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".
Fractals and stars are two of the most beautiful and complicated-looking classes of geometric objects out there. We're going to explore these objects and how to carve them on a pumpkin. Unlike the last one on carving polyhedral pumpkins, where we used the entire pumpkin to carve a 3 dimensional shape, the pumkin carving in this post will involve two-dimensional images on a small part of the pumpkin's surface.
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...
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:
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.
I built this the other day from those weird gear plans from Clayton Boyer.
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...
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.
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.
Halloween is coming up, so many of you may have a need or desire to carve a pumpkin and turn it into a Jack O' Lantern. This week we are going to explore carving our pumpkins into interesting geometric shapes. In this post, we will carve the pumpkins into spherical versions of polyhedra, and in Thursday's post we will carve 2 dimensional stars and some simple fractal designs into the pumpkins.
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.
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.
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?
Thanksgiving. It's sadly over. But happily replaced by the Christmas season!
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.
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.
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.
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.
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.
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.
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.
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.
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.
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!
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.
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
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.
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...
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.
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.
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.
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.
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.
This is just too cool. As soon as I saw this, I thought, "Math Craft!"
Each curved module replaces the equilateral triangle of a simple octahedron. Inspired and copied from Cory's post with original artwork by Richard Sweeney
Below, polyhedron animation test #1. The model was folded using Cory Poole's modular origami tutorial.
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.
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.
So beautiful... I'm looking forward to tackling this one: Via David Petty:
Compound of two cubes with a Minecraft theme.