I just picked up a copy of The USSR Olympiad Problem Book, by D.O. Shklarsky, N.N. Chentzov, and I.M. Yaglom, and it looks delightful. The book’s foreword states that it is intended for high-school students, although outstanding middle-school students might also give it a go. Complete solutions are given, which are particularly detailed for the … Read more
I was reading the delightful blog Ask A Mathematician / Ask A Physicist (in particular, this post), when I encountered this noteworthy comment (and this one) from one of that blog’s readers. The post is about why the earth orbits the sun, and the essence of the two comments is that science is unable to … Read more
One way to specify a sequence of numbers is recursively; that is, the first one or more terms in the sequence are stated, and then a formula for the general term of the sequence is given in terms of one or more previous terms. For example, in the famous Fibonacci sequence, the first two terms … Read more
This YouTube video shows an impressive memory trick by Derren Brown. The Amazing Kreskin has previously pulled off something similar, with a simultaneous match against Viktor Korchnoi and Robert Byrne; the trick there was that Kreskin was also blindfolded! But I believe that Kreskin used the same pairing trick that Brown used; so which is … Read more
Well, it’s been a while, but here at last is the promised solution to the treadmill puzzle posted here. I saw a version of the puzzle here (in the midst of a great discussion of extreme examples and counterexamples) at the excellent blog of Dave Richeson, who cites The Futility Closet. Here is the puzzle: … Read more
Alice and Basil are bored while waiting in an airport. They decide to play a game with one of the nearby “moving sidewalks” (treadmills). They decide that Alice will walk on the treadmill at constant speed $v$ (with respect to the treadmill) for a distance $y$, and then turn around and walk back to the … Read more
The Journal of Humanistic Mathematics, a new online-only, peer-reviewed mathematics journal, is in its first issue. The Journal of Humanistic Mathematics aims to provide an open forum for both academic and informal discussions on the various threads of mathematical inquiry. The focus of submitted papers should be on the aesthetic, cultural, historical, literary, pedagogical, philosophical, … Read more
I’ve spent a lot of my time in the past few days working around the house, constructing bookshelves (from store-bought Ikea-like kits), tearing down some interior walls in our basement, and whatnot. I found myself thinking about the physics courses I’ve taught in the past, and how some key points in the courses were perfectly … Read more
I heard on the radio last week that most birds spend a few days out of the nest before they are able to fly. They are particularly vulnerable in this period, obviously, as they can only hop away from predators, and aren’t strong enough to fly more than a couple of feet. I saw this … Read more
I posted this puzzle a few days ago: Consider 12 identical resistors connected to form a cube. That is, each resistor lies on the edge of a cube, and there is an electrical connection joining three resistors at each of the cube’s eight vertices. What is the effective resistance between two vertices across a body … Read more