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: 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.
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.
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:
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: 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.
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: 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.
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 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?
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: 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...
Math Craft Monday: Community Submissions (Plus How to Make a Magic Square Tetraflexagon)
It's Monday, which means once again, it's time to highlight some of the recent community submissions posted to the Math Craft corkboard. In this post, we'll also make a flexagon, which is a type of transformable object.
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: 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: 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: 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.
How To: Make a Two Circle Wobbler from CDs
One of my favorite simple projects is building two circle wobblers. I love how such a simple object amazes with its motion. The two circle wobbler is an object made out of two circles connected to each other in such a way that the center of mass of the object doesn't move up or down as it rolls. This means that it will roll very easily down a slight incline. It will also roll for a significant distance on a level surface if you start it by giving it a small push or even by blowing on it!
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".
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: Sonobe modular Fun
Made some Sonobe modules with some note cards. I made a big one with poster paper...Paper magic
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 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...
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 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: DIY Fractal Gingerbreadmen
After I made a blog and sent it to my friends about how I made Gingerbreadman Map fractal holiday cookies, one of them linked me back to the Sierpinski Carpet cookies, which I loved! So, I thought I'd share my how-to with everyone as well!
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.
How To: Make Yin-Yang Pillow Boxes
Here's a Math Craft project that takes less than 20 minutes, has an attractive, practical result, and is at least a little mind-blowing due to folding along curves.
How To: Make Nested Cube and Octahedron Boxes
These boxes are inspired by a comment from Imaatfal Avidya on a corkboard post on Platonic polyhedra from sonobe units. Imaatfal was commenting about how the cube and octahedron are related to each other.
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: Three-Dimensional Weaving with Sticks
These are a few examples of my latest craze. It is basically a 3d weave of cocktail sticks—just lots of them. I have made them from chopsticks and skewers as well, but have given those as presents and don't have any pictures.
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 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: Modular Paper Sculptures Based off of Richard Sweeney's Work
Here's my version of his icosahedron: I colored it in this one so that you can see the pentagonal faces of a dodecahedron:
News: Curvy origami designs I am working on:
I have a lot more images at hyperqbert's Profile • Instagram.
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.
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.
News: Sierpinski Christmas Tree
This three dimensional Sierpinski tetrahedral structure was created with a lot of help from my Year 10, 12 and 13 classes. It is inspired by the Sierpinski triangle fractal.