Math Craft Features

News: Mathematical Quilting

I got hooked on origami sometime after Math Craft admin Cory Poole posted instructions for creating modular origami, but I had to take a break to finish a quilt I've been working on for a while now. It's my first quilt, and very simple in its construction (straight up squares, that's about it), but it got me thinking about the simple geometry and how far you could take the design to reflect complex geometries. Below are a few cool examples I found online.

How To: Make Yin-Yang Modular Polyhedra

Last Thursday's post demonstrated how to Make Yin-Yang Pillow boxes, which were based on equilateral triangles and squares. The units for making these boxes were created by Phillip Chapman-Bell, who runs an amazing origami blog and has a spectacular flickr photostream. Using these units, you can make also make 4 of the 5 platonic solids. I made an additional template based on the regular pentagon so that the dodecahedron can be built completing the set.

You Won't Believe They Roll: How to Build Half Circle and Elliptical Wobblers

If you thought the last post on Two Circle Wobblers was wild, then wait until you see what happens when you build wobblers out of two half circles or two ellipses. In both of these cases, the center of gravity still remains constant in the vertical direction, allowing them to roll down the slightest of inclines or even travel a significant distance on a level surface if given a push or even when blown on.

News: More String Art

I was browsing yesterday and noticed this post. User guyanonymous (yes I am really crediting him regardless of his name!) had posted up this string-art picture which has parabolic curves created from straight lines and gave me permission to post it up here on the corkboard. I love the repeating "flower" pattern.

How To: Carve Polyhedral Pumpkins

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.

News: M.C. Escher Square Tessellation Ornaments

Imatfaal's awesome post on Escher's tessellations on Polyhedra reminded me of some ornaments I made this summer. I made some of Escher's square tessellations onto cubes and then reprojected them onto spheres. I actually used a 60 sided Deltoidal hexecontahedron since that net is fairly easy to fold and looks pretty round.

Mathematical Holiday Ornaments: Escher "Snow Flakes"

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.

How To: Make a Sonobe Jasmine Dodecahedron

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.

News: Escher Tessellated Polyhedra

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!)

How To: Make Fractal Cupcakes

Last post, we looked at fractal cookies based off of the recipe by Evil Mad Scientist Laboratories. In this post, we'll follow their recipe for fractal cupcakes based off of the Koch Snowflake, which we used previously to decorate pumpkins for Halloween.

News: Parabolic Art in EL-Wire by Ben Yates

This is a new line of work I've started - inspired by string art of Archimedean Lines, these are 3-dimensional sculptures made using Electro-Luminescent Wire weaved around a clear acrylic frame. They hang on the wall, but each has a sense of depth so their look alters from different angles. The EL-Wire is a copper wire coated with a phosphor so it glows its entire length, and then coated with a plastic sleeve so that it can be handled and bend around any shape.

News: Mathematical Knitting

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.

News: Math Craft Inspiration of the Week: Electrically Generated Fractal Branching Patterns

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.

News: A 3-in-1 Model

These drawings were made with Google SketchUp. There is a dodecahedral model, icosahedral model, and a third I don't know the name of, made of rhombic faces obtained by connecting vertices of the other two. The final image is all three models together. I'll use a ShopBot CNC router to cut out the pieces this week.

Math Craft Monday: Community Submissions (Plus Polyhedral Stellation)

It's another Monday, which means it's once again time to highlight some of the recent community submissions posted to the Math Craft corkboard. Additionally, I thought we'd take a look at the process of stellation and make some stellated polyhedra out of paper.Rachel Mansur of Giveaway Tuesdays posted a video from animator Cyriak Harris, which zooms into fractal hands, where each fingertip also has a hand and fingers. A few more details can be found here, as well as some other really cool pic...

How To: Make Knot Sculptures from Soft Metals

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.

News: Twisted Small Stellated Dodecahedron Tensegrity

This is a zigzag tensegrity based on a small stellated dodecahedron. There are string pentagons on the outside of the model where the vertices have opened. It is made of thirty units, consisting of a barbecue stick pair with a loop of elastic. The stick pairs are all "floating", and weave through the model without contacting any other stick pairs. It is quite tricky to assemble, but can be done entirely by hand.

News: Modular Origami

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

News: More Kirigami Snowflakes

I spent a little bit more time making 6 sided Kirigami Snowflakes using the method of this post. I'm really happy with how all of these turned out. I'd love to see other people post up some snowflakes. They're easy and a lot of fun. And I could use some more inspiration!