Unit Fractions, Math Models

Last crawled date: 6 years, 8 months ago

Unit fractions (1/N, for an natural number N) are interesting ideas in mathematics, dating all the way back to the ancient Egyptians. There are numerous ways to write a rational number as the sum of unit fractions. This is an an entry-level design project, allowing students to use their designs to play with basic ideas behind fractions. Among the files, 1 = 1/2 + 1/3 + 1/6, 1= 1/2 + 1/4 + 1/6 + 1/12, (1 = 1/2 + 1/3 + 1/10 + 1/15), (1 = 1/2 + 1/4 + 1/10 + 1/12 + 1/15), and 1 = 1/3 + 1/4 + 1/6 + 1/10 + 1/12 + 1/15. Of course, there are other ways to explore these ideas such as fraction bars and even 3D models (see Liu Hui's cube dissection).

Other combinations are possible but are physically less interesting:

1 = 1/2 + 1/3 + 1/8 + 1/24
1 = 1/2 + 1/3 + 1/9 + 1/18
1 = 1/2 + 1/4 + 1/5 + 1/20
1 = 1/2 + 1/5 + 1/6 + 1/8 + 1/120
1 = 1/2 + 1/5 + 1/6 + 1/10 + 1/30
1 = 1/2 + 1/5 + 1/6 + 1/12 + 1/20
1 = 1/3 + 1/4 + 1/5 + 1/6 + 1/20
1 = 1/3 + 1/4 + 1/5 + 1/8 + 1/20 + 1/24
1 = 1/3 + 1/4 + 1/5 + 1/9 + 1/10 + 1/180
1 = 1/3 + 1/4 + 1/5 + 1/9 + 1/18 + 1/20
1 = 1/3 + 1/4 + 1/5 + 1/10 + 1/12 + 1/30
1 = 1/3 + 1/4 + 1/6 + 1/7 + 1/14 + 1/28
1 = 1/3 + 1/4 + 1/6 + 1/8 + 1/12 + 1/24
1 = 1/3 + 1/4 + 1/6 + 1/9 + 1/12 + 1/18

References

http://mathworld.wolfram.com/EgyptianFraction.html
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fractions/egyptian.html