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Unit Fractions, Math Models

3D model description

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

3D printing settings

Rafts:

No

Supports:

No

Resolution:

.2

Infill:

5-25%

  • 3D model format: STL

Creator

STEAM educator, learning from and working with K-12 STEAM teachers to explore new ideas of teaching and engagement. I firmly believe ART is at the core of STEM learning or all human learning! I owe my ideas and designs to the hundreds of K-12 children and teachers and university professors I have had the pleasure of working with, in multiple disciplines-- math, science,engineering language arts, social studies, early childhood education and more! All mistakes, of course, are mine! There is no warranty or liability whatsoever implied or explicit behind the designs or ideas. They are all posted for their potential educational values.

When working with children, please strictly observe all safety and health procedures! Please refer to the NSTA safety guides: http://www.nsta.org/safety/.

LGBU Contact: LGBU@SIU.EDU

License

CC BY


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