What proportion of all numbers less than a given size N have a 9 in their decimal expansion? A naive argument would be that, since 9 is one of ten distinct digits, the answer must be about 10%. But this is not "remotely close" to the true answer. Counting the Nines It is a simple … Continue reading Numbers with Nines
Month: June 2018
Optical Refinements at the Parthenon
The Parthenon is a masterpiece of symmetry and proportion. This temple to the Goddess Athena was built with pure white marble quarried at Pentelikon, about 20km from Athens. It was erected without mortar or cement, the stones being carved to great accuracy and locked together by iron clamps. The building and sculptures were completed in … Continue reading Optical Refinements at the Parthenon
“Dividends and Divisors Ever Diminishing”
Next Saturday is Bloomsday, the anniversary of the date on which the action of Ulysses took place. Mathematical themes occur occasionally throughout Ulysses, most notably in the penultimate episode, Ithaca, where the exchanges between Leopold Bloom and Stephen Dedalus frequently touch on weighty scientific matters. [Last week's ThatsMaths post] In Ithaca, the narrator takes every … Continue reading “Dividends and Divisors Ever Diminishing”
Leopold Bloom’s Arithmetical Adventures
As Bloomsday approaches, we reflect on James Joyce and mathematics. Joyce entered UCD in September 1898. His examination marks are recorded in the archives of the National University of Ireland, and summarized in a table in Richard Ellmann's biography of Joyce (reproduced below) [TM140 or search for “thatsmaths” at irishtimes.com]. The marks fluctuate widely, suggesting some lack of … Continue reading Leopold Bloom’s Arithmetical Adventures
ThatsMaths 