19th Century
John Scott Russell
Imagine, if you will, that you have decided to go for a horse ride along a canal towpath. You see a canal barge making its way along the canal and in front of the barge [more…]
Mathematics
Health
A Brief Face To Face With Death
I was bored the other day and decided to download the Office of National Statistics Weekly Death data for England and Wales for the last 5 years (as you do). It can be found here [more…]
Health
Lives, damned lives and statistics
On January 11th, the BBC and Sky each made great play of ‘the worst excess deaths since the second world war’ announced for 2020. This clearly conveyed a message that the corona virus was indeed [more…]
20th Century
Benford’s Law
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…]
Hobbies
The Padovan Sequence and the Plastic Ratio
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…]
18th Century
Sophie Germain Primes and Cunningham Chains
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…]
Mathematics
The Infinity of the Primes
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…]
19th Century
Holography, Part Four
Holograph Examples The PFG-01 holographic film that I’ve used in the examples below is ideally suited to making transmission holograms but it can also be used to make reflection holograms. Reflection Holograms One of the [more…]
Mathematics
The Number of Derangements
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…]