Mathematics Learning Platform

Master Math
From First Principles

Explore Algebra, Geometry, and Trigonometry through clear diagrams, clean formulas, and structured lessons designed to build real understanding.

Three Core Topics

From solving equations to measuring angles, each topic builds on the last to give you a complete mathematical foundation.

Key Diagrams

Visual representations of the most important concepts across all three topics.

Unit Circle
(cos θ, sin θ) θ 1 x y I II III IV
Quadratic Function y = ax² + bx + c
vertex x₁ x₂ x y y = ax² + bx + c
Right Triangle — Pythagorean Theorem
b (base) a c (hyp) θ a² + b² = c² sin θ = a/c | cos θ = b/c | tan θ = a/b
Sine & Cosine Waves
1 -1 T = 2π sin(x) cos(x)
Circle — Key Measurements
d = 2r r arc A = πr² C = 2πr Sector area = ½r²θ
Linear Function y = mx + b
run rise b (y-int) m = rise/run x y
Quick Reference
Essential Formulas

The most important formulas across all three topics, ready to reference at a glance.

Algebra
Quadratic Formula
x = (−b ± √(b²−4ac)) / 2a
Solves any quadratic equation ax² + bx + c = 0
Slope-Intercept Form
y = mx + b
m = slope, b = y-intercept of a line
Exponent Rules
aˣ · aʸ = aˣ⁺ʸ  ·  (aˣ)ʸ = aˣʸ
Product and power rules for exponents
Difference of Squares
a² − b² = (a+b)(a−b)
Factoring shortcut for squared terms
Geometry
Pythagorean Theorem
a² + b² =
Relates the three sides of any right triangle
Circle Area & Circumference
A = πr²  ·  C = 2πr
r = radius, d = diameter = 2r
Triangle Area
A = ½ · b · h
b = base, h = perpendicular height
Sphere Volume
V = ⁴⁄₃ · π · r³
Volume of a sphere with radius r
Trigonometry
Pythagorean Identity
sin²θ + cos²θ = 1
Fundamental trig identity — always true
SOH CAH TOA
sin = opp/hyp · cos = adj/hyp
tan = opp/adj — right triangle ratios
Law of Cosines
c² = a² + b² − 2ab·cosC
Generalizes Pythagorean theorem to any triangle
Double Angle
sin = 2·sinθ·cosθ
cos2θ = cos²θ − sin²θ