The session started with an example of Egyptian representations of whole numbers.
The next image shows the Egyptian symbols and two examples using this system:
We then looked at some examples of Egyptian Fractions.
Unit Fractions are represented by the symbol of a mouth with the denominator written below.
We then looked at examples where two (or more) unit fractions can be used to show what would be a non-unit fraction amount.
Participants then explored different ways to express fractions in the “Egyptian way”, i.e. as a sum of unit fractions.
One approach used we described as the “Greedy Algorithm” in which the unit fractions are generated by finding the largest unit fraction you can use, then finding the largest unit fraction of what remains, and so on. We had two wonderings about this approach: (1) “Is this process finite?” And (2) “Is this process efficient?”. In some of our explorations, this approach required several unit fractions and moved into fractions with very large denominators. For example, we found that 17/23 is very close to ½ + 1/6 + 1/18 + 1/72+1/360. It did appear that this process would end, but it was getting tricky and we didn’t finish! Also, each new term was getting significantly smaller.
This led us to a new wondering… would Egyptians require the level of accuracy provided by using 4 or more unit fractions, or would an approximation using 2 or 3 unit fractions be sufficient for their needs and purposes.
While we may not have answered all of our questions, we did get a lot of practice generating Egyptian Fractions!
Some resources:
- Slide deck with prompts & notes: https://jamboard.google.com/d/1Ht9vaws_YhjqrxxYuhLiZ2KzxvkV5AmXujatk_XMBoU/edit?usp=sharing
- Divide Like an Egyptian article: https://drive.google.com/file/d/1tqU2kKdRF2iRRmQplwhRB2j2i-cQACKr/view?usp=sharing
- Gardiner list of hieroglyphic signs: http://web.ff.cuni.cz/ustavy/egyptologie/pdf/Gardiner_signlist.pdf
- Wikipedia: https://en.wikipedia.org/wiki/Egyptian_fraction
Present: Cindy A., Eric A., Sarah L., Sophie G.
This is Amazing numerology