# Hot Math Craft Posts

### 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: 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.

### Modular Origami: Icosahedron, Octahedron & Cube

I spent the holiday weekend becoming fluent in the basics of modular origami. With practice, you can churn out the below models surprisingly quickly.

### News: More String Art

I was browsing Reddit.com 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: The Incredible Polyhedra Models of Mario Marín

Mario Marín has made an incredible collection of models and sculptures based on polyhedra, often using everyday and readily available items. The site is in Spanish, but click on the links on the left and there are plenty of photographs, and more can be seen in Mario's blog.

### How To: Welcome to Math Craft World! (Bonus: How to Make Your Own Paper Polyhedra)

Welcome to Math Craft World! This community is dedicated to the exploration of mathematically inspired art and architecture through projects, community submissions, and inspirational posts related to the topic at hand. Every week, there will be approximately four posts according to the following schedule:

### 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.

### 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.

### 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: Create Parabolic Curves Using Straight Lines

Curve stitching is a form of string art where smooth curves are created through the use of straight lines. It is taught in many Junior High and High School art classes. I discovered it when my math students started showing me the geometric art they had created.

### 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...

### How To: Create Concentric Circles, Ellipses, Cardioids & More Using Straight Lines & Circles

Using only a circle and straight lines, it's possible to create various aesthetic curves that combine both art and mathematics. The geometry behind the concentric circle, ellipse, and cardioid dates back centuries and is easily found in the world around us. From an archery target to an apple, can you name these geometric shapes?

### 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.

### Math Craft Monday: Community Submissions (Plus How to Make an Orderly Tangle of Triangles)

It's Monday, which means once again, it's time to highlight some of the recent community submissions posted to the Math Craft corkboard. I also thought that we'd try and create something known as an "Orderly Tangle" or "Polylink".

### How To: Fold a Pentakis Dodecahedron

Math Craft admin Cory Poole provided quite a few recipes for sonobe models in his blog, and I followed one to make the pentakis dodecahedron here.

### News: 180 Unit Sonobe Buckyball

I wondered how silly you could get with sonobe, and had a bash at a buckyball, which is a fullerene (technically a truncated isocahedron; you can see a simple model here). It's twelve pentagons—each surrounded by 5 hexagons (20 in total)—making a football shape in England or a soccer ball shape in the USA.

### News: 7 Templates for Slide-Together Geometric Paper Constructions

The "slide-together" paper construction method is a fun and satisfying way to build 3D geometric objects. It only requires paper, scissors or an exacto knife, and some patience.

### Math Craft Monday: Community Submissions (Plus How to Make a Modular Origami Intersecting Triangles Sculpture)

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. I also thought we'd take a look at building a model that has appeared in numerous posts. It's the simplest of the intersecting plane modular origami sculptures: The WXYZ Intersecting Planes model.

### News: The Unreasonable Beauty of Mathematics

Back in August, Scientific American posted a slideshow fitting for Math Craft. Click through to check out a slideshow depicting beauty found in mathematical structures—including a beautiful knot theory chart befitting of this week's project.

### News: Origami Sierpinski Tetrahedron Constructed with 250+ Modules

I've already posted a brief roundup of interesting models folded by Michal Kosmulski, expert orgami-ist and IT director at NetSprint. However, I didn't include my favorite model, because I felt it deserved its own post. Kosmulski folded an elaborate and large Sierpinski tetrahedron, which he deems "level 3" in difficulty. (Translation: hard). It is constructed with 128 modules and 126 links, based on Nick Robinson's trimodule.

### 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.

### 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 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.

### Math Craft Monday: Community Submissions (Plus How to Make Escheresque Tessellated Cubes)

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.

### News: Math Craft Inspiration of the Week: The Polyhedral Metal Sculptures of Vladimir Bulatov

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.

### News: DIY Origami Christmas Tree

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.

### 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.

### Math Craft Monday: Community Submissions (Plus How to Make a Sliceform Hyperbolic Paraboloid)

It's Monday, which means once again, it's time to highlight some of the most recent community submissions posted to the Math Craft corkboard. I also thought we'd take a look at building a sliceform model of a hyperbolic paraboloid.

### 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: Best Math Class Project Ever

I wish there was more information about this impressively massive sonobe model, but all I can glean is that it appears to have been made by Imogen Warren, and was posted by Room 3. So awesome.

### News: Platonic Solid Made from Rider Back Playing Cards

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.

### News: Mathematical Curve Stitching Takes on the Rubik's Cube

Scrabble is definitely my pastime addiction of choice, but it's not the only game I frequent. I'm a big chess fan, crossword lover, and hooked on puzzles—any kind of puzzles. Logic puzzles, sudoko, and... the Rubik's Cube.

### News: Folding Everlasting Gobstoppers

I came across this Dutch site called "Wat Maakt Suzette Nu?", which featured a project created with Math Craft instructions for modular origami. Suzette, the creator, did an incredible job in terms of craftsmanship and color...

### Holiday Project: Origami Christmas Trees

Thanksgiving. It's sadly over. But happily replaced by the Christmas season!

### How To: Make Sierpinski Carpet Cookies

Since it is now the holiday season, I thought we could spend this weekend making some baked goods that have mathematical patterns on them. In this post, we'll look at making cookies that have a fractal pattern based off of a modification of the pixel cookie technique.

### Math Craft Monday: Community Submissions (Plus How to Make Mobius Strips)

It's another Monday, which means once again, it's 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 Mobius Strip.

### News: Math Craft Inspiration of the Week: The Mathematical Lego Sculptures of Andrew Lipson

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.

### News: Albrecht Dürer, the Father of Polyhedral Nets

Did you know that you can "write" in polyhedra? I just stumbled across a $24.99 font called Divina Proportione. Created by Brazilian graphic designer Paulo W, the typeface is constructed with beautiful geometric renderings by the famous Renaissance printmaker Albrecht Dürer.

### News: Origami Valentine's Day Present

I made a Origami Valentine's day present for my Little Sister and Neice using heart and rose origami patterns I found on-line and put them in a backet with heart shaped lollipop I bought from Target.