Geometric Complexity of Crop Circles

Some people still buy the “party line” from standard news media about crop circles being all man-made. The speed and precision with which they are all appear would negate the notion of human hands (and feet) being involved. The crops are often flattened in spiral patterns with the middle tufts left standing in a matter of seconds.

There have been numerous accounts of a “special energy” within these patterns (some are no longer round, not circles) that causes machines to malfunction and people to feel elated, relaxed or even healed of physical ailments. This would be a bit difficult for humans to create just as they left the pattern they finished making.

However, by far the most convincing reason for a non-human force to be involved is the geometric precision with which they are created. I’m going to demonstrate this with one of the designs, a bi-heptagon. This pattern appeared in Wiltshire, England in 1998. Please view the drawing below (Figure 1). We start out with a series of two heptagons or 7-sided structures. They are arranged so that the inner one (pink line) touches the exact center of the outer one (yellow line). Then two four-sided figures are drawn inside (green lines) touching all the corners of the outer figure.

Figure 1

Finally, a similar structure is drawn inside the larger structure but exactly half the size of the outer structure (Figure 2)

Figure 2



It was nearly 10 years after the crop circle appeared that the correct geometric structure was found. As Nick Kollerstrome explains, “What was the mind which conceived these haunting 14-fold geometries, of such complexity…. It’s maths, but not as we know it: as if some master geometer were attuned to Mathematics, Mysticism, and Architecture.” (

Here is the finished shape.

crop circle 1

If you wish to know more about crop circles I recommend this recently published book by Freddy Silva, a veteran researcher and international author, Secrets in the Fields: The Science and Mysticism of Crop Circles. The best way to understand the instant and complex creation of these patterns is to see them happening. Please watch this trailer to the DVD, “What on Earth?” by Suzanne Taylor.


The Power of Crop Circles by Bert Janssen