Hot Math Craft Posts

News: Making Art with the Golden Ratio

You can do some pretty cool stuff with the golden ratio. The image above is made from taking each quarter-circle in the golden spiral and expanding it into a full circle. In the second image, the spiral and the golden rectangles are overlaid on the the first image, showing how it works.

How To: Holy String Art, Batman! 6 of the Coolest Thread Art Projects Ever

You may remember string art from your elementary school days. If so, it probably makes you think of the 2D geometrical designs that took every ounce of patience you had as a kid. Or those laborious curve stitch drawings, which string art was actually birthed from. But thanks to some innovative modern artists, string art has gotten a lot more interesting. Here are some of the most creative applications so far.

News: Tom Friedman's Twisted Math Art

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.

Silver & Gold: DIY Modular Origami Christmas Ornaments

After becoming addicted to basic sonobe modular origami, I decided to make ornaments for relatives as Christmas gifts. I tried using fancy paper from stores like Paper Source, and cutting it to proper origami size, but I could never get the tight folds I wanted with non-traditional, non-origami paper. I ended up using this metallic origami paper that folds beautifully, and I'm pretty happy with the tiny models I ended up with. Forgive these pictures (iPhone/Instagram), I don't have my regular...

How To: Make the Platonic Solids Out of Playing Cards

Computer Science Professor Francesco De Comité has a fantastic gallery of mathematical images on Flickr. As part of this collection, he has a few hundred images of real or rendered polyhedra made out of paper or playing cards which he calls "slide togethers." These are constructed by making cuts and then sliding one component into the other, creating a shape without using any glue. He constructed the entire set of the platonic solids—the cards form their edges—which can be seen in the image b...

Modular Origami: How to Make a Cube, Octahedron & Icosahedron from Sonobe Units

Modular origami is a technique that can be used to build some pretty interesting and impressive models of mathematical objects. In modular origami, you combine multiple units folded from single pieces of paper into more complicated forms. The Sonobe unit is a simple example unit from modular origami that is both easy to fold and compatible for constructing a large variety of models. Below are a few models that are easy to make using this unit.

How To: Make a Hyperbolic Paraboloid Using Skewers

In Monday's post, we created a sliceform model of a hyperbolic paraboloid. In today's post, we will create a similar model using skewers. The hyperbolic paraboloid is a ruled surface, which means that you can create it using only straight lines even though it is curved. In fact, the hyperbolic paraboloid is doubly ruled and is one of only three curved surfaces than can be created using two distinct lines passing through each point. The others are the hyperboloid and the flat plane.

Modular Origami: How to Make a Truncated Icosahedron, Pentakis Dodecahedron & More

Last post, the Sonobe unit was introduced as a way to use multiple copies of a simply folded piece of paper to make geometric objects. In this post, we are going to explore that concept further by making two more geometric models. The first is the truncated icosahedron, which is a common stitching pattern for a soccer ball. The second was supposed to be the pentakis dodecahedron, but through systematic errors last night, I actually built a different model based off of the rhombic triacontahed...

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.

News: Math Craft Inspiration of the Week: The Kinetic Wave Sculptures of Reuben Margolin

Reuben Margolin builds large scale kinetic sculptures based off of mechanical waves. Some of his sculptures contain hundreds of pulleys all working in harmony with each other to create sinusoidal waves and their resulting interference patterns. He designs them all on paper and does all of the complicated trigonometric calculations by hand. Everything is mechanical; there are no electronic controllers.

How To: Make Icosahedral Planet Ornaments

In honor of the new Astronomy World, I thought we should look at a few planetary icosahedrons. The icosahedron is the most round of the Platonic solids with twenty faces, thus has the smallest dihedral angles. This allows it to unfold into a flat map with a reasonably acceptable amount of distortion. In fact, Buckminster Fuller tried to popularize the polyhedral globe/map concept with his Dymaxion Map.

How To: Make Torus Knots from Soft Metals

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.

How To: Make 6-Sided Kirigami Snowflakes

We've all made them. I remember making hundreds of paper snowflakes when I was in elementary school. You take a piece of paper and fold it in half, then fold it in half again. You now have a piece that is one fourth the size of the original. Now you fold it in half diagonally. You then cut slices out of the edges of the paper, and unfold to find that you have created a snowflake. The resulting snowflake has four lines of symmetry and looks something like this: If you fold it in half diagonall...

News: DIY Papercraft Architecture with Lighting

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.

How To: Make a 'Flex Mex'—A Mathematically Delicious Hexaflexagon Burrito

Here's a great excuse to play with your food—and learn some math while you're at it. We've all seen a hexaflexagon folded out of paper, but how about a burrito? Vi Hart, a "mathmusician" over at the Khan Academy, came up with the Flex Mex, a burrito folded into a hexaflexagon with all the toppings inside. The spreadable ingredients (guacamole, sour cream and salsa) go inside the folds, then it's topped with beans and cheese.

News: Palm-Sized Pentakis Dodecahedron

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).

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.

News: Math Craft Inspiration of the Week: The Curved Geometric Paper Sculptures of Richard Sweeney

Richard Sweeney is an incredible artist whose body of work consists mainly of sculptures made from paper. His art is often related to origami, and much of his work is related to geometrical forms. I personally really love his modular forms in paper. Many of them are based off of the platonic solids, which have been discussed in previous posts this week. Below are a small number of his sculptures, which are very geometric in nature.

News: Cyriak Harris' Fractal Freakiness

I'm sure many of you have already seen this, but being Halloween and mathematically inspired, I thought I'd dig up an old favorite for those who may have missed it. Original post with quote from Cyriak here. More fractal hands: Tim Hawkinson's "Fruit" Series

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