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Wilton Windmill was a unique formation in many ways. It potentially embodied a unique feature verifiable as a key element of Mathematics. Unlike the Pi formation of an earlier year which embodied a key number we all learn at school, this one codified an equation. Although the codes presented, namely the Ascii Codes, used universaliy to transform one`s keyboard symbols into a string of ones(1) and noughts(0), the errors displayed in the field presented a tantalising puzzle. Firstly there were 12 radial lines representing the codes of each of the equation`s symbols, Fig.1. It is seen that where there are code lines present, this represents a 1 (one) and no line a 0 (zero). However, for each radial there is the complementary code (exchanging 1`s for 0`s and vice-versa anti-clockwise of each radial). These lines form their own codes which in fact are pure integer numbers ranging from 200-300 plus. It turns out that the average of these is 274 and this it happens is twice the number 137. In Quantum Physics this is known as the **Fine Structure Constant**, arguably the most important number in this branch of Physics!

Also, since there are 8 symbols in an Ascii Code, this also reminds us of the diatonic scale (white notes on the piano) which we find everywhere in Earth Energies. Thus each radial has a left and right hand code(scale sequence) associated with it. Playing these `tunes` on the piano however, did not turn out to offer very inspiring music!

A recognisable equation only emerges when its first symbol is aligned with the Windmill. Reading the codes on the clockwise side of each radial yields the equation –

** e^(hi)pi)1=0 ** - (1)

Those having studied Mathematics will recognise its very close similarity to the well known Euler Identity. It is so named after the 18thcentury prolific Swiss mathematician Leonard Euler who for the first time linked together several apparently unrelated branches of the his beloved subject. The true equation is given by-

**- (2)** **eiTT**** + 1= 0 **

Here, **e** is Euler`s own number having the value 2.7183… , ** i** is the square root of -1, hence its so called imaginary status with

**TT**being the number we all learn at school, the ratio of the circumference of a circle to its diameter, namely 3.141592.. However, equation 1 is in fact an incorrectly formed equation in several ways. Firstly. parenthetically it is unbalanced. The most obvious mistake is the third -

**)**which should most obviously be a -

**+**, c.f the real Euler Equation - (2). Secondly why use

**pi**instead of the well known Greek symbol

**TT**which has its own Ascii code. Thirdly, what is

**h**in this context. If it is a general variable, then it would be common practice to use

**and hence be placed after the**

*x***pi**. Could it be that it represents Planck`s Constant which is universally denoted by

**h.**If the latter, then why locate it in this particular location? We conclude from this two things –

- the Circle Makers (real variety) simply screwed up in the field since
**)**and**+**differ by only one digit in their respective Ascii codes

- the (virtual) Circle Makers are keeping us on our toes by introducing deliberate errors into the formation

Euler`s equation is best understood in a graphical form as shown in Fig.2. The constant **e** is expanded in a series form which is how Euler derived it with each term in the series represented by the length of a line. The *x*-axis is for real numbers in the series and the *y*-axis is for imaginary numbers identified by the preface *i.* So equation 2 is effectively presented as a converging rectangular spiral homing in on the number -1. Now if this simple form of crop circle had been displayed in the field, there would have been no argument as to both its origin and indeed accuracy. Surely , a straight line crop formation is far easier to produce for both real and virtual Circle Makers than the one seen at Wilton?

If a mathematically correct formation in the format seen in the field is sought, then it is possible to encode equation 2 directly but this time needing only 6 –fold geometry. Fig. 3 shows what should have been seen in the field if we were to be totally convinced that the Circle Makers are truly competent mathematicians.

jwlyons

**Sept. 2010**