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Math Model, Series Model for Third of Square or Triangle

3D model description

What do most kids think of when you ask them about simple fractions such as one half, one third, etc. I have used series models to stimulate discussions about fractions and some of the beautiful ideas behind them. There are numerous nice models or processes. Here are two of them for one third (1/3). The side length is about 50mm; the wall is 1mm thick and 5mm or 10mm high.

Question: What is the sum of all the squares/triangles with bottoms, if we allow the pattern to go on forever and ignore the walls between them?

In general, let R be a real number with R > 1. Then,

\left \sum_{i=1}^{\infty} \frac{1}{R^i} = \frac{1}{R-1}. But, what does it look like at least in some cases?

3D printing settings

Rafts:

No

Supports:

No

Resolution:

0.2 mm

Infill:

10-20%

Notes:
TPU flexible filament works well, too.

  • 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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