Standard Euclid
Steps
5
| step | A | B | q | r |
|---|---|---|---|---|
| 1 | 240 | 46 | 5 | 10 |
| 2 | 46 | 10 | 4 | 6 |
| 3 | 10 | 6 | 1 | 4 |
| 4 | 6 | 4 | 1 | 2 |
| 5 | 4 | 2 | 2 | 0 |
Instrument-Lab Explorations into Euclid, Ratios, and Rhythm
Core Algorithm
Standard Remainders Versus Least-Absolute Remainders
Steps
5
| step | A | B | q | r |
|---|---|---|---|---|
| 1 | 240 | 46 | 5 | 10 |
| 2 | 46 | 10 | 4 | 6 |
| 3 | 10 | 6 | 1 | 4 |
| 4 | 6 | 4 | 1 | 2 |
| 5 | 4 | 2 | 2 | 0 |
Steps
4
Saved
1
| step | A | B | q | r | |next| |
|---|---|---|---|---|---|
| 1 | 240 | 46 | 5 | 10 | 10 |
| 2 | 46 | 10 | 5 | -4 | 4 |
| 3 | 10 | 4 | 3 | -2 | 2 |
| 4 | 4 | 2 | 2 | 0 | 0 |
Claim Status
Fun Fact
Gabriel Lamé's Euclid analysis is a classic early complexity result: Fibonacci pairs force the slowest standard run.
Related Labs
Sources