Public Articles
The Number Line
# The Number Line  ## Plain English first A number line is a straight …
Base 10 and Place Value
# Base 10 and Place Value  ## Plain English first We only have 10 digit …
Zero — The Number That Changed Everything
# Zero — The Number That Changed Everything  ## Plain English first Zero is the …
What Is a Number?
# What Is a Number?  ## Plain English first Before numbers existed, …
Visual Inverse Trig and atan2 Without Math Libraries
# Visual Inverse Trig and atan2 Without Math Libraries  ## Plain English first Regular trig starts with an …
Visual Calculus for Programmers
# Visual Calculus for Programmers  ## Plain English first Calculus is the study of **change** and **accumulation**. - **Derivatives** answer: how …
Visual Limits for Programmers
# Visual Limits for Programmers  ## Plain English first A limit asks: **what value is a …
Visual Integrals for Programmers
# Visual Integrals for Programmers  ## Plain English first An integral adds up a huge number of tiny …
Visual Optimization for Programmers
# Visual Optimization for Programmers  ## Plain English first Optimization means finding the **best** answer: …
Visual Tangent Without Math Libraries
# Visual Tangent Without Math Libraries  ## Plain English first Tangent answers the question: **how steep …
Visual Angle Wrapping
# Visual Angle Wrapping  ## One picture Angles work like a clock. After a full turn, you …
Visual Degrees vs Radians
# Visual Degrees vs Radians  ## Plain English first Both degrees and radians measure angles. …
Visual Radians Without Math Libraries
# Visual Radians Without Math Libraries  ## Plain English first A radian is an angle measured by …
Visual Pi Dependencies
# Visual Pi Dependencies  ## Plain English first Take any circle — a coin, a …
Visual Unit Circle Sine and Cosine Without Math Libraries
# Visual Unit Circle Sine and Cosine Without Math Libraries  ## One picture Put a point on a …
Visual Triangle Geometry
# Visual Triangle Geometry  ## Plain English first A triangle is three points connected by three straight …
Math Without Libraries — Table of Contents
# Math Without Libraries How math functions work underneath programming libraries. ## Topics - Absolute value - Clamp - Modulo and wrapping - Square roots - Sine and cosine approximations …
Visual Calculus — Table of Contents
# Visual Calculus Calculus explained visually before symbols. ## Path 1. Change 2. Slopes 3. [Visual Limits for Programmers](/articles/78ce0fe1-1e06-4fd6-98a1-b539a8b5c99f) 4. Derivatives 5. Area accumulation 6. [Visual Integrals for Programmers](/articles/01b9a7a2-ec93-49ec-9c96-b71a39dc11dd) 7. …
Visual Geometry and Trigonometry — Table of Contents
# Visual Geometry and Trigonometry A visual-first path through triangles, circles, angles, and trig. ## Geometry - [Visual Triangle Geometry](/articles/794e2e02-16a0-43fc-955a-ab27f8d1de8d) ## Angles and circles - [Visual Pi Dependencies](/articles/ec3ebdf4-f6cc-47bf-b597-56fc7b53d130) - [Visual …
Math Foundations — Visual Table of Contents
# 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 …