Unit Fractions, Math Models

cults3d

Unit fractions (1/N, for a natural number N) have been fascinating mathematicians since ancient Egypt. There are numerous ways to express a rational number as the sum of unit fractions. This project is perfect for beginners, allowing students to play with basic fraction concepts using their designs. 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, other ways to explore these ideas include fraction bars and even 3D models (see Liu Hui's cube dissection). Other combinations are possible but lack the physical appeal: 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