Henry Segermen’s 3D Printed Mathematical ArtHenry Segermen is a mathematician and mathematical artist who works mainly with three-dimensional geometry and topology, and 3D printing.

The images above are extremely cool. 3D printed spheres of various designs cast interesting shadows as the spheres’ designs are stereographically projected onto a flat surface with a shining light placed directly above.

The Math: Stereographic Projections- According to Wikipedia, a stereographic projections is a particular mapping that projects a sphere onto a plane. The projection is defined on the entire sphere, except at one point: the projection point. Try to find the projection point in the images above!Here is a picture, from Wikimedia Commons, of a Cartesian grid and its distorted appearance on a sphere:

The Cartesian grid projection can be seen in Henry Segermen’s art, above (upper left and lower right).

It seems to be common opinion that these 3D printed spheres would make awesome lampshades or party lights. Go to Henry Segermens’ website for even more mathematical art!

Creating the Sierpinski triangle fractal with rotating triangles. [more] [code] [inspiration]

Mathematics of the Rubik’s CubeErnö Rubik invented the Cube in the spring of 1974 in his home town of Budapest, Hungary. He wanted a working model to help explain three-dimensional geometry and ended up creating the world’s best selling toy. More than 350 million cubes had been sold worldwide making it the world’s top-selling puzzle game.

Algorithms exist for solving a cube from any specific position it is currently in, but typically there is no optimal solution; how quick a cube may be solved depends on the individual who is solving the cube and how quickly they are able to deal with the cube. An algorithm is a list of well-defined instructions for completing one’s work from a given situation. During the initial steps of solving the cube, the algorithms effect on other “cubies” are insignificant; however, later on, the chosen algorithm typically destroys the rest of the cube. Many of these algorithms are available to everyone, and memorizing them is beneficial to everyone who participates in Rubik’s Cube competitions. In 1995, with a lot of practice and effort, Michael Reid used a method known with a table of cosets to prove that any cube may be solved in twenty-nine turns. In the past few years, another individual proved the method required fewer steps. The current world record for single time on a 3×3×3 Rubik’s Cube was set by Mats Valk of the Netherlands in March 2013 with a time of 5.55 seconds at the Zonhoven Open in Belgium

Just like a majority of real life situations, the cube also consists of a grand number of combinations and permutations that it can be twisted into. The number of possible positions - permutations - of Rubik’s cube is

That is

43 quintillionways to possibly organize the cube. To put this into perspective, if one had as many standard sized Rubik’s Cubes as there are permutations, one could cover the Earth’s surface 275 times. If we stacked 43 quintillion pennies, the stack would be tall enough to reach the sun and return to the earth four thousand billion times. If you turned the Rubik’s cube once every second it would take you 1400 trillion years to go through all the configurations. If you had started this project during the Big Bang, you still would not have done it yet, since the universe is just 13.8 billion years old. The puzzle is often advertised as having only “billions” of positions, as the larger numbers are unfamiliar to many.However, there is a problem; the 43 quintillion ways to organize the cube dramatically increases when you take into consideration the centre cubes. These six centre cubes are more difficult to get to the original orientation. If one marks it the very first time, they will realize that most of the time the centre cubes are positioned differently. That is why, when one distinguishes the beginning orientation, it comes out that there are more ways that the cube may be organized. Thus orientations of centres increases the total number of possible cube permutations from 43,252,003,274,489,856,000 (4.3×10

^{19}) to 88,580,102,706,155,225,088,000 (8.9×10^{22}).

Today’s Classic: Adam and Eve Expulsion from Paradise1. By Alexandre Cabanel (1887)

2. By James Barry (c. 1750)

3. By Charles-Joseph Natoire (1740)

4. By Marioto Albertinelli (1514)

5. By Domenichino (1626

Néle Azevedo :Ice Men Figuriines in Belfast, Irelandbrazilian artist néle azevedo ,presented as part of the belfast

festival at queen’s university in northern ireland.

the artwork is a collection of hundreds of carved ‘ice-men’, ‘Monumento Minimo’, perched readily side by side on the steps of custom house in the city of belfast, a carefully prepared intervention that slowly thawed under the heat of the day. the figures sit slouched, with legs dangling – an oddly charming set of characters

full of aloof charisma. the project was selected by the curator of the event as a tribute to titanic victims, the ephemeral artwork a powerful expression of the transitory nature of life, and death.