- Choose a race mode, keep all four algorithms on, and run the default target once.
- Check the winner card, then compare the chart and table together instead of reading one number in isolation.
- Load another sample or copy the URL when you want to reuse the same classroom setup.
Use the same time budget for every algorithm and compare the number of matching digits reached.
Ask which algorithm reaches the same digit target first. This phase keeps the target small on purpose.
Lower values produce denser chart points. Higher values reduce noise in the log and CSV.
Keep all four selected for the clearest comparison. Remove one only when you want to focus on a specific gap.
Race chart
The chart uses elapsed time on the x-axis and matching digits on the y-axis. It is meant for trend reading, not for claiming exact performance on every device.
Comparison table
| Algorithm | Estimate | Absolute error | Matching digits | Iterations | Elapsed ms | Status |
|---|
Teacher notes
- Use fixed time when you want students to feel that “same effort” does not mean “same accuracy.”
- Use fixed digits when you want to shift the discussion from progress curves to target-reaching speed.
- Gregory remains valuable because its slowness makes convergence visible instead of invisible.
- Chudnovsky wins quickly here, but this phase still treats it as a comparison method, not as a giant digits generator.
FAQ
Why do the algorithms separate so quickly?
They package information about pi very differently, so one extra step does not mean the same amount of progress across methods.
Why is Gregory so slow?
Its series is simple enough to explain from first principles, but each new term improves the estimate only a little.
Why is Chudnovsky faster here?
It converges far more aggressively, so one additional term can add many more correct digits than a basic series.
What is the difference between fixed time and fixed digits?
Fixed time compares how far each algorithm gets within the same budget. Fixed digits compares how long each algorithm needs to reach the same target.
What happens when I press stop?
The current run is cancelled immediately so the page stays responsive, and the last completed values remain visible.