Public Articles

Mathematics Has an Architecture Nobody Showed You

# Mathematics Has an Architecture Nobody Showed You ![Mathematics dependency tree — blueprint poster](https://askrobots.com/files/public/d2c9442a-573d-4363-86fe-7e55d5a3ff50/) There is a moment, somewhere around the third time you drag a slider and watch a …

By dan Jun 2, 2026
Circle Equation — Center and Radius on a Grid

# Circle Equation — Center and Radius on a Grid ## Plain English first A circle is every point that is exactly distance r from a center point (h, k). …

By dan Jun 2, 2026
Quadratic Formula — Finding Where a Parabola Crosses Zero

# Quadratic Formula — Finding Where a Parabola Crosses Zero ## Plain English first A quadratic equation is any equation with an x² in it: ax² + bx + c …

By dan Jun 2, 2026
Pyramid and Prism Volumes

# Pyramid and Prism Volumes ## Plain English first **Prism:** Any shape with a uniform cross-section from bottom to top. Take the area of that cross-section, multiply by the height. …

By dan Jun 2, 2026
Parallelogram and Trapezoid Areas — Rearranging Rectangles

# Parallelogram and Trapezoid Areas — Rearranging Rectangles ## Plain English first Both of these shapes are rectangles in disguise. The trick in each case is to cut a piece …

By dan Jun 2, 2026
Pi from Randomness — Monte Carlo

# Pi from Randomness — Monte Carlo > **Animation coming** — full Sora 2 prompt below. Video will replace this placeholder. ## Plain English first Throw darts randomly at a …

By dan Jun 2, 2026
Pi — The Diameter That Wraps Around

# Pi — The Diameter That Wraps Around <video src="https://askrobots.com/files/public/396fe289-0fac-4015-bb62-fb05ee3bce33/" controls width="100%" style="border-radius:8px;margin:1rem 0"></video> ## Plain English first Take any circle. Pull the diameter out — the straight line through …

By dan Jun 2, 2026
Distance Formula — Pythagorean on a Grid

# Distance Formula — Pythagorean on a Grid > **Animation coming** — full Sora 2 prompt below. Video will replace this placeholder. ## Plain English first You have two points …

By dan Jun 2, 2026
Slope and Linear Equations — Rise Over Run

# Slope and Linear Equations — Rise Over Run > **Animation coming** — full Sora 2 prompt below. Video will replace this placeholder. ## Plain English first Slope is steepness. …

By dan Jun 2, 2026
Sine and Cosine — Waves from a Spinning Point

# Sine and Cosine — Waves from a Spinning Point > **Animation coming** — full Sora 2 prompt below. Video will replace this placeholder. ## Plain English first Put a …

By dan Jun 2, 2026
Sphere Volume — Archimedes' Discovery

# Sphere Volume — Archimedes' Discovery > **Animation coming** — full Sora 2 prompt below. Video will replace this placeholder. ## Plain English first Archimedes figured this out around 250 …

By dan Jun 2, 2026
Cone Volume — One Third of a Cylinder

# Cone Volume — One Third of a Cylinder > **Animation coming** — full Sora 2 prompt below. Video will replace this placeholder. ## Plain English first A cone has …

By dan Jun 2, 2026
Cylinder Volume — A Circle Grown Tall

# Cylinder Volume — A Circle Grown Tall > **Animation coming** — full Sora 2 prompt below. Video will replace this placeholder. ## Plain English first A cylinder is just …

By dan Jun 2, 2026
Pythagorean Theorem — Squares on Sides

# Pythagorean Theorem — Squares on Sides > **Animation coming** — full Sora 2 prompt below. Video will replace this placeholder. ## Plain English first Draw a right triangle. Now …

By dan Jun 2, 2026
Circle Area — Why πr²?

# Circle Area — Why πr²? > **Animation coming** — full Sora 2 prompt below. Video will replace this placeholder. ## Plain English first Take a circle and lay a …

By dan Jun 2, 2026
Triangle Area — Half a Rectangle

# Triangle Area — Half a Rectangle > **Animation coming** — full Sora 2 prompt below. Video will replace this placeholder. ## Plain English first Draw a rectangle. Now cut …

By dan Jun 2, 2026
Rectangle Area — Counting the Grid

# Rectangle Area — Counting the Grid > **Animation coming** — full Sora 2 prompt below. Video will replace this placeholder. ## Plain English first A rectangle is the simplest …

By dan Jun 2, 2026
Where Mathematics Came From

# Where Mathematics Came From ![Four origins of mathematics: commerce, land, astronomy, art and architecture](https://askrobots.com/files/public/a5b89775-24a4-45a9-b0a7-b0686250a9e7/) ## Plain English first Mathematics was not invented by professors in a room deciding to …

By dan Jun 2, 2026
Absolute Value — Distance from Zero

# Absolute Value — Distance from Zero ![Absolute value — equal arrows from zero to +3 and -3, showing identical distance](https://askrobots.com/files/public/7a7b19e8-b7f1-4ebc-b8b6-16e37b181dcb/) ## Plain English first Absolute value answers one question: …

By dan Jun 2, 2026
Negative Numbers

# Negative Numbers ![Negative numbers — number line with real-world analogies for above and below zero](https://askrobots.com/files/public/f3f9c585-b0a2-4d1b-8e08-874b2b4e02f4/) ## Plain English first Counting numbers stop at zero. But the world needs numbers …

By dan Jun 2, 2026