Torus knots are beautiful knots formed by wrapping a line around a torus and tying the ends together to form a loop. The resulting knot has a star-like appearance when viewed from above. The 36 examples with the least number of crossings can be seen at the Knot Atlas's page on torus knots.
This is probably the least "Mathy" thing I will ever post. In my opinion, it's impossible to have architecture that isn't mathematical in some sense, so I am posting it anyway. Two years ago, I made a papercraft version of a cathedral in Christchurch New Zealand (It was severely damaged in an earthquake earlier this year) and cut holes for all of the windows and lit it with LED lights. I gave it to my Mom as a Christmas gift. I thought it made for a pretty amazing "Christmas Village" piece.
These boxes are inspired by a comment from Imaatfal Avidya on a corkboard post on Platonic polyhedra from sonobe units. Imaatfal was commenting about how the cube and octahedron are related to each other.
Vladimir Bulatov makes sculptures of fantastic variations on polyhedra and other geometric objects. His site is full of incredible metal, glass, and wooden geometric sculptures, including a full section on pendants and bracelets. Here are just a dozen or so of the hundreds of beautiful objects that he has produced.
Download the Software Go to the Antiprism downloads page. Download and install Antiprism 0.20.
Erik Demaine is a Professor of Electronic Engineering and Comp Sci at MI, but he is also an origami folder who has had work displayed at the Museum of Modern Art in NYC. He makes some beautiful models and intricate puzzles, but in my opinion the really inspirational work is the curved creased models. In Erik's own words describing the above models: "Each piece in this series connects together multiple circular pieces of paper (between two and three full circles) to make a large circular ramp ...
It's once again Monday, which means it's time to highlight some of the most recent community submissions posted to the Math Craft corkboard. Since two of these posts were on polyhedral versions of M.C. Escher's tessellations, I thought we'd take a look at building a simple tessellated cube based off of imitations of his imagery.
This week's post on creating 6-sided Kirigami Snowflakes got me interested in seeing whether I could use the process to create tessellation snowflakes using the method. I still haven't succeeded, but I did decide to make some ornaments based off a few of the tessellations by M.C. Escher that have a 6 sided symmetry.
In mathematics, a knot is a closed circle in a three-dimensional space that crosses itself multiple times. Since it is closed, it has no ends to tie, meaning you can't actually create such a knot. However, if you tie the ends together after you create a knot in the standard way, you will have something that is close to the mathematical description. In this post, we will explore the creation of mathematical knot sculputures using copper tubing and solid solder wire.
Just watched PBS origami doc Between the Folds last night. If you haven't seen it, I highly recommend it. It's a beautiful film, really inspiring. Lots of Math Craft-related subject matter. Available instant on Netflix, or for rent on iTunes.
I decided I would make those earrings I alluded to in Monday's Post on orderly tangles. I had to shrink the templates down so that the triangles are about 2 cm on a side. I used 110 lb cardstock and and painted them using metallic leafing paint in gold, silver, copper, and brass. I would put up a tutorial, except I think that this project would be too frustrating for most people. All I can suggest is that you make the orderly tangle of 4 triangles multiple times and just keep shrinking the si...
Natural processes often create objects that have a fractal quality. Fractal branching patterns occur in plants, blood vessel networks, rivers, fault lines, and in several electrical phenomena. Many of these processes take lifetimes, or even occur on geological timescales. But this is not the case for electrical phenomena. They often occur near instantaneously. One example would be the branching patterns that sometimes occur in lightning.
The initial idea for this project was to use magnets in the tips of the stellated octahedron and the intersections of the metal rings for either suspension or even a sort of weightless rotation. This turned out to be a bit too ambitious considering I'm working with found mirror and hot glue. So instead, I scrapped the magnets and went with simply mounting it on a skateboard bearing so it can freely rotate and not be bound to the base.
If you take two flat mirrors and place them front to back and look at them, you can see an infinite number of reflections. While this is a self-replicating pattern and can be somewhat mesmerizing, it isn't anywhere as interesting as looking at the chaotic scattering of light that can occur between 3 or 4 spheres.
After I made a blog and sent it to my friends about how I made Gingerbreadman Map fractal holiday cookies, one of them linked me back to the Sierpinski Carpet cookies, which I loved! So, I thought I'd share my how-to with everyone as well!
