Every curve in the plane has several other curves associated with it. One of the most interesting and important of these is the evolute. Suppose the curve $latex {\gamma}&fg=000000$ is specified in parametric form $latex {(x(t), y(t))}&fg=000000$ for $latex {t \in [0,1]}&fg=000000$. The centre of curvature $latex {\Gamma = (X, Y)}&fg=000000$ at a particular point … Continue reading The Evolute: Envelope of Normals
Month: February 2018
Galileo’s Book of Nature
In 1971, astronaut David Scott, standing on the Moon, dropped a hammer and a feather and found that both reached the surface at the same time. This popular experiment during the Apollo 15 mission was a dramatic demonstration of a prediction made by Galileo three centuries earlier. Galileo was born in Pisa on 15 February … Continue reading Galileo’s Book of Nature
Hardy’s Apology
Godfrey Harold Hardy's memoir, A Mathematician's Apology, was published when he was 63 years old. It is a slight volume at just 90 pages, but is replete with interesting observations and not a few controversial opinions. After 78 years, it is still in print and is available in virtually every mathematics library. Though many of … Continue reading Hardy’s Apology
Staying Put or Going with the Flow
The atmospheric temperature at a fixed spot may change in two ways. First, heat sources or sinks may increase or decrease the thermal energy; for example, sunshine may warm the air or radiation at night may cool it. Second, warmer or cooler air may be transported to the spot by the air flow in a … Continue reading Staying Put or Going with the Flow
ThatsMaths 