Mathematics is not just about numbers and calculations. It is also about discovering beautiful relationships between seemingly different ideas.
Euler's Identity
eiπ + 1 = 0
Euler's Formula
eiθ = cosθ + i sinθ
Pythagorean Theorem
a² + b² = c²
Quadratic Formula
x = (−b ± √(b² − 4ac)) / 2a
Binomial Theorem
(a + b)n = Σk=0n C(n,k)an−kbk
Geometric Series
1 + r + r² + r³ + ··· = 1/(1−r), |r| < 1
Area Under a Curve
∫ab f(x) dx
Fundamental Theorem of Calculus
∫ab f(x) dx = F(b) − F(a), where F′(x) = f(x)
De Moivre's Formula
(cosθ + i sinθ)n = cos(nθ) + i sin(nθ)
Fibonacci Sequence
Fn = Fn−1 + Fn−2
Golden Ratio
φ = (1 + √5)/2
These formulas show how mathematics connects algebra, geometry, trigonometry, calculus, complex numbers, and even patterns found in nature.
Mathematics is where simplicity and complexity meet. ∞