The Silent Night Chapel (Stille-Nacht-Kapelle) is located in the town of Oberndorf bei Salzburg in the Austrian province of Salzburg, and is a monument to the Christmas carol Silent Night and its librettist, Joseph Mohr [more…]
The third Sunday of Advent – #Joy. A traditional English carol from the 16th century or earlier. © OldTrout
This is a poem written by Christina Rossetti, set to music first by Gustav Holst in 1906 and then by Harold Darke in 1911. This is by Darke : © OldTrout
Today is the first Sunday of Advent. It is time to light the first candle. #Hope. O come, O come, Emmanuel, And ransom captive Israel, That mourns in lonely exile here, Until the Son of [more…]
Benford’s Law is a theory of leading digits in numerical data sets. Whilst one might think that the frequency of the leading digit would be equally distributed across the nine digits each with approximately 11% [more…]
The golden ratio is well known and is associated with the Fibonacci sequence of numbers. (phi) is the positive root of the quadratic equation . The exact value is given by Its continued [more…]
A Sophie Germain prime is a prime number such that is also a prime number. That is, , where and are both prime. For example, . The sequence begins Sophie Germain () explored these primes [more…]
Euclid’s Elements, Book IX, Proposition 20. Theorem : Prime numbers are more than any assigned multitude of prime numbers. That is, there are infinitely many primes. Proof : Suppose that there are primes : Let [more…]
Read as : the limit, as approaches infinity, of subfactorial divided by factorial is equal to divided by which approximates to , where is Euler’s number, The Hat Check Problem, as first described by Montmort [more…]
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