Thingiverse
Recursive Triangle by hdelgad2
by Thingiverse
Last crawled date: 4 years, 1 month ago
This is a recursive geometric designed created in OpenScad. George Mason University Math 493 for Mathematics Through 3D Printing.
This design was inspired from the following link: http://users.math.yale.edu/public_html/People/frame/Fractals/ .The figure, iterated triangle, is generated by multiple isosceles triangle. Each layer has a sequence defined recursively by the geometric series ( https://en.wikipedia.org/wiki/Geometric_series ) for n ≥ 0, where x = 3
∑_(n=0) to ∞ x^n =1+x+x^2+x^3+⋯+x^n
The sum of the series at layer n is equal to the number triangles. Capturing the number of triangles at layer n = 6 gives 3^6 = 729 at the six layer.
There is a chart showing x^n and how rapidly the function increases as n increases.
3^n --- n --- triangles
3^0 --- 0 --- 1
3^1 --- 1 --- 3
3^2 --- 2 --- 9
3^3 --- 3 --- 27
3^4 --- 4 --- 81
3^5 --- 5 --- 243
3^6 --- 6 --- 729
This design was inspired from the following link: http://users.math.yale.edu/public_html/People/frame/Fractals/ .The figure, iterated triangle, is generated by multiple isosceles triangle. Each layer has a sequence defined recursively by the geometric series ( https://en.wikipedia.org/wiki/Geometric_series ) for n ≥ 0, where x = 3
∑_(n=0) to ∞ x^n =1+x+x^2+x^3+⋯+x^n
The sum of the series at layer n is equal to the number triangles. Capturing the number of triangles at layer n = 6 gives 3^6 = 729 at the six layer.
There is a chart showing x^n and how rapidly the function increases as n increases.
3^n --- n --- triangles
3^0 --- 0 --- 1
3^1 --- 1 --- 3
3^2 --- 2 --- 9
3^3 --- 3 --- 27
3^4 --- 4 --- 81
3^5 --- 5 --- 243
3^6 --- 6 --- 729