Minimal Posters - Six Women Who Changed Science. And The World.
Geeky Math Equation Creates Beautiful 3-D World
They call it the Mandelbulb. The 3-D renderings were generated by applying an iterative algorithm to a sphere. The same calculation is applied over and over to the sphere’s points in three dimensions. In spirit, that’s similar to how the original 2-D Mandelbrot set generates its infinite and self-repeating complexity.
The Lorenz system is a system of ordinary differential equations (the Lorenz equations) first studied by Edward Lorenz. It is notable for having chaotic solutions for certain parameter values and initial conditions. In particular, the Lorenz attractor is a set of chaotic solutions of the Lorenz system which, when plotted, resemble a butterfly or figure eight.
The first 4,000,000 digits of Pi, visualized in a single image
Pi is what’s known as an irrational number, which means that its decimal representation is both infinite and non-repeating.
We’ve been using computers to calculate the digits of Pi for decades. In 1949, John von Neumann and his colleagues used ENIAC — the world’s first general-purpose electronic computer — to calculate Pi to the 2,037th digit. We surpassed the million-digit milestone in 1973. And on October 17, 2011, after 371 days of computing, Shigeru Kondo finished calculating Pi to 10 trillion decimal places.
The picture up top is adapted from a rather simple but effective piece of data visualization, created by the folks at design studio TWO-N, which represents the first four-million digits of Pi in a brilliant mess of interactive pointillism.
Each digit, from 0-9, was assigned a color based on the legend pictured here, and then rendered as a single, 1x1 pixel. Line the pixels up in the order designated by Pi, confine them to a 4-millon pixel image, and you get this interactive applet here, which lets you soar around the entire image, inspecting 500,000-digit sections at a clip. There’s even an interesting search function that lets you probe the mathematical mosaic for number up to eight digits in length. [TWO-N via information aesthetics]
MUSIC IS MATH
How Einstein Came Up With Special Relativity
Time dilation. Length contraction. The fact that time moves faster at your face than it does at your feet. These are all experimentally verified consequences of the Special Theory of Relativity, proposed in 1905 by Albert Einstein. But the theory also helped explain one of the most nagging questions of modern physics, namely: how anything other than light can move. Minutephysics’ Henry Reich explains, with the help of some sliding switcheroos. [Via Henry Reich]
Creative, diagrammatic self-portraits of the artist, by Minjeong An
Proof by rearrangement of four identical right triangles
The animation consists of a large square, side a + b, containing four identical right triangles. The triangles are shown in two arrangements, the first of which leaves a square c2 uncovered, the second of which leaves two squares a2 and b2 uncovered. But as these uncovered areas with the areas of the four triangles fill the large square, the uncovered areas must be equal, so a2 + b2 = c2.
Ostomachion, also known as loculus Archimedius (Archimedes’ box in Latin) and also as syntomachion, is a mathematical treatise attributed to Archimedes. This work has survived fragmentarily in an Arabic version and in a copy of the original ancient Greek text made in Byzantine times
The game is a 14-piece dissection puzzle forming a square. One form of play to which classical texts attest is the creation of different objects, animals, plants etc. by rearranging the pieces: an elephant, a tree, a barking dog, a ship, a sword, a tower etc. Another suggestion is that it exercised and developed memory skills in the young. James Gow, in his Short History of Greek Mathematics (1884), footnotes that the purpose was to put the pieces back in their box, and this was also a view expressed by W. W. Rouse Ball in some intermediate editions of Mathematical Essays and Recreations, but edited out from 1939.
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.
How the Airplane got its Shape
Modern aviation arguably has its roots in Sir George Cayley. In 1799, he sketched the overall design of a fixed wing flying machine that used “flappers” to provide lift and a movable tail as a rudder for directional control. Although the design is awkward and ungainly, it’s striking to note that this is the first time the control forces of flight were treated separately – the rudder moved independent of the wings. Made of wooden support and treated fabric, Cayley did achieve moderate success with his designs, though his flights were more like short hops and the vehicle often stayed tethered to the ground.Really, he created gliders that relied on sufficient wind for lift. (Right, a series of Cayley’s glider designs.)
The most interesting mathematical mistake in the solar system
Johann Elert Bode is the author of Bode’s Law, one of the most contentious laws in astronomy. It’s a ridiculous idea which juggles numbers, seemingly for no reason, and it ends up revealing the spacing of the planets in the solar system. Or does it?
Find it here
How much energy would the Death Star require to destroy Earth?
As iconic as the spherical death-bringer is, the inner tinkerings of the Death Star still remain a great mystery. For example, if the Death Star suddenly materialized in the Solar System, how much energy would the vessel require to pulverize the Earth into bloody gravel?
A group of physics students at the University of Leicester took it upon themselves to divine the Death Star’s energy requirements (using many an admittedly radical assumption). From the paper titled "That’s No Moon":
This planet is going to be modelled after earth with the exception that it is a solid planet. It is then possible to use the gravitational binding energy of the target planet to estimate the amount of energy required to be supplied to the Death Star’s laser beam in order to destroy it […] The energy required to destroy the planet in question is 2.25 ⨉ 10^32 J. However, the destruction of large planets such as Jupiter can require much larger energy demands […] we can estimate this energy to be 2 ⨉ 10^36 J […]
Since the Death Star outputs energy equal to several main-sequence stars, even if the actual composition of Earth is used in equation, the value yielded is only a few orders of magnitudes larger and the Death Star can still easily afford to output that energy due to its tremendous power source. However as mentioned above Jupiter requires much greater energy demands which would put considerable strain on the Death Star. To destroy a planet like Jupiter it would probably have to divert all remaining power from all essential systems and life support, which is not necessarily possible.
I wouldn’t put it above the evil Empire to cut off the oxygen just to eke out that last joule of murder. When you’re spending $15.6 septillion, a Luxembourg worth of Stormtroopers is but a drop in the bucket.