# Egyptian Fractions

At this session we welcomed some guests: high school students and non-math teachers. It was really exciting to share our math circle more widely!

We explored Egyptian fractions. This was a way to write a fraction, like 3/5, by adding together unit fractions without repetition. For example 3/5 could be written as 1/2+1/10. We followed along with worksheets from the LA Math Circle, available here:

- Part 1: http://www.math.ucla.edu/~radko/circles/lib/data/Handout-1309-1347.pdf
- Part 2: http://www.math.ucla.edu/~radko/circles/lib/data/Handout-1318-1350.pdf

We found that once you have an Egyptian Fraction Representation (EFR) it’s easy to modify it to get other EFRs for the same fraction. So EFRs are not unique. We learned about the “greedy algorithm” for finding EFRs. And we worked through a proof that the greedy algorithm always works. We focused on the greedy algorithm, but we did at least start to see some other ways to find EFRs.

More information on Egyptian fractions is here:

- https://www.ics.uci.edu/~eppstein/numth/egypt/ (including discussion of various algorithms for EFRs beyond the greedy algorithm)
- http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fractions/egyptian.html
- https://www.simonsfoundation.org/2015/12/10/new-erdos-paper-solves-egyptian-fraction-problem/