Math Facts!
0! = 1
\text{(Factorial of zero is defined as 1)}
Math Facts!
\text{Order of Operations:}
\text{Parentheses, Exponents,}
\text{Multiplication/Division (left to right),}
\text{Addition/Subtraction (left to right)}
Math Facts!
A = \frac{1}{2} \times b \times h
\text{(Area of a triangle formula)}
Math Facts!
2 \text{ is the only even prime number}
\text{(All other primes are odd)}
Math Facts!
F_n = F_{n-1} + F_{n-2}
\text{(Fibonacci sequence where } F_1=1, F_2=1)
Math Facts!
X\% \text{ of } Y = Y\% \text{ of } X
\text{(Percentage calculation trick)}
Math Facts!
\mathbb{Q} = \left\{\frac{a}{b} \mid a,b \in \mathbb{Z}, b \neq 0\right\}
\text{(Definition of rational numbers)}
Math Facts!
\text{1089 Trick: Reverse any 3-digit number,}
\text{subtract, reverse result, add → always 1089}
Math Facts!
a^2 + b^2 = c^2
\text{(Pythagorean theorem for right triangles)}
Math Facts!
\text{Sum of interior angles}
\text{in a hexagon } = 720^\circ
Math Facts!
\text{Four color theorem:}
\text{Any map can be colored with just 4 colors}
\text{so no adjacent regions match}
Math Facts!
1010_2 = 10_{10}
\text{(Binary to decimal conversion example)}
Math Facts!
\text{Perfect number: } 28 = 1+2+4+7+14
\text{(Equals sum of its proper divisors)}
Math Facts!
\text{Sum of angles in any triangle } = 180^\circ
\text{(Euclidean geometry fundamental)}
Math Facts!
A = \pi r^2
\text{(Area of a circle)}
Math Facts!
\text{All primes } >3 \text{ can be written as } 6n \pm 1
\text{(Useful pattern in prime numbers)}
Math Facts!
e^{i\pi} + 1 = 0
\text{(Euler's identity connecting 5 fundamental constants)}
Math Facts!
x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}
\text{(Quadratic formula for solving } ax^2+bx+c=0)
Math Facts!
\phi = \frac{1+\sqrt{5}}{2} \approx 1.618
\text{(Golden ratio appearing in nature and art)}
Math Facts!
\text{Pascal's Triangle:}
\text{Row sums } = 2^n
\text{(Binomial coefficients pattern)}
Math Facts!
\text{Birthday Paradox:}
P(\text{match}) > 50% \text{ with just 23 people}
\text{(Probability surprise)}
Math Facts!
T_n = \frac{n(n+1)}{2}
\text{(Triangular numbers formula)}
\text{(Example: } 1+2+3+4=10)
Math Facts!
C = \pi d = 2\pi r
\text{(Circumference of a circle)}
Math Facts!
\text{Monty Hall Problem:}
P(\text{win}) = \frac{2}{3} \text{ when switching doors}
\text{(Counterintuitive probability result)}
Math Facts!
\text{Roman numerals:}
\text{IV} = 4, \text{IX} = 9, \text{XL} = 40
\text{(Subtractive notation principle)}
Math Facts!
\int x^n dx = \frac{x^{n+1}}{n+1} + C \ (n \neq -1)
\text{(Power rule of integration)}
Math Facts!
\frac{d}{dx}x^n = nx^{n-1}
\text{(Power rule of differentiation)}
Math Facts!
\log(ab) = \log a + \log b
\text{(Logarithm product rule)}
Math Facts!
a_n = a_1 \times r^{n-1}
\text{(Geometric sequence formula)}
Math Facts!
V = \frac{1}{3}\pi r^2 h
\text{(Volume of a circular cone)}
Math Facts!
\text{Palindrome numbers:}
121, 1331, 14641 \text{ (also binomial coefficients)}
Math Facts!
\text{9 times table pattern:}
09, 18, 27, 36, 45, 54, 63, 72, 81, 90
\text{(Digits always sum to 9)}
Math Facts!
i = \sqrt{-1}
\text{(Imaginary unit, fundamental to complex numbers)}
Math Facts!
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} = 2R
\text{(Law of Sines, } R \text{=circumradius)}
Math Facts!
c^2 = a^2 + b^2 - 2ab\cos C
\text{(Law of Cosines for any triangle)}
Math Facts!
S_n = \frac{n(n+1)}{2}
\text{(Sum of first } n \text{ natural numbers)}
Math Facts!
V = \frac{4}{3}\pi r^3
\text{(Volume of a sphere)}
