In 13 , I wrote “Time has three layers.” That coordinate time and proper time are different. ds² = The square of the spacetime interval. It represents the separation between two events (a set of “when ...

In mid-May, OpenAI announced that an internal AI model had disproved the Erdős unit distance conjecture, a famous problem in discrete geometry that had stumped human mathematicians for the last 80 ...

My doctor wrote computer glasses for the wrong distance. ChatGPT, Claude, and Gemini agreed on the problem and the results. The AI-derived glasses worked where the first pair failed. I recently ...

The Pythagorean theorem is usually taught as the brainchild of one Greek philosopher: Pythagoras. It’s one of the simplest, most elegant, and most important theorems in all of mathematics. But ...

👉 In this playlist, you will learn what the distance and midpoint formulas are and how to apply them. The distance formula is derived from the Pythagorean theorem given the coordinates of two points.

In the study of circular functions, the unit circle plays a central role in linking angles with trigonometric values. By defining sine, cosine, and tangent in terms of coordinates on a circle of ...

Pythagoras' Theorem (also called the Pythagorean theorem) has been used from antiquity to modern times to solve practical problems in situations from surveying, construction and design that involve ...

Every summer, scores of tourists take to the bustling streets of Barcelona, a city known for its breathtaking architecture. Nicolás Atanes Santos, a young Spanish mathematician, sees this as an ...

Gravity Probe B orbiting the Earth to measure “space-time,” a four-dimensional description of the universe including height, width, length, and time. Credit: NASA/Public Domain Mathematical equations ...