Unit Fractions, Math Models

thingiverse

Unit fractions (1/N, for a natural number N) have been fascinating mathematicians since ancient Egypt. Various ways exist to express a rational number as the sum of unit fractions. This entry-level design project allows students to apply their designs and experiment with basic ideas behind fractions. Files containing 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 illustrate these ideas. Exploring other concepts such as fraction bars and 3D models can also be done, like in Liu Hui's cube dissection. Other possible combinations exist but are less interesting physically: 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: 1. http://mathworld.wolfram.com/EgyptianFraction.html 2. http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fractions/egyptian.html