Wednesday, October 7, 2020

Assignment 1-- Extension about Egyptian Fraction

(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. )

From Egyptian Mathematical Papyrus, we found that ancient Egyptians could handle of fractions 4000 years ago. They only have notations for Unit Fractions, but they can represent more general rational numbers as a sum of distinct unit fraction.   
                                

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. 

5 comments:

  1. But -- you still need to post a personal reflection on what you learned and what you take away from the project.

    ReplyDelete
    Replies
    1. Prof Gerofsky, I have posted my reflection. Thank you for reminding me. Cheryl

      Delete
  2. Thanks 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

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