Recursive Triangle

thingiverse

This is a geometrically designed creation produced by OpenScad. George Mason University's Math 493 course on Mathematics Through 3D Printing inspired this design. The figure, an iterated triangle, was generated using multiple isosceles triangles. Each layer has a sequence defined recursively by the geometric series for n ≥ 0, where x = 3. The sum of the series at layer n is equal to the number of triangles. Capturing the number of triangles at layer n = 6 results in 729 triangles at the six-layer level. A chart displays x^n and how rapidly the function increases as n increases. The following table shows x^n, n, and the corresponding triangle count: 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 Print Settings: Printer Brand: MakerBot Printer: MakerBot Replicator (5th Generation) Rafts: No Supports: No Notes: Two STL files were created: Recursive.stl and Triangle.stl. The two STL files were merged together in MakerBot to create the "Recursive" image. The entire print time took approximately 4 hours. Designing This Creation The recursive design was created up to the sixth layer (n=6), then a cut extrude using the difference function in OpenScad removed all layers except the top layer, leaving one layer in the attached STL file called Iterated_Triangle.