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Golden Curve/Spiral

3D model description

The first few turns of a golden spiral, following the patterns of a Fibonacci sequence {1, 1, 2, 3, 5, 8, 13, 21, ... }. This is a great starting project for students to learn about 3D design using what they know about number sequences and their geometric representations. The curve, of course, has interesting properties that are worthwhile for a K-12 STEAM class. Have fun!

3D printing settings

Rafts:

No

Supports:

No

Resolution:

.1mm to .2mm

Infill:

5-20%

Notes:
Have fun! And see why the curve is smooth and in what sense it is called a golden curve.

Lesson Plan and Activity
Make a spiral (golden curve), starting with two 1 by 1 squares, followed by a 2 by 2 square, a 3 by 3 square, a 5 by 5 square, a 8 by 8 square, and so on.

Questions:

How can we find the ratio between the lengths of two adjacent arcs?
How does that ratio change as the spiral gets bigger and bigger?
What is the limit of that ratio?
Pose your own question.
Extension:

A 2D golden spiral can also be neatly constructed using GeoGebra (www.geogebra.org). Please consider using GeoGebra to play with the golden curve before seeking a 3D model. I have included a GeoGebra fil

  • 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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