Crop Circle 22 May 2010 Wilton Windmill, Wiltshire UK (Euler Identity)
A new crop picture at Wilton Windmill on May 22, 2010 showed the famous "Euler Identity" from complex mathematics in 8-bit ASCII computer code.
A new crop at Wilton Windmill on May 22, 2010 broke new grounds of expression between the crop artists and ourselves, in terms of the sophistication and coding level of their message. Thus it showed a series of 12 x 8 binary digits in standard 8-bit ASCII code (see ASCII), repeated in duplicate within various parts of the message. When translated into modern English, those 96 binary digits give the result:
e ^ (hi)pi) 1 = 0
On our planet, the famous "Euler Identity" from complex mathematics is often written in abbreviated form as (see Euler's_identity):
e ^ (i pi) + 1 = 0
Thus their crop-based message shows two slight differences from what we call the "Euler Identity". First, it does not seem to contain a "plus sign" on the right. Yet if those crop artists were not perfectly familiar with all aspects of our ASCII code, they could easily have written "right parentheses" for "plus" by a single one-bit error. In which case, the crop formula would become:
e ^ (hi)pi + 1 = 0
which is a close fit to our Euler Identity. The second difference is that they seem to write our complex imaginary symbol "i" as "hi".
Many modern scientists and mathematicians regard that Euler Identity to be the "most beautiful mathematical formula ever" (see Leonhard_Euler), or the "greatest equation ever" (see Euler's_identity). It follows as a special case from Euler's more general formula:
e ^ (i x) = cos (x) + i sin (x)
when x = pi.