Flower Field

thingiverse

Flower Field by Gabriela Castaneda Guzman 09/14/2022 George Mason University Math 401: Mathematics Through 3D Printing The print was successfully sliced through ultimaker cura to print on Makerbot 3D printer. overall print was 6 hours, as hexagonal shapes (2 hrs) were printed separately from the flower shape (4 hrs), no supports were needed. This flower field tiles the xy-plane under the wallpaper symmetry group p3m1. Some traits of this group are order-3 rotations, that the axes of reflections are inclined 60° to one another, and all centers of rotation lie on the reflection axes. Main grid for tiling are equilateral triangles, which served me as a baseline for what equations to use to find perfect dimensions for tiling pattern. Using the tiling program from Image block 1 I was able to construct an inspiration for a flower field. Using power point, we see in Image block 3 and 4, I was able to create a geometric pattern that would make for 2 and only 2 distinct shapes. Because of the nature of p3m1 pattern, it is more practical to form a tiling with 3 distinct shapes. For this class particularly, I was to achieve a 2 distinct shape tiling. Some mathematical equations used during drafting and final code were: Distance formula: d = sqrt((x2-x1)^2 + (y2-y1)^2) Midpoint formula: m = ((x1 + x2) / 2, (y1 + y2) / 2)