News: Mathematical Quilting


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.

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.


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...


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 Concentric Circles, Ellipses, Cardioids & More Using Straight Lines and a Circle

Using only a circle and straight lines, it's possible to create many different curves that are quite pleasing to look at and well known mathematically. Most of the curves that are going to be explored in this post are featured at this site, which has a program for generating them, and this site which explores some of the geometry used in creating these curves. I recommend exploring both of them if you are going to create any of the designs below.

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: 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: 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.

News: More String Art


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...

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.

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: Origami Sierpinski Tetrahedron Constructed with 250+ Modules


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


How To: Make Torus Knots from Soft Metals




News: DIY Papercraft Architecture with Lighting


News: DIY Origami Christmas Tree


News: Mathematical Knitting


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.

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