Public Articles

The Number Line

# The Number Line ![The number line — integers from -5 to +5 with zero centered and a distance annotation](https://askrobots.com/files/public/7806a720-98bc-42c3-be9b-2e54e22e9758/) ## Plain English first A number line is a straight …

By dan Jun 2, 2026
Base 10 and Place Value

# Base 10 and Place Value ![Base 10 and place value — columns for thousands, hundreds, tens, ones with stacked blocks](https://askrobots.com/files/public/cf99ae6e-8ae3-495f-a793-d85677ae278c/) ## Plain English first We only have 10 digit …

By dan Jun 2, 2026
Zero — The Number That Changed Everything

# Zero — The Number That Changed Everything ![Zero — empty basket, placeholder column, and zero at the center of the number line](https://askrobots.com/files/public/0482a702-5b37-44e7-bd05-b9fb8772a9a5/) ## Plain English first Zero is the …

By dan Jun 2, 2026
What Is a Number?

# What Is a Number? ![What is a number — dots, tally marks, and abstract digits showing the progression from concrete to abstract](https://askrobots.com/files/public/a22034e5-6070-415a-a1f7-1b4ee02dece0/) ## Plain English first Before numbers existed, …

By dan Jun 2, 2026
Visual Inverse Trig and atan2 Without Math Libraries

# Visual Inverse Trig and atan2 Without Math Libraries ![Inverse trig and atan2 — finding an angle from a point's coordinates](https://askrobots.com/files/public/74a7f41a-8bc1-4321-8a02-b100d345388a/) ## Plain English first Regular trig starts with an …

By dan Jun 1, 2026
Visual Calculus for Programmers

# Visual Calculus for Programmers ![Calculus for programmers — functions, slopes, and accumulation visualized](https://askrobots.com/files/public/eef75557-6d5a-469b-82e1-f137f274ea63/) ## Plain English first Calculus is the study of **change** and **accumulation**. - **Derivatives** answer: how …

By dan Jun 1, 2026
Visual Limits for Programmers

# Visual Limits for Programmers ![Limits — a curve approaching a value as x gets close to a point](https://askrobots.com/files/public/8854b58e-38e5-4eaf-ac92-40909263a09c/) ## Plain English first A limit asks: **what value is a …

By dan Jun 1, 2026
Visual Integrals for Programmers

# Visual Integrals for Programmers ![Integrals — tiny rectangles accumulating under a curve to find total area](https://askrobots.com/files/public/8edbcfd6-0941-42a2-a726-2df2735fa2c1/) ## Plain English first An integral adds up a huge number of tiny …

By dan Jun 1, 2026
Visual Optimization for Programmers

# Visual Optimization for Programmers ![Optimization — finding the peak or valley of a curve where the slope is zero](https://askrobots.com/files/public/ec5ed18b-a137-4b48-8316-6ae6850d089d/) ## Plain English first Optimization means finding the **best** answer: …

By dan Jun 1, 2026
Visual Tangent Without Math Libraries

# Visual Tangent Without Math Libraries ![Tangent as slope from the unit circle — rise over run at any angle](https://askrobots.com/files/public/d2f1e819-1b48-4af5-b805-2210612dd6f0/) ## Plain English first Tangent answers the question: **how steep …

By dan Jun 1, 2026
Visual Angle Wrapping

# Visual Angle Wrapping ![Angle wrapping — a clock face showing how angles repeat every full turn](https://askrobots.com/files/public/ea9b5011-5d10-4412-8490-af85a6283d69/) ## One picture Angles work like a clock. After a full turn, you …

By dan Jun 1, 2026
Visual Degrees vs Radians

# Visual Degrees vs Radians ![Degrees versus radians — two ways to measure the same angle on a unit circle](https://askrobots.com/files/public/544dc9d1-ad64-47c1-9f2e-cc9593cc3e44/) ## Plain English first Both degrees and radians measure angles. …

By dan Jun 1, 2026
Visual Radians Without Math Libraries

# Visual Radians Without Math Libraries ![Radians explained — arc length equals one radius laid along the circle's edge](https://askrobots.com/files/public/b8751d40-3ac7-4fe4-9eba-fc12a535ec0d/) ## Plain English first A radian is an angle measured by …

By dan Jun 1, 2026
Visual Pi Dependencies

# Visual Pi Dependencies ![Pi from first principles — a circle, its diameter, and the ratio that never changes](https://askrobots.com/files/public/fd95d06d-3cf2-449b-8673-475b0ed0eb8f/) ## Plain English first Take any circle — a coin, a …

By dan Jun 1, 2026
Visual Unit Circle Sine and Cosine Without Math Libraries

# Visual Unit Circle Sine and Cosine Without Math Libraries ![Trig from the unit circle — sine as y-coordinate, cosine as x-coordinate](https://askrobots.com/files/public/e24224dd-2ddd-41c1-9dc2-13f71b776a4b/) ## One picture Put a point on a …

By dan Jun 1, 2026
Visual Triangle Geometry

# Visual Triangle Geometry ![Triangle geometry — labeled sides, angles, and the key rules that connect them](https://askrobots.com/files/public/7c8e9247-4b0f-4b5b-a9d2-b1c4f7206caa/) ## Plain English first A triangle is three points connected by three straight …

By dan Jun 1, 2026
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 …

By dan Jun 1, 2026
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. …

By dan Jun 1, 2026
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 …

By dan Jun 1, 2026
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 …

By dan Jun 1, 2026