Following through from inspiration in class, I want to look at physically rendering mathematical equations, and the beauty of these shapes before moving onto posts on practical applications and innovative creations possible with 3D-printing.
So many forms that we see in the natural world are governed by mathematical concepts, and the Golden Ratio, which is based on a series of numbers.
Mathematical patterns seen in the world around us
As explained in Wired’s article “This is what math equations look like in 3D”, the philosopher Descartes realised that the geometric shapes that Greeks drew, can be described with “algebraic equations in x’s and y’s”. Hundreds of years later, German mathematician Klein (famous for the Klein bottle), created many 3D models of equations painstakingly out of plaster.
These copies of Klein’s models are in a collection here at UIUC
Days would have gone into manually creating these models while also insuring their mathematical accuracy (See wired article for details). Today, any of these can be created very quickly through 3d printing. Some geometries that were too complex to create before, can also be made through 3D printing. It means that today we have so many available tools to incorporate mathematical ideas and design into things that we create. 3D printing allows us to play around with these equations and create these designs so easily.
Mathematical designs and shapes can create beautiful pieces of artwork and accessories.
A favourite of mine, is the mobius strip (surface with only one side) created as a set of toothed gears by a Berkelee student (here). He 3D printed it to prove that it was possible.
Drawing inspiration from nature, all kinds of designs can be realised, and are possible with 3D printing:
A particularly fun application is 3D printing lampshades with mathematical or geometric designs, so that the light shining out casts patterned shadows on the surrounding walls.
As a student, I feel like I always have random papers, folders, and envelopes floating around. This cute holder would help me keep my documents organized. To adjust it more for my life, I would include separators in between the two ends, to even further organize between certain documents.
I love using my GoPro whenever I travel, and sometimes shots or video can get ruined because of accidentally fumbling or not resting it on a steady-enough surface. To make this more suitable for my life, I think I would change it so that it was more of a tripod mount, as opposed to the two pillared sides. But if that’s how it stays steady then okay!
I love displaying flowers, and this little instant vase creator would allow me to turn any household glass into a vase. Obviously I would need to adjust the diameter of the larger end to fit the glasses I already own, but I think that would be worth it instead of having to spend the money on the vase to fit the flowers.
I frequently chop up my veggies almost every night for dinner, and this would be extremely helpful! Except this picture doesn’t look like it accurately depicts how to chop vegetables. A lot of the time I only use my thumb and index finger, so I wonder if it’s possible to make one just for those fingers? Or modify the shape in which you hold different vegetables.