Today, I stumbled upon an article highlighting the world’s most transformative equations. It was a bit like a trip down memory lane, but instead of nostalgia, it felt like trying to decipher hieroglyphics. Remembering some of these equations from school gave me a headache and made me question all my life choices. Thought I’d share the joy (and the pain :)
1.Pythagoras’s Theorem
a 2 + b 2 = c 2 a^2 + b^2 = c^2 a 2 + b 2 = c 2 2.Logarithms
log x y = log x + log y \log xy = \log x + \log y log x y = log x + log y 3.Calculus
d f d t = lim h → 0 f ( t + h ) − f ( t ) h \frac{df}{dt} = \lim_{h \to 0} \frac{f(t+h) - f(t)}{h} d t df = h → 0 lim h f ( t + h ) − f ( t ) 4.Law of Gravity
F = G m 1 m 2 r 2 F = G\frac{m_1 m_2}{r^2} F = G r 2 m 1 m 2 5.The Square Root of Minus One
i 2 = − 1 i^2 = -1 i 2 = − 1 6.Euler’s Formula for Polyhedra
V − E + F = 2 V - E + F = 2 V − E + F = 2 7.Normal Distribution
Φ ( x ) = 1 2 π σ e − ( x − μ ) 2 2 σ 2 \Phi(x) = \frac{1}{\sqrt{2\pi} \sigma} e^{\frac{-(x-\mu)^2}{2\sigma^2}} Φ ( x ) = 2 π σ 1 e 2 σ 2 − ( x − μ ) 2 8.Wave Equation
∂ 2 u ∂ t 2 = c 2 ∂ 2 u ∂ x 2 \frac{\partial^2 u}{\partial t^2} = c^2 \frac{\partial^2 u}{\partial x^2} ∂ t 2 ∂ 2 u = c 2 ∂ x 2 ∂ 2 u 9.Fourier Transform
( ω ) = ∫ − ∞ ∞ f ( x ) e − 2 π i ω x d x (\omega) = \int_{-\infty}^{\infty} f(x)e^{-2\pi i \omega x}dx ( ω ) = ∫ − ∞ ∞ f ( x ) e − 2 πiω x d x 10.Navier-Stokes Equation
ρ ( ∂ v ∂ t + v ⋅ ∇ v ) = − ∇ p + ∇ ⋅ T + f \rho \left( \frac{\partial v}{\partial t} + v \cdot \nabla v \right) = - \nabla p + \nabla \cdot \mathbf{T} + f ρ ( ∂ t ∂ v + v ⋅ ∇ v ) = − ∇ p + ∇ ⋅ T + f 11.Maxwell’s Equations
∇ ⋅ E = 0 \nabla \cdot \mathbf{E} = 0 ∇ ⋅ E = 0 ∇ ⋅ H = 0 \nabla \cdot \mathbf{H} = 0 ∇ ⋅ H = 0 ∇ × E = − 1 c ∂ H ∂ t \nabla \times \mathbf{E} = -\frac{1}{c} \frac{\partial \mathbf{H}}{\partial t} ∇ × E = − c 1 ∂ t ∂ H ∇ × H = 1 c ∂ E ∂ t \nabla \times \mathbf{H} = \frac{1}{c} \frac{\partial \mathbf{E}}{\partial t} ∇ × H = c 1 ∂ t ∂ E 12.Second Law of Thermodynamics
d S ≥ 0 dS \geq 0 d S ≥ 0 13.Relativity
E = m c 2 E = mc^2 E = m c 2 14.Schrödinger’s Equation
i ℏ ∂ ψ ∂ t = H ψ i\hbar \frac{\partial \psi}{\partial t} = H \psi i ℏ ∂ t ∂ ψ = H ψ 15.Information Theory
H = − ∑ p ( x ) log p ( x ) H = - \sum p(x) \log p(x) H = − ∑ p ( x ) log p ( x ) 16.Chaos Theory
x t + 1 = k x t ( 1 − x t ) x_{t+1} = k x_t (1 - x_t) x t + 1 = k x t ( 1 − x t ) 17.Black-Scholes Equation
1 2 σ 2 S 2 ∂ 2 V ∂ S 2 + r S ∂ V ∂ S + ∂ V ∂ t − r V = 0 \frac{1}{2} \sigma^2 S^2 \frac{\partial^2 V}{\partial S^2} + r S \frac{\partial V}{\partial S} + \frac{\partial V}{\partial t} - r V = 0 2 1 σ 2 S 2 ∂ S 2 ∂ 2 V + r S ∂ S ∂ V + ∂ t ∂ V − r V = 0