(Video: Phil Torrone, Community Commons)
Looking at this video, we see the Adafruit‘s pt riding on a bicycle with square wheels, yet the ride is totally smooth. How can this be? The secret is that the surface must be the right one. In his fascinating book One Hundred Essential Things You Didn’t Know You Didn’t Know: Math Explains Your World, author John D. Barrow covers this and other fascinating phenomena.
Mathematics can reveal and illuminate things about the surprisingly complex world we live in that just can’t be learned any other way. Have you ever wondered why you always seem to get stuck in the longest line? Why two’s company but three’s a crowd? What determines the intricate pattern of a leopard’s spots? With simple math, lucid explanations, and accompanying illustrations, he sheds light on the dark and shadowy corners of the physical world we all think we understand so well.
In #64, A Bike With Square Wheels, Barrow explains:
The shape of the road surface that gives a steady ride on square wheels is created when you hang two ends of a chain from two points at the same height above ground. This is called the catenary… If we turn it upside down we obtain the shape that is used for many of the great arches of the world. But if you take a catenary arch and repeat it over and over again along a line you get a sequence of undulations of the same height. This is the shape of the ground surface that gives us the smooth ride on square wheels.
As the title suggests, there are a hundred phenomena that Barrow covers. Here are some of my favorites:
#49: Who was the cunning criminal who inspired Doyle’s Professor Moriarity?
#63: How do pendulum clocks keep perfect time?
#77: The physics of a diamond’s sparkle.
zeroeth zeroth law of robotics.
#87: Tautological maps.
These examples show how Barrow mixes it up with more soft and fuzzy topics that may be grouped along with hard-core math and physics, but remain more accessible. However, even the ‘pure math’ topics remain easy to understand. As can be seen in the ‘bike with square wheels’ example, Barrow does a great job of explaining the math behind the phenomenon without boring or confusing the math-disinclined. Many of the chapters come with diagrams or illustrations, which help explain the math and also serve to break up the text.
One Hundred Essential Things You Didn’t Know You Didn’t Know: Math Explains Your World is an engaging read that gets the ol’ neurons firing without requiring an advanced degree or a great deal of time. And you’ll learn a lot of fun facts!