### 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…]

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…]

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…]

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…]

During a presidential debate, a little old lady, her grey hair in a bun, asks, “Name the three most important Space Race countries”. Sleepy-creepy Jo Biden, from his basement and with the benefit of voice [more…]

A Simple Dual Beam Setup We’ve got our film, developer and a safety lamp. Now we need a holographic camera. Well, not exactly a camera. You can’t take a picture of rolling hills or a [more…]

Apparently, some subset of younger people are upset and intimidated about the use of full stops in text and other messages. I am not sure what they would think about the ellipsis, … , or [more…]

A Holographic Camera Standard photography uses a lens system to focus an image onto a film or an electronic sensor. If you recall from part one, Dennis Gabor had a problem with his electron microscope’s [more…]

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