jtotheizzoe:

Computational Origami

Erik and Martin Demaine are a father-son team exploring the mathematical mysteries in folded paper. When circular sheets are crinkled along concentric circumferences, it results in exotic projections like the ones seen above. 

This is a form of paper art that has been explored since the 1920’s, but the Demaines are using modern computation to unravel the complex algorithms behind the shapes. Starting with different curvatures and rotations in flat paper, they don’t always know what will come out the other end.

More of their curved-crease sculpture here, and their book.

(via Brain Pickings)

expose-the-light:

Photographer Loves Math, Graphs Her Images

Here are some of the pictures the photographer named Nikki Graziano have captured. Graziano, is a math and photography student at Rochester Institute of Technology, she overlays graphs and their corresponding equations onto her carefully composed photos.

    “I wanted to create something that could communicate how awesome math is, to everyone,” she says.

Graziano doesn’t go out looking for a specific function but lets one find her instead. Once she’s got an image she likes, Graziano whips up the numbers and tweaks the function until the graph it describes aligns perfectly with the photograph. See more of her Found Functions series at Nikkigraziano.com.

fantastic

matthen:

If you roll a circle inside one 3 times its size, it will actually trace out a 4 pointed star shape called an Astroid (this shape is traced out in the animation in orange).  But what if inside the smaller circle, there is an even smaller one tracing out a smaller Astroid?  This animation shows the intricate shape that is generated by adding the effects of all the Astroids.  [code] 

cooool

14-billion-years-later:

The Hexagon

Hexagons have to be one of my favorite shapes, it’s hard to say why but I just think they’re neat. They have internal angles that add up to 720 or 4 lots of pi for those who prefer radians (everyone). The other neat thing is that the length between a vertex and the one opposite is twice the length of one of the sides in a regular hexagon. This in turn means that hexagons can be constructed from equilateral triangles. The area for a hexagon is given by the formula A=((3√3)/2)t^2 where t is the length of one of the sides, or alternatively simply A=1.5dt where d is the length between parallel sides. The elegant construction discovered by Euclid is also pictured.

Hexagons also pop up a lot in nature, being the shape of honey combs (for it’s space optimizing ability), igneous basalt columns, crystal structures, benzene rings, snow flakes and the clouds on Saturn’s north pole.

coool

scienceisbeauty:

Fast simulation of laplacian growth. Laplacian instability is the physical mechanism that drives pattern formation in many disparate natural phenomena.

Credits: Theodore Kim, Jason Sewell, Avneesh Sud, Ming Lin IEEE Computer Graphics and Applications

Source, Media Arts and Technology, University of California, Santa Barbara

euphoriaformyeyes:

The Garden of Cosmic Speculation is at Portrack House, near Dumfries in South West Scotland. It is a private garden created by Charles Jencks. The garden is inspired by science and mathematics, with sculptures and landscaping on these themes, such as Black Holes and Fractals.

oh wow yes #earth porn

very good

quantumaniac:

Stephen Hawking as You’ve Never Seen Him Before. 

Stephen and Jane Hawking on their wedding day; 1965.