Tessellations And Modular Origami From Fabric And Paper

You may be familiar with origami, the Japanese art of paper folding, but chances are you haven’t come across smocking. This technique refers to the way fabric can be bunched by stitches, often made in a grid-like pattern to create more organized designs. Often, smocking is done with soft fabrics, and you may have even noticed it done on silk blouses and cotton shirts. There are plenty of examples of 18th and 19th century paintings depicting smocking in fashion.

[Madonna Yoder], an origami enthusiast, has documented her explorations in origami tessellations and smocking, including geometric shapes folded from a single sheet of paper and fabric smocked weave patterns. Apart from flat patterns, she has also made chain-linked smocked scarves stitched into a circular pattern and several examples of origami tessellations transferred to fabric smocking. Similar to folds in origami, the stitches used aren’t complex. Rather, the crease pattern defines the final shape once the stitches and fabric are properly gathered together.

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This Artist Drags His Feet Across Sand And Snow

You may have seen Simon Beck’s work a few years back. The snow artist, known for creating large-scale works of art with nothing but snowshoes, has been creating geometrically inspired fractals and mathematical forms for years. An orienteer and map-maker by day, he typically plans out his works in advance and chooses sites based on their flat terrain. The lack of slopes prevents skiers from traversing the area beforehand and helps with measuring the lines needed to create the drawing.

He starts off by measuring the distance he has to be from the center by using a compass and walking in a straight line towards a point in the distance, making curves based on relative position to other lines. Once the primary lines are made, he measures points along the way using pace counting and joins secondary lines by connecting the points. The lines are generally walked three times to solidify them before filling in the shaded areas. The results are mesmerizing.

He has since expanded to sand art, using the same techniques that gained him fame in ski resorts and national parks on the sandy shores. Unfortunately, tidal patterns, seaweed, and beach debris make it slightly harder to achieve pristine conditions, but he has managed to create some impressive works of art nonetheless.

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Building Your Own Tensegrity Structure

It seems that tensegrity structures are trending online, possibly due to the seemingly impossible nature of their construction. The strings appear to levitate without any sound reason, but if you bend them just the right way they’ll succumb to gravity. 

The clue is in the name. Tensegrity is a pormanteau of “tension” and “integrity”. It’s easiest to understand if you have a model in your hand — cut the strings and the structure falls apart. We’re used to thinking of integrity in terms of compression. Most man-made structures rely on this concept of engineering, from the Empire State Building to the foundation of apartment building.

Tensegrity allows strain to be distributed across a structure. While buildings built from continuous compression may not show this property, more elastic structures like our bodies do. These structures can be built on top of smaller units that continuously distribute strain. Additionally, these structures can be contracted and retracted in ways that “compressionegrities” simply can’t exhibit.

How about collapsing the structure? This occurs at the weakest point. Wherever the load has the greatest strain on a structure is where it will likely snap, a property demonstrable in bridges, domes, and even our bodies.

Fascinated? Fortunately, it’s not too difficult to create your own structures.

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Hand-Carving Geometric Art

[Scott Cramer] is a retired professional woodworker who specializes in geometric art made from beautifully joined wood. In this project he’s carving four interlocked cloverleaf rings from a block of basswood. First he made a series of cuts to turn the block into a cuboctahedron, a geometric solid comprising six squares and eight triangles. Then he drew on the basic lines of the rings on the wood and went to work with a chisel, smoothing and separating the rings and carving out the interior. You can see more shots of the project on his Facebook post, which is included after the break.

To see more of [Scott]’s projects you can follow his Twitter feed. Our favorites include this 70″ pentagonal icosatetrahedron built out of hemlock that [Scott] says is the “largest in Coös County, NH” — what, there are others? He also made a magogany representation of a Hamiltonian circuit of a dodecahedron’s vertices.

We love math art on Hackaday — see our interview with Francisco do Comité we ran earlier this year.

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Arduino + Geometry + Bicycle = Speedometer

It is pretty easy to go to a big box store and get a digital speedometer for your bike. Not only is that no fun, but the little digital display isn’t going to win you any hacker cred. [AlexGyver] has the answer. Using an Arduino and a servo he built a classic needle speedometer for his bike. It also has a digital display and uses a hall effect sensor to pick up the wheel speed. You can see a video of the project below.

[Alex] talks about the geometry involved, in case your high school math is well into your rear view mirror. The circumference of the wheel is the distance you’ll travel in one revolution. If you know the distance and you know the time, you know the speed and the rest is just conversions to get a numerical speed into an angle on the servo motor. The code is out on GitHub.

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Animate Your Artichoke With A Lathe And Camera

Spirals, fractals, and even bone length proportions whisper of a consistent ratio woven into the universe. Math is hidden in the fabric of things, and when this fact is observed in art, magic happens. Professor, artist, and inventor [John Edmark] draws inspiration from geometric patterns found in nature and builds sculptures using the golden ratio as a standard for design. In this project, he expresses these characteristics through animated biomorphic zoetropes.

goldenratio2[John] modeled several 3D sculptures in Rhino containing similar geometric properties to those found in pinecones and palm tree fronds. As the segments grow from those objects in nature, they do so in approximately 137.5 degree intervals. This spacing produces a particular spiral appearance which [John] was aiming to recreate. To do so, he used a Python script which calculated a web of quads stretched over the surface of a sphere. From each of the divisions, stalk-like protrusions extend from the top center outward. Once these figures were 3D printed, they were mounted one at a time to the center of a spinning base and set to rotate at 550 RPM. A camera then films the shape as it’s in motion at a 1/2000 sec frame rate which captures stills of the object in just the right set of positions to produce the illusion that the tendrils are blooming from the top and pouring down the sides. The same effect could also be achieved with a strobe light instead of a camera.

[John] has more information on his instructables page. He also provides a video of this trick working with an actual artichoke; one of the living examples of the golden ratio which this project was inspired by. Thank you, [Charlie Nordstrom] for helping him document these awesome sculptures and for telling us about them!

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Learn The Geometry To Draw An Analog Clock On A Graphic LCD Screen

Does the image of the clock above make you shutter with fear because of the math you’d need to use to recreate your own version of the project? We certainly understand that High School geometry is becoming a very distant memory, but it’s really not as hard as you think. [Janw] built this analog clock using a graphic LCD and he’s done a great job of explaining the concepts behind it.

The hardware he’s using is pretty standard for an electronic hobby clock; an ATmega16, graphic LCD, DS1307 real-time clock, and supporting hardware like a potentiometer, resistors, and buttons. The code is written in Bascom, but like we said, [Janw] explains the concepts behind drawing the hands on the clock so you can recreate this with any microcontroller or software language you prefer. We  recommend grabbing a calculator and some blank paper. It took us a few tries to brush the cobwebs out and really grasp what he’s doing with each equation.