Thing 1: Astronomy. There are interesting news reports going around about observations of huge bursts of radio energy, unknown until a few years ago. They say that they release in a millisecond as much energy as the Sun puts out in 300,000 years. (Big explosions! Who doesn’t like that!) The sources are unknown as yet, but the prime suspects are magnetars, neutron stars with immensely strong magnetic fields (which would kill you at 1000 km). Again, totally cool. I was really glad to be led to look up magnetars (which are pretty recently discovered/generally accepted objects) so I thought I’d pass it along.
Thing 2: Math. In looking over some materials from the amazing Park City Math Institute (particularly their wonderful Secondary Schools Teachers’ Program) I was led to look up the notions of an Euler brick and a perfect cuboid. An Euler brick is a simple gadget: it’s just a rectangular box with integer side lengths and integer face diagonals. Algebraically, it’s a solution to three linked quadratic Diophantine equations—or more simply, it’s three linked Pythagorean triples. Some solutions were known before Euler, but he came up with a way to generate whole families of solutions. Now, such gadgets are cool enough, but the real interesting bit is to try to find a perfect cuboid: an Euler brick that also has an integer body diagonal (from one corner to the opposite corner). (Algebraically, that adds one more quadratic equation, with one more variable.) Nobody knows if such a thing exists, but nobody has proved it can’t exist, either. A very natural, easy to describe, and presumably devilishly hard problem! Check out the link above for more. I’ll try to make a video about these things at some point. Too cool not to share!