What quantity did you change?
Labs / Mathematics
Euclid's Algorithm
Two numbers set the sides of a rectangle. The algorithm keeps carving off the biggest square it can, then repeats on whatever strip is left over. Tap the canvas or hit auto-run — the side of the very last square is the greatest common divisor of your two numbers.
Labs / Mathematics / Euclid's Algorithm
Euclid's Algorithm
Two numbers set the sides of a rectangle. The algorithm keeps carving off the biggest square it can, then repeats on whatever strip is left over. Tap the canvas or hit auto-run — the side of the very last square is the greatest common divisor of your two numbers.
Why it matters
Why explore this?
Mathematics helps us describe patterns precisely and predict what comes next. This model turns an abstract relationship into something you can change and observe.
Explore
Try the model
rect 8 × 12squares 0GCD …
Investigate
Questions to test
Predict first, try it in the model, then use what you observe to answer.
What to try
- Set a and b to two neighbouring Fibonacci numbers like 13 & 21. Why does the tiling take so many steps, and what is the GCD?
- Make one number an exact multiple of the other. How many different square sizes appear before it finishes?
- Switch to the Table view. Where does each square in the tiling show up as a quotient in the division rows?
- Can you find two numbers whose GCD is 1? What does a “GCD of 1” tiling look like compared with one that shares a big factor?
- Move a by one, then by two. Which small change causes the biggest jump in the number of steps — and can you predict it?
Explain
Make sense of what happened
State the pattern in words, test it with another example, and then connect it to the mathematical rule or representation shown in the model.
Check
Before you leave
What pattern did you observe?
Does the pattern work for another example?
If you can answer all three using evidence from the model, you understand the main idea. If not, return to Explore and change one setting at a time.