Archive for February, 2018

The Evolute: Envelope of Normals

Every curve in the plane has several other curves associated with it. One of the most interesting and important of these is the evolute.


Sin t (blue) and its evolute (red).

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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 1564, just 454 years ago today [TM133 or search for “thatsmaths” at].


Image: NASA

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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 Hardy’s opinions are difficult to support and some of his predictions have turned out to be utterly wrong, the book is still well worth reading.


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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 process called advection. Normally, the two mechanisms act together, sometimes negating and sometimes reinforcing each other. What is true for temperature is also true for other quantities: pressure, density, humidity and even the flow velocity itself. This last effect may be described by saying that “the wind blows the wind” [TM132 or search for “thatsmaths” at].


Hurricane Ophelia approaching Ireland, 16 October 2017, 1200Z. Image from

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