac{\sigma ^2}{2}S^2\frac{\partial ^2V}{\partial S^2}+rS\frac{\partial V}{\partial S}+\frac{\partial V}{\partial t}-rV=0$ F. Black, M. Scholes (1990)

As I said, it’s actually a lot more than about the equations. For example, the first chapter about Pythagoras theorem will of course present the history of this well known formula and some ideas about the proof of it. But a big part of the chapter is about the history of mathematical symbolism and how we went from the original Pythagoras theorem, that was a sentence, to the current notation $a^2 + b^2 = c^2$, the difference between math and science knowledge at that time and math nowadays (for example about the shape of Earth). The chapter will also evoke all the mathematical field of geometry, mentioning Elements by Euclid, the definition of trigonometry and its usage for map making and astronomy for example, the existence of non-Euclidean geometry, and even more!

I would highly recommend you this book if you like science and/or engineering, and even if you’re not a particularly a big fan of math.

Si vous voulez un aperçu de ce livre, vous pouvez lire des extraits sur Google Books pour la version française ou la version anglaise ou Amazon pour la version anglaise par exemple.

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