Telcos send routers with default passwords to their customers, who
never change them, and once they’re compromised, they automatically scan
neighboring IP space for more vulnerable routers from the same ISP.
More than 40,000 infected routers from 1,600 ISPs all over the world
have been documented. They’re enlisted for massive denial-of-service
attacks, and in their spare time, they crawl the rest of the Internet
and recruit more ISP-supplied equipment to join them or snoop on their
owners’ traffic.
If this seems bad, remember that the Internet of Things is coming, and
every lightbulb in your house will have the smarts to participate in a
botnet, and will be supplied by a company that lacks the smarts to
prevent it.
The largest mathematical proof in history is generally considered to be the classification of finite simple groups. The proof consists of tens of thousands of pages, published in several hundred journal articles, by about 100 authors, mostly between 1955 and 2004. It states that every finite simple group is isomorphic to one of the following groups:
The diagram above gives an overview of the 26 sporadic finite simple groups and the relations between them. The largest group is called the Monster and has order 808017424794512875886459904961710757005754368000000000. Nineteen other sporadic groups are involved in the Monster as subgroups or quotients of subgroups; together with the Monster group itself they form the “happy family”. The other six groups have no connection with the Monster and are called the “pariahs”. An arrow in this diagram means that one group is a homomorphic image of a subgroup of the other.
This animation is about one of the most significant problems in the history of mathematics: the brachistochrone challenge.
If a ball is to roll down a ramp which connects two points, what must be the shape of the ramp’s curve be, such that the descent time is a minimum?
Intuition says that it should be a straight line. That would minimize the distance, but the minimum time happens when the ramp curve is the one shown: a cycloid.
Johann Bernoulli posed the problem to the mathematicians of Europe in 1696, and ultimately, several found the solution. However, a new branch of mathematics, calculus of variations, had to be invented to deal with such problems. Today, calculus of variations is vital in quantum mechanics and other fields.
The word, origami, comes from the traditional Japanese art of paper folding. The unique characteristic of origami that realizes three-dimensional structures from two-dimensional materials have long attracted attention from various fields such as design, education and mathematics. Many of today’s engineers are using this oriental art to solve problems. It can be used as an inspiration to some architectural designs, and can also be used as fabrication method of robot design or MEMS process.
By using this origami structure, the deformable wheel can be built without using many mechanical parts; the wheel is built with a single piece of sheet, with specific folds. Moreover, because of the characteristic that the structure constrains its own movement, it is possible to control the shape of the wheel using only a few actuators. When the robot run into the small slit smaller than the wheel diameter, the robot can deform the wheel and it is possible to get through the terrain. The proposed design for the deformable wheel shows the possibility of using origami structure as a functional structure with its own mechanism.
Pianophase.com is a performance and visualization of the first section from Steve Reich’s 1967 piece Piano Phase. Two pianists repeat the same twelve note sequence, but one gradually speeds up. The musical patterns are visualized by drawing two lines, one following each pianist. The sound is performed live in the browser with the Web Audio API, and drawn with HTML5 Canvas.
