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Suppose a circle is divided by two radii and the two arcs a and b are in the golden ratio:
b / a = ( a + b ) / b = φ ≈ 1.618
Then the smaller angle formed by the radii is called the golden angle. It is equal to about 137.5° or 2.4 radians. We will denote the golden angle by γ. Its exact value, as a fraction of a complete circle, is ( 3 – √5 ) / 2 ≈ 0.382 cycles.
Bragging about mathematical ineptitude is not cool. There is nothing admirable about ignorance and incompetence. Moreover, everyone thinks mathematically all the time, even if they are not aware of it. Can we all do maths? Yes, we can! [See this week’s That’s Maths column (TM064) or search for “thatsmaths” at irishtimes.com].
When you use a map of the underground network, you are doing topology.
O God, I could be bounded in a nutshell, and count myself a king of infinite space …
[Hamlet]
Euclid. Left: panel from series Famous Men by Justus of Ghent. Right: Statue in the Oxford University Museum of Natural History.
For 150 years the city of Lvov was part of the Austro-Hungarian Empire. After Polish independence following World War I, research blossomed and between 1920 and 1940 a sparkling constellation of mathematicians flourished in Lvov [see this week’s That’s Maths column in The Irish Times (TM063, or search for “thatsmaths” at irishtimes.com).
The Scottish Café, Lvov in earlier times (left), now Hotel Atlas in Lviv (right).
ThatsMaths 