"All the world's a stage we pass through." - R. Ayana

Saturday, 27 February 2010

Easy as Pi: Astrophysicist solves crop circle riddle

Easy as Pi: 
Astrophysicist solves riddle of Britain's most complex crop circle

 It is - by any calculation - a creation stunning in its ingenuity. 
 
Carved out in a barley field, this 150ft wide pattern is said to be a pictorial representation of the first ten digits of Pi, one of the most fundamental symbols in mathematics. 

Believers in extra-terrestrials could argue it was made by mathematically-minded aliens on a field trip to Earth.

Crop circle
Mystery: The crop circle in a barley field near Wroughton in Wiltshire is a coded version of pi

Sceptics will think it the work of humans with a fondness for figures and a penchant for puzzles. 

But whatever its origins, the experts say it is the most complex crop circle ever seen in Britain. 

The pattern appeared earlier this month near Barbury Castle, an Iron Age hill fort above the village of Wroughton in Wiltshire. 

Initially, crop circle enthusiasts were stumped as to its meaning and even a number of experts said it was 'mind-boggling'. 

Then retired astrophysicist Mike Reed saw a photograph of it and made the mathematical link.

Crop circle
Complex: The formation is 150 metres in diameter

He said the crop pattern 'clearly shows' the first ten digits of pi,  which - as many will remember from their schooldays  -  is used to calculate the area of a circle using the formula Pi /r squared.

Mr Reed said: 'I noticed a photo of the Barbury Castle pattern. It shows a coded image representing the first ten digits of Pi  -  the ratio of the circumference of a circle to the diameter. 

'The tenth digit has even been correctly rounded up. 

'The little dot near the centre is the decimal point. The code is based on ten angular segments, with the radial jumps being the indicator of each segment.' 

After working out the sequence, Mr Reed produced the accompanying diagram. The image is an example of what is known as a fractal, or geometric pattern. 

Fractals have been a staple of crop circle designs for many years, the most well known being the Mandelbrot Set or the Julia Set, which appeared 12 years ago in Avebury Trusloe, Wiltshire.
Lucy Pringle, a renowned researcher of crop formations, has the largest database in the world on the phenomenon. 

She said yesterday: 'This is an astounding development - it is a seminal event.'

Although numerous-individuals have come forward over the years admitting they had been making crop circles, many people still believe the rings are linked with the paranormal or civilizations in far-flung galaxies. 

As yet, no one has claimed responsibility for the Barbury Castle circle.

How it works

Although  it appears complicated at first glance, the puzzle does make perfect sense if approached logically and taken step by step. 

The coded image depicts 3.141592654, the first ten digits of Pi. How is it done? 

Firstly, the diagram is divided into ten equal sections (a bit like a dartboard, or a cake sliced ten ways) because there are ten staggered edges located at strategic points around the crop circle. 


Banbury Castle Crop Circle


To help understand how this is arrived at, look again at the photo above and imagine a giant ruler being aligned with the edges (ignore the tractor lines, which were there before the circle was created). 

That sets the basic framework. Next, each number in Pi is represented in the diagram by a corresponding number of coloured blocks. 

Beginning in the centre with the arrow marked 'Start', the first number, three, is represented by three red blocks from clockwise.
Follow this round and this takes you to the decimal point, which is depicted by a small circle in the barley. 

The number after the decimal point is one, represented by one green block. 

The same pattern continues for each of the numbers - four purple blocks, one orange, five blue, nine yellow, two purple, six red, five green, then four dark blue, followed by three circles, or dots, acknowledging that Pi is infinite. 



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