Mathematics Puzzle: Round-trip On A Treadmill

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

Journal of Humanistic Mathematics

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

Experience Before Instruction, Examples Before Theorems

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

Distraction Displays Of Backyard Robins

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

Puzzle: A Cube Of Resistors, Updated With Links To Solutions

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

Mistakes In Education

We adults tend to fear making mistakes. We weren’t like that as children; watch any child learn to walk, or learn to ride a skateboard, shoot baseline jumpers over and over, or do just about anything that requires practice. Children keep at it, despite making mistakes repeatedly, because it’s fun. That is, the activity they’ve … Read more