10 Math Formulas That Changed the World (And Why You Use Them Every Day)
1. Pythagorean Theorem
\( a^2 + b^2 = c^2 \)
Used in: architecture, navigation, construction, and computer graphics.
Helps calculate distances and build accurate structures in design and construction.
2. Newton’s Second Law of Motion
\( F = ma \)
Used in: engineering, space travel, car crash safety design, sports analysis.
Used to design safe and efficient transportation systems and sports equipment.
3. Quadratic Formula
\( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)
Used in: calculating profit margins, projectile motion, optimization problems.
Solves second-degree equations common in physics, engineering, and economics.
4. Law of Universal Gravitation
\( F = G \frac{m_1 m_2}{r^2} \)
Used in: astronomy, physics simulations, orbit predictions.
Calculates the gravitational force, essential in predicting planetary motions.
5. Compound Interest Formula
\( A = P \left(1 + \frac{r}{n}\right)^{nt} \)
Used in: finance, banking, retirement planning, investment growth.
Used to calculate how savings grow over time with interest.
6. Exponential Growth/Decay
\( N(t) = N_0 e^{rt} \)
Used in: population studies, radioactive decay, viral spread modeling.
Models how quickly things grow or decline in science and health.
7. Euler’s Identity
\( e^{i\pi} + 1 = 0 \)
Used in: quantum mechanics, signal processing, complex numbers.
A deep identity used in complex number math, especially in physics.
8. Shannon Entropy
\( S = -k \sum p_i \log p_i \)
Used in: information theory, cryptography, data compression, AI.
Measures information content, crucial for digital communication and AI.
9. Fourier Transform
\( f(x) = \int_{-\infty}^{\infty} F(k)e^{2\pi ikx} \, dk \)
Used in: music/sound processing, medical imaging (MRI), electronics.
Breaks down signals for audio analysis, image compression, and MRIs.
10. Black-Scholes Equation
\( \frac{\partial V}{\partial t} + \frac{1}{2} \sigma^2 S^2 \frac{\partial^2 V}{\partial S^2} + rS \frac{\partial V}{\partial S} - rV = 0 \)
Used in: financial markets to price options and manage risk.
Helps investors assess risk and determine fair prices of financial options.
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