Math Craft admin Cory Poole posted instructions on How to Make a Cube, Octahedron & Icosahedron from Sonobe Units, plus some great complex models in his article, How to Make a Truncated Icosahedron, Pentakis Dodecahedron & More. These models use the standard sonobe unit and a coloured variant.
It's Monday, which means once again, it's time to highlight some of the recent community submissions posted to the Math Craft corkboard. In this post, we'll also make a flexagon, which is a type of transformable object.
Here's my version of his icosahedron: I colored it in this one so that you can see the pentagonal faces of a dodecahedron:
Tom Friedman is one of my favorite artists. He's got a great sense of humor, and his work is meticulous and beautiful. He forays into Math Art, and from a partisan perspective, he seems to be inspired by mathematics, but the end results are more of a whimsical twist than a mathematically "correct" execution. But I could be totally wrong. Comment below and fill me in.
Based off these instructions posted up by Justin Meyers of Scrabble World. I made it out of Glossy Photo Paper so it is really shiny.
Below, my construction of a Platonic Solid made from playing cards. To make your own, templates can be found at George Hart's site; there are also full step-by-step instructions here.
After Cory Poole posted some great Escher snowflakes, and Cerek Tunca had the great idea of using it as a base for a tetrahedron, well, I just had to give it a go. I will post a few more pictures and variants later (I think this was what Cerek was envisaging—if not let me know!)
Since today (11/11/11) is the last 6 digit binary date this century, I thought we should look at some kinetic binary calculators.
So I really like the new colour scheme. This sonobe pentakis dodecahedron uses twelve colours; one for each face.
This is how my version of an origami Christmas tree turned out based on the instructions I posted awhile back. Cory also made a version from white glossy paper, which looks great. I opted for the green and brown look, but it wasn't easy.
Halloween is coming up, so many of you may have a need or desire to carve a pumpkin and turn it into a Jack O' Lantern. This week we are going to explore carving our pumpkins into interesting geometric shapes. In this post, we will carve the pumpkins into spherical versions of polyhedra, and in Thursday's post we will carve 2 dimensional stars and some simple fractal designs into the pumpkins.
Much more complex than I had to make it- that's why I posted it. I think it looks cool...
I have a lot more images at hyperqbert's Profile • Instagram.
Cory has posted some great picture of Father Magnus' intersecting cubes (the great man is holding one in his right hand) - well the above is what happens when five tetrahedra intersect. It is modular origami and made from just ten sheets of origami paper. technically in a folding sense it is easy - but putting it together is mind-warping
Fractals and stars are two of the most beautiful and complicated-looking classes of geometric objects out there. We're going to explore these objects and how to carve them on a pumpkin. Unlike the last one on carving polyhedral pumpkins, where we used the entire pumpkin to carve a 3 dimensional shape, the pumkin carving in this post will involve two-dimensional images on a small part of the pumpkin's surface.
A source of inspiration... Models folded and photographed by Michal Kosmulski. There are only two sets of instructions on the site, but they are very well done. I wish he had covered more of the models. Here are a few I would like to tackle (I'll admit my eyes are bigger than my plate):
Andrew Lipson builds sculptures based off of Mathematical objects using standard Lego bricks. He has built models of knots, Mobius strips, Klein bottles, Tori, Hoberman spheres (using Lego technic pieces), and recreations of M.C. Escher works.
Looking into mathematical quilting, I came across a community of mathematical knitters. Check out Dr. Sarah-Marie Belcastro's (research associate at Smith college and lecturer at U Mass Amherst) mathematical knitting resource page.
Someone made this awesome pie, or is it two, in the shape of the standard two circle Venn Diagram.
Cory's post with instructions and templates Here's my first attempt at the 30 squares model. I needed to be a little bit more careful in the measuring and cutting as not everything matches up - but it is still a really pleasing shape.
I finally got around to making the pentakis dodecahedron from the instructions in Math Craft admin Cory Poole's blog post. It's not tightened/straightened up yet because I just noticed that I have two black and white and two blue and green compound modules next to each other (but no purple and pink modules next to each other—to the math experts, this is a parity thing, as you can only have even numbers of modules paired up next to each other).
Each curved module replaces the equilateral triangle of a simple octahedron. Inspired and copied from Cory's post with original artwork by Richard Sweeney
Here's my Sonobe Jasmine Dodecahedron built from Imatfaal's instructions.
Made some Sonobe modules with some note cards. I made a big one with poster paper...Paper magic