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.
Continue reading ‘Golden Moments’
Published March 12, 2015
Tags: Geometry, History
O God, I could be bounded in a nutshell, and count myself a king of infinite space …
Euclid. Left: panel from series Famous Men by Justus of Ghent. Right: Statue in the Oxford University Museum of Natural History.
Continue reading ‘A King of Infinite Space: Euclid I.’
Published March 5, 2015
Tags: Analysis, 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).
Continue reading ‘Café Mathematics in Lvov’