# Logarithmic Spiral, Golden Triangle, Golden Gnomon, Spira Mirabilis

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## 3D model description

Logarithmic Spiral, Golden Triangle, Golden Gnomon, Spira Mirabilis
A golden triangle is an isosceles triangle, where the longer sides and the short one has the golden ratio ϕ= (sqrt(5)+1)/2, and the three interior angles are 72°, 72°, and 36° , respectively. Starting from a golden triangle, one can construct inwards and/or outwards an infinite number of (similar) golden triangles, thus creating a logarithmic spiral. In the design, I have kept the triangles for children to ponder over the beautiful relationships among these geometric gems.

Severn sizes are available. The dimension refers to the length of the short side of the outmost triangle. The spirals are 8mm in width and 2mm in thickness. The smaller ones are a little thinner.

References
https://en.wikipedia.org/wiki/Golden_triangle_(mathematics)
Huntley, H.E. (1970). The Divine Proportion: A Study in Mathematical Beauty. New York, NY: Dover Publications.

## 3D printing settings

Rafts:

No

Supports:

No

Resolution:

.1 to .2mm

Infill:

5-20%

• 3D file format: STL
• Publication date: 2018/05/29 at 10:23

## 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