Math Foundations — Visual Table of Contents

Mathematics is the science of skillful operations with abstract concepts, symbols, and rules — developed to recognize patterns, solve problems, and reason logically. These concepts were invented or discovered to describe patterns and relationships in the world.

Mathematics has four faces: Number for quantity, Geometry for shape and space, Logic for proof and reasoning, and Pattern for symmetry, elegance, and beauty.

Start Here

• Where Mathematics Came From — why math was discovered, and what problems forced it into existence

Face 1 — Number: Quantity and Counting

What numbers are, where they come from, and how they behave.

• What Is a Number?
• Zero — The Number That Changed Everything
• Base 10 and Place Value
• The Number Line
• Negative Numbers
• Absolute Value — Distance from Zero

Face 2 — Geometry: Shape, Space, and Measurement

Area, volume, and the formulas that make them visible.

Area — 2D Shapes

• Rectangle Area — Counting the Grid (foundation for all other area)
• Triangle Area — Half a Rectangle
• Parallelogram and Trapezoid Areas — Rearranging Rectangles
• Circle Area — Why πr²?

Pi

• Pi — The Diameter That Wraps Around 🎬 video
• Pi from Randomness — Monte Carlo (animation coming)
• Visual Pi Dependencies

Volume — 3D Shapes

• Cylinder Volume — A Circle Grown Tall
• Cone Volume — One Third of a Cylinder
• Sphere Volume — Archimedes' Discovery
• Pyramid and Prism Volumes

Coordinate Geometry

• Pythagorean Theorem — Squares on Sides
• Distance Formula — Pythagorean on a Grid
• Slope and Linear Equations — Rise Over Run
• Circle Equation — Center and Radius on a Grid
• Quadratic Formula — Finding Where a Parabola Crosses Zero

Trigonometry

• Sine and Cosine — Waves from a Spinning Point (animation coming)
• Visual Radians Without Math Libraries
• Visual Degrees vs Radians
• Visual Angle Wrapping
• Visual Triangle Geometry
• Visual Unit Circle Sine and Cosine
• Visual Tangent Without Math Libraries
• Visual Inverse Trig and atan2

Face 2 — Calculus: Continuous Change

What happens when things move, accumulate, and approach limits.

• Visual Calculus for Programmers (start here)
• Visual Limits for Programmers
• Visual Integrals for Programmers
• Visual Optimization for Programmers

Face 3 — Logic and Proof (coming soon)

How to reason carefully, and how to know when something is always true.

Face 4 — Pattern, Symmetry, and Elegance (coming soon)

The mathematical structures behind beauty — symmetry groups, fractals, the golden ratio.

Math Without Libraries

Implementation from scratch — no sin(), cos(), sqrt(), or π imports.

• Visual Geometry and Trigonometry — Series TOC
• Visual Calculus — Series TOC
• Math Without Libraries — Series TOC