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...

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: 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 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: 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 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.

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

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: 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 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: Math Craft Inspiration of the Week: The Curve-Crease Sculptures of Erik Demaine

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 ...

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.

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 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: 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.

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.

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!)

News: Nice Range of Modular Models

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):

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: 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.

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