(I put the reference at the beginning is because this is a great webpage about Egyptian fraction. I highly recommend you to visit it if you are interested in the Egyptian fraction. Using copy and paste if the hyperlink doesn't work. )
Here are two algorithms for finding Egyptian Fraction (during my presentation, I only introduced one):
Method 1: Using Splitting Equation
Example: 2/6
Decompose a fraction into the sum of unit fractions
2/6 = 1/6 + 1/6
(All the unit fractions should be different. That's because when ancient Egyptian repeated the process of dividing, the reminder gets smaller and smaller.)
Convert one of the repeated unit fractions into the sum of distinct unit fraction by using the splitting equation:
2/6 = 1/6 + 1/7 + 1/42
Method 2: Fibonacci's Greedy Algorithm
Fibonacci proved and gave this method in his book Liber Abaci, the same book for Fibonacci Number.
Reflection (written on Nov 17th):
Due to some technical issue with my computer, my part of the presentation went not well on that day. After I shared my screen, the audience looked at a screen that was different from what I looked at. We realized this problem when I almost reached the last piece of slides. I think if I were not that nervous and talking slowly, we could notice that problem earlier.
Fortunately, the two most important and interesting slides, "Egyptian solution" and "Fibonacci’s Greedy Algorithm" were presented without a problem. There are so many interesting topics under Egyptian Fractions, and I just presented the tip of the iceberg of it. There is so much fun to learn about the history of mathematic, so I think I will introduce it to my students in the future.
Great work, Cheryl and group!
ReplyDeleteBut -- you still need to post a personal reflection on what you learned and what you take away from the project.
ReplyDeleteProf Gerofsky, I have posted my reflection. Thank you for reminding me. Cheryl
DeleteSorry, I will do it right away.
ReplyDeleteThanks for adding your reflections, Cheryl! I'm sorry that the technical glitch was a difficulty, but don't worry -- your presentation was still very good!
ReplyDelete