Arithmetic billiards

High school (ages 12+)
Mathematics & Numbers

Name:

Date:

Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/arithmetic-billiards

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. What is the mathematical domain?Recreational mathematics, number theory, dynamical systems
2. What is the simulated process?A particle's straight-line trajectory with specular reflections off boundaries
3. How does the ball move in arithmetic billiards?The ball starts at one corner and travels straight at a 45‑degree angle. When it hits a wall, it bounces off, keeping the same angle of incidence as reflection.
4. Why do we use a rectangle with sides a and b?The rectangle’s width and height are the two numbers we want to study. The way the ball moves inside this rectangle tells us about the GCD and LCM of those numbers.

Dynamical Billiards: The study of particles moving and reflecting within geometric boundaries, often exhibiting complex behavior.
Specular Reflection: A type of reflection where the angle of incidence equals the angle of reflection, like a mirror.