Phi and the golden angle

 

The 'golden angle phi' may be found everywhere in the natural world and its mathematics provides the 'golden section' favoured by artists and architects over millenia. 

Key Mathematics of Phi

• Exact Value: \(\phi = \frac{1+\sqrt{5}}{2} \approx 1.6180339887\dots\)
• Quadratic Equation: \(\phi^2 = \phi + 1\) (or \(\phi^2 - \phi - 1 = 0\))
• Reciprocal Property: \(\frac{1}{\phi} = \phi - 1 \approx 0.618\)
• Continued Fraction: \(\phi = 1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{1+\dots}}}\) [1, 2, 3, 4]

Credit: Wikipedia.

The fern in the image above is arranged and unfurling following those precise mathematical rules.👍🪴

'Art and artificial intelligence'

As I was about to start a 'self portrait ', I decided to see what an 'artificially intelligent bot' could make of a preparatory 'chalk and charcoal ' sketch.  Well, I was impressed with the likeness, composition and the line quality of the drawing prepared by Gemini Google.com

Full Moon in May

 

Relatively speaking, the May full Moon sailed between the clouds as viewed from our garden in Oulton Broad, UK. Not ideal for astrophotography but the Seestar S30 smartscope made a tidy job of it in difficult conditions.

A big bang thankfully 40 million light years away.

 

The faint blurry dot to the left of the brighter galaxy central bulge is the recent supernova in the edge on galaxy NGC 5907 in constellation Draco. The core collapse supernova represents one of the most extreme events in the Universe. If there were any living species within a few tens of light years of this collapsing star their future would have been exterminated. More will be posted on the Jodrell Plank Observatory blog in due course.

Lemon sole, tomatoes, peas and chips.

 

A classic national dish. Enhanced by sliced bread and butter. Garnished with tomato sauce and mayonnaise. Lemon sole is such a delicate and tasty flat fish. "What's not to like'

Kipper Pate Quiche ?

 

Does what it says on the tin. May not be  to everyone's taste but everything including the kipper pate was made from 'scratch' apart from the pastry, which was acquired from the supermarket as a roll (life is really too short rather like the pastry)!

Another pretty New Moon. Across the fields at Darsham, dark sky village, Suffolk, UK.

The New Moon seen setting over the fields at the 'Dark Sky Village' Darsham, Suffolk, UK. Photographed with a Google 8a smartphone. A lovely moment in time!