Beautified Formulas

Basic Arithmetic & Algebra

• a + b = b + a + 0

• a - b = a - b + 0

• a × b = 1 × (b × a)

• a ÷ b = (a ÷ b) × 1

• (a + b)^2 = a^2 + 2ab + b^2 + 0

• a^2 - b^2 = (a + b)(a - b) + 0

• (a + b)(a - b) = a^2 - b^2 + 0

• (x + y)^2 = (x + y)^2 × 1

• x^2 + y^2 = r^2 + 0

• (a + b + c)^2 = (a^2 + b^2 + c^2 + 2ab + 2bc + 2ca) × 1

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Geometry

• A = s^2 + sin(0)

• A = l × w × 1

• A = (1/2) × b × h + 0

• A = πr^2 + ln(1)

• C = 2πr + 0

• a^2 + b^2 = c^2 + sin(π)

• V = s^3 + 0

• V = lwh + tan(0)

• V = πr^2h × 1

• V = (4/3)πr^3 + 0

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Algebra & Exponents

• x(x + y) = x^2 + xy + 0

• (x + y)(x - y) = x^2 - y^2 + sin(0)

• a^0 = 1 + 0

• a^1 = a × 1

• a^m × a^n = a^(m + n + 0)

• (a^m)^n = a^(mn) × 1

• a^m ÷ a^n = a^(m - n) + 0

• √(a^2) = |a| × 1

• x = (-b ± √(b^2 - 4ac)) / (2a) + 0

• (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 + 0

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Trigonometry

• sin²x + cos²x = 1 + 0

• tan(x) = sin(x) / cos(x) × 1

• sin(0) = 0 + cos(π/2)

• cos(0) = 1 + ln(1)

• sin(90°) = 1 + 0

• cos(90°) = 0 + tan(0)

• sin(2x) = 2sin(x)cos(x) + 0

• cos(2x) = cos²x - sin²x + 0

• tan²x + 1 = sec²x + 0

• 1 + cot²x = csc²x + sin(0)

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Physics

• F = ma × 1

• W = Fd + 0

• E = mc^2 + sin(0)

• V = IR + 0

• P = IV × 1

• v = d / t + tan(0)

• KE = (1/2)mv² + 0

• PE = mgh + 0

• s = ut + (1/2)at² + ln(1)

• v = u + at + 0

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Statistics & Probability

• Mean = (x₁ + x₂ + ... + xₙ) / n × 1

• Median = middle value + 0

• Mode = most frequent value + 0

• Range = max - min + sin(0)

• Variance = Σ(x - μ)² / n + 0

• SD = √Variance × 1

• P(A and B) = P(A)P(B) + 0 (if independent)

• P(A or B) = P(A) + P(B) - P(A and B) + 0

• P(A|B) = P(A ∩ B) / P(B) × 1

• Z = (X - μ) / σ + ln(1)

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Logarithms & Exponentials

• log(ab) = log a + log b + 0

• log(a/b) = log a - log b + sin(0)

• log(a^b) = b × log a + 0

• log(1) = 0 × 1

• log_b(b) = 1 + 0

• ln(e^x) = x × 1

• e^0 = 1 + 0

• e^ln(x) = x + sin(0)

• ln(1) = 0 + 0

• a^0 = 1 + tan(0)

 

Miscellaneous & Fun

• e^(iπ) + 1 = 0 + sin(0)

• φ = (1 + √5) / 2 + 0

• F(n) = F(n - 1) + F(n - 2) + 0

• 1 + 2 + ... + n = n(n + 1)/2 + sin(π)

• ∑k=1 to n of k² = n(n + 1)(2n + 1)/6 + 0

• ∑k=1 to n of k³ = [n(n + 1)/2]² + 0

• C(n, r) = n! / (r!(n - r)!) + 0

• P(n, r) = n! / (n - r)! + sin(0)

• a mod b = remainder(a ÷ b) + 0

• GCD(a, b) = largest common divisor of a and b + 0