A great mathematician speaks to us across the ages: lessons in cubic geometry from elsewhere in space or time!  

So far this summer we have seen four novel “cubes” in English crops at Danebury on July 6, Cley Hill on July 9, Fosbury on July 17, and now Horton on August 9. All four of those cubic images were inscribed within hexagons, and have their own distinctive meanings:

Danebury (6-7) referred symbolically to Metatron’s Cube, Cley Hill (9-7) to Leonardo da Vinci’s Cube, Fosbury (17-7) to Archimedes’ Cube, and now Horton (9-8) to an ancient geometric proof written down first perhaps by Euler or Archimedes (see cley hill or 2010_crop_circle_season).  

Horton of August 9, 2010 shows us a clever geometrical result from ancient times  

As shown below, Horton shows us one particular cross-section of a cube, where a triangular pyramid shares all four of its vertices with those of a cube within which it has been inscribed: 

What might be the volume of that small pyramidal cross-section, relative to the volume of the entire cube itself? After some lengthy calculations, using trigonometry in three dimensions, we find that the answer is “one-sixth”. And as if to confirm that answer, the crop artist drew a long tube of square cross-section around the entire “pyramid and cube” at Horton, then divided it into six equal parts (see above on the upper left).  

Is this the first time we have been shown ancient geometry in crops? Certainly not! Gerald Hawkins found four ancient geometrical proofs by Euler in early crop pictures from 1990 to 1995, and even predicted a “fifth theorem” which appeared in crops the next summer (see ilyes or hawkins or www.youtube.com). 

Other “cubic” crop pictures appeared during the summer of 2007 

More recently during the summer of 2007, a whole series of “cubic” crop pictures likewise appeared. Some of those provided us with a numerical countdown towards an important astronomical event that year: namely an inferior conjunction of Venus with our Sun on August 18, 2007. First a great crop picture appeared in East Field on July 7, showing three lunar cycles of 29 days ending on August 12, followed by another six days to reach August 18. Then at Sugar Hill on August 1, we saw a clever depiction of Metatron’s Cube, which contained 18 single cubes as if to say “18 days left until August 18” (as noted by Janet Ossebaard at the time). Next at Stanton on August 12, we saw a Mayan number six as if to say “6 days left until August 18” (any Sun-Venus conjunction would be an important day in their Calendar Round).  

Finally at West Overton on August 17, we saw a Flower of Life that had been constructed from a series of small triangular pyramids, as shown in both lower parts of the diagram above. After doing some lengthy calculations, we learned that each triangular cross-section of a cube about its vertex contains just one-sixth the volume of an entire cube, within which it has been inscribed. Six of those triangular pyramids were then drawn together as a circle at West Overton, as if to say “6 x 1/6 or one day left until August 18”.  

Horton of August 2010 clearly recapitulates West Overton of August 2007  

The crop artists at Horton on August 9, 2010 have clearly recapitulated what they first showed us at West Overton on August 17, 2007. Just as in the summer of 2007, a series of very clever “cubic” crop pictures have appeared, and each has taught us something concerning ancient three-dimensional geometry, of the kind once practiced by Euler or Archimedes. Then the same “one-sixth volume” theorem has appeared in both cases, for a triangular pyramid inscribed within a cube at all four of its vertices.  

Could any of these “cubic” crop picture be human-made fakes? Possibly although it seems doubtful. Could all of these “cubic” crop pictures be human-made fakes? Not a chance, unless you also believe in Santa Claus or the Easter Bunny!  

Modern crop pictures are our “Tiananmen Square”: where is Julian Assange when we need him?  

Recently I was talking with a young Chinese girl who, although very intelligent, had never heard of the historic events at Tiananmen Square in 1989 (see http://en.wikipedia.org/wiki/Tiananmen_Square_protests_of_1989). What had happened was that the Chinese government, fearful of another popular uprising for democracy, had censored the news of that important event completely out of all of their history books and media discussions, so that as far as many young people living in China today would know, the big protest “never happened”.  

A symbolic parallel here with modern crop pictures seems overwhelming. Those remarkable transmissions through space and time, using a technology which is far beyond anything we have today, have been going on now for twenty years from 1990 to 2010, approximately fifty times each summer across southern England or Europe (mainly). Yet insofar as the great majority of people living on Earth today would say, such crop pictures “never existed”, because they have been completely censored out of all history books or mainstream newspaper reports.  

The governmental authorities in England or other countries must be quite fearful of what modern crop pictures portend, in order to treat them in such a serious fashion. Julian Assange, where are you? There is an important task for you here!  

CMM Research