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.
Origami Wheel Robot
From BioRobotics Lab at Seoul National University
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.
created by Alexander Chen