When mathematicians closely examined Van Gogh’s flowing artwork such as Starry Night, they found that he had somehow exactly captured the movement of turbulent flow, a highly complicated pattern found in fluid dynamics that is still not completely understood.

This musical instrument is completely hand made. It made the front page of Youtube a while back, and has since amassed over 20 million views, and for good reason. Although I haven’t watched them, there are two videos he has since released the shows how he made them. I will include them below for those so inclined.

From David Wells’ Archimedes Mathematics Education Newsletter:

Draw two parallel lines. Fix a point on one line and move a second point along the other line. If an equilateral triangle is constructed with these two points as two of its vertices, then as the second point moves, the third vertex of the triangle will trace out a straight line.

The ordinary tetrahedron, or triangular pyramid, has no diagonals — every pair of vertices is joined by an edge. How many other polyhedra have this feature? In 1949, Hungarian topologist Ákos Császár found the specimen above, which has 7 vertices, 14 faces, and 21 edges.

But so far these two are the only residents in this particular zoo. “It isn’t known if there are any other polyhedra in which every pair of vertices is joined by an edge,” writes David Darling in The Universal Book of Mathematics. “The next possible figure would have 12 faces, 66 edges, 44 vertices, and 6 holes, but this seems an unlikely configuration — as, indeed, to an even greater extent, does any more complex member of this curious family.”

A few of you might know that I’m very fond of making polyhedrons out of cardstock. It takes a lot of time with the really complicated ones (though not nearly as complex as the one above!!) but it’s a rewarding task and the result is (hopefully) pleasing to the eye. If you are interested in trying your hand at making some yourself this summer, this is a very good source for templates.

In this clip, Science presenter Steve Mould demonstates how wave vibrations can be made visible by using couscous or some other fine material that show the different patterns created by a vibrating plate. These Chladni figures are named after German physicist Ernst Chladni who discovered them in the 18th century.

Engineer Guy Bill Hammack details the engineering choices underlying the design of a beverage can. He explains why it is cylindrical, outlines the manufacturing steps needed to created the can, notes why the can narrows near it lid, show close ups of the double-seam that hold the lid on, and details the complex operation of the tab that opens the can.

Shinobu Kobayashi, a Japanese woodworker, demonstrates the flexibility and utility of the kawai tsugite joint, which was invented by a professor at Tokyo University. Explanation below.