## Library

All

Algebra

Combinatorics

Foundations

Geometry

Stewart’s Theorem for Triangles

Ceva’s Theorem for Triangles

Pitot’s Theorem

Cyclic Quadrilaterals

Power of a Point Theorem

Inscribed Angle Theorem

Converse of Thales’s Circle Theorem

Thales’s Circle Theorem

The Law of Cosines

Point-Line Distance Formula

Chebyshev’s Inequality

Schur’s Inequality

Cauchy-Schwarz Inequality

Arithmetic-Geometric Mean Inequality

Sophie Germain Identity

Difference and Sum of Powers

Vieta’s Polynomial Formulas

Polynomial Remainder and Factor Theorems

Complex Conjugates of Polynomial Roots

Polynomial Integer Root Theorem

Polynomial Rational Root Theorem

Why is $\deg(0)=-\infty$?

Square Root of a Complex Number

The Quadratic Formula

$n^{\text{th}}$ Roots of a Complex Number

De Moivre’s Formula

Complex Triangle Inequality

Triple Angle Trig Identities

Double & Half Angle Trig Identities

Pythagorean Theorem

Angle Bisector Theorem

Exterior Angle Theorem

Interior Angle Theorem

Sum of Powers of Positive Integers

Telescoping & Partial Fraction Decomposition

Geometric Series

Arithmetic Series Using Gauss’s Formula

Floor and Ceiling Sum Bounds

Hermite’s Floor Identity

Reverse Triangle Inequality

Real Triangle Inequality

Compound vs. Simple Interest

Bernoulli’s Inequality

Real Archimedean Property

Discrete Fubini’s Principle

Harmonic Series Divergence

Counting the Pages of a Book

Logarithmic Change of Base Identity

Rationalizing a Denominator

Unique Even and Odd Parts of a Function

Inverses in a Binary Operation are Unique

Identity Element of a Binary Operation is Unique

Cantor’s Paradox in Set Theory

Cantor’s Theorem in Set Theory

Bijective Function if and only if Inverse Exists

Bertrand Russell’s Paradox in Set Theory

Subset Relation is a Partial Order

Bounded Quantifiers in Logic

De Morgan’s Laws in Logic

The Principle of Explosion in Logic

Why Modus Ponens and Modus Tollens are Valid