# 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](/articles/f070428e-3a70-4645-8139-d2047e4abbc5) — 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?](/articles/8510b9a8-a3ad-4790-a928-b2360ac8679e)
- [Zero — The Number That Changed Everything](/articles/6995c841-40bf-4d34-a787-c459d6084b5d)
- [Base 10 and Place Value](/articles/c92b632e-5a6d-4e17-b5fa-ec41f0db4d3f)
- [The Number Line](/articles/257eeafa-74c5-43e0-b09b-af90a9cd0d3c)
- [Negative Numbers](/articles/45845a19-b08f-4d9c-a7f6-edf47d0e9af7)
- [Absolute Value — Distance from Zero](/articles/44353274-42cc-4b6f-a40e-8dfbfec3a31d)
---
## Face 2 — Geometry: Shape, Space, and Measurement
*Area, volume, and the formulas that make them visible.*
### Area — 2D Shapes
- [Rectangle Area — Counting the Grid](/articles/66820765-0ec9-4197-8cfa-55bb81c2bf6d) *(foundation for all other area)*
- [Triangle Area — Half a Rectangle](/articles/6efb3a21-cfdd-4358-bc66-87ad756cb042)
- [Parallelogram and Trapezoid Areas — Rearranging Rectangles](/articles/4c1861bd-c163-4d9b-a3c9-474eaa7b10a6)
- [Circle Area — Why πr²?](/articles/6156ae8e-6c73-4c17-8916-8259a21cad23)
### Pi
- [Pi — The Diameter That Wraps Around](/articles/22502f1a-d965-46f6-96d9-366a4cf6ac41) 🎬 *video*
- [Pi from Randomness — Monte Carlo](/articles/42c405ab-b891-42c0-bb36-cc8ed87628f4) *(animation coming)*
- [Visual Pi Dependencies](/articles/ec3ebdf4-f6cc-47bf-b597-56fc7b53d130)
### Volume — 3D Shapes
- [Cylinder Volume — A Circle Grown Tall](/articles/7f98e02b-50ce-41a4-828c-c2fb80b30d97)
- [Cone Volume — One Third of a Cylinder](/articles/306a7711-f573-481b-86a2-edfe3e7e55b7)
- [Sphere Volume — Archimedes' Discovery](/articles/c55c6c40-4b1b-4101-9d58-f634e3c68e5b)
- [Pyramid and Prism Volumes](/articles/56b2e167-c544-4efa-8936-c3ffcffbd368)
### Coordinate Geometry
- [Pythagorean Theorem — Squares on Sides](/articles/4d64ff4e-28db-4c2b-8415-8751fd5adecf)
- [Distance Formula — Pythagorean on a Grid](/articles/3c8025ce-c59a-46bf-987f-975ae59d68ca)
- [Slope and Linear Equations — Rise Over Run](/articles/6ec5ca49-0c06-4ee7-b4bf-3eb494ecce47)
- [Circle Equation — Center and Radius on a Grid](/articles/e9590a40-75fc-4553-96c2-6743ff2ab9ca)
- [Quadratic Formula — Finding Where a Parabola Crosses Zero](/articles/336624aa-eded-477e-b2c5-7f6d63a9421e)
### Trigonometry
- [Sine and Cosine — Waves from a Spinning Point](/articles/d80a1d77-f009-41f8-8cf6-824aac810291) *(animation coming)*
- [Visual Radians Without Math Libraries](/articles/7090a8d6-5f02-456e-82ec-31741bd1fe38)
- [Visual Degrees vs Radians](/articles/4bc70fd7-fa6e-4989-988f-834ff34babdf)
- [Visual Angle Wrapping](/articles/0acc962a-e6a0-4e1f-a9bd-bb7c7c71b9b8)
- [Visual Triangle Geometry](/articles/794e2e02-16a0-43fc-955a-ab27f8d1de8d)
- [Visual Unit Circle Sine and Cosine](/articles/ad8e2329-9d21-42bb-9d33-2ef79f1fa21f)
- [Visual Tangent Without Math Libraries](/articles/79e757c8-c0af-4543-b5f0-e68ac4c39e39)
- [Visual Inverse Trig and atan2](/articles/85a06148-d17c-4c25-a18d-d4dd62e87dff)
---
## Face 2 — Calculus: Continuous Change
*What happens when things move, accumulate, and approach limits.*
- [Visual Calculus for Programmers](/articles/cbda355b-86cb-4c12-aebb-de239c2eb6b4) *(start here)*
- [Visual Limits for Programmers](/articles/78ce0fe1-c93e-4e53-9d35-a38f4a9bb6d8)
- [Visual Integrals for Programmers](/articles/01b9a7a2-d04e-4b71-b49d-82ea6c06fd04)
- [Visual Optimization for Programmers](/articles/2752f4e0-5af1-4ef3-b9d9-8399e5e1af3c)
---
## 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](/articles/6e6fe0ba-ee87-48bd-9734-6fc7196323ac)
- [Visual Calculus — Series TOC](/articles/fea3e669-d48e-4ad4-813e-be3148c38562)
- [Math Without Libraries — Series TOC](/articles/c4e2c82d-89f2-4ca6-bf35-45e9a6ddfa6a)