Using a great twitter thread from Freya Holmér for a geometry project with my younger son

Yesterday I saw this amazing twitter thread from Freya Holmér:

given three points, you can always find a circle passing through them all

1. draw lines from a to b to c
2. draw perpendicular bisectors (dashed)
3. the circle center is their intersection point
4. the circle radius is the distance from the center to any of the three points pic.twitter.com/9VceD4N8vG

— Freya Holmér (@FreyaHolmer) October 16, 2020

The idea in Holmér’s thread is one that we’ve looked at previously, but I still thought it would make a great weekend project.

Before showing my son the thread, I asked him if he knew how to make a circle passing through three randomly chosen points in a plane:

After that introduction to the problem, we talked through Holmér’s thread:

Next we returned to the white board and I had my son attempt to construct the circle using the method in Holmér’s tweet. Here he used a ruler and compass:

Finally, I gave him a little challenge – can you make the circle without using a straight edge?

This was a really fun project, I’m really grateful to Freya Holmér for sharing her work on twitter!