My wife isn't a fan of base 10 or of dividing the circle by 360 intervals. We're also a tau household rather than a pi one.
- Quarter divisions: These will occur at every right angle ((\frac{\tau}{4}), (\frac{\tau}{2}), etc.).
- Eighth divisions: These will fill in the gaps between the quarters ((\frac{\tau}{8}), (\frac{3\tau}{8}), etc.).
This approach gives us more intuitive reference points around the circle.
Here’s the plot of a circle with intuitive divisions based on (\tau), marked at every quarter and eighth of (\tau) radians. The purple points highlight these key intervals, making it easy to visualize positions at right angles and in between.