|
 Welcome
to this 'Hypermaths' Website, concerning the geometry of crop circles.
It is designed for school maths teachers who wish to bring a bit of inspiration
into their lessons; to bring out the Harry Potter in their pupils, as it
were.
Each unit contains a line-diagram of the
essential form. Wherever possible there is a web-link to a photograph,
of the formation; there may also be coloured-in figures, web-links to the
work other geometers and feedback reports on use of the program. The modern
maths teacher has a 'whiteboard' onto which she or he can download web-material.
The review of my book 'Crop circles,
The Hidden Form' in the School Maths teachers journal observed www.atm.org.uk/reviews/books/cropcircles.html
that it was 'a must for any school library.' It helps if you have a copy
of that book www.wessexbooks.co.uk/cropcircles-hiddenform.htm
and also, why not order the pack of six full-colour Hypermaths posters
www.wessexbooks.co.uk/posters.htm
while you're at it?
My understanding is that the forms that
have arrived in English cornfields in the last decade or so are new, and
are not an echo of what is found in texts about sacred geometry nor in
old temple designs. I, as a science historian, have experienced a novelty
here. They are a form of communication, and the message is nonverbal.
Websites that deal with crop circle geometry
are to be found here:
www.korncirkler.dk/cccorner/geometry.art.html.
Most of them open our minds to the mystical. This site has, however, a
different goal. It aims to help ordinary students to learn mathematics,
in a unique approach that is artistic as well as intellectual. The Circlemakers
have given us a repertoire of forms that are consciousness-expanding, a
kind of holistic mathematics. Even students who can't do the trig can get
value from colouring in the forms! Some of the geometry sites give a bewildering
array of lines used in their reconstructions, but I here try not to lose
sight of a primal simplicity with which the Circlemakers have done their
work. For this, we will be drawing on the pioneer work of persons such
as Bert Janssen http://%20www.bertjanssen.nl/cropcircles.html
, John Martineau and Michael Glickman.
We look at what Aristotle called the 'formal'
cause, which is the mathematical structure of the phenomenon. Of his four
types of causes, the others will not concern us: the 'final' cause which
asks for what purpose they were made, the 'efficient' cause which
is the process by which they are made (planks? ultrasound?) and
the 'material' cause as the substance (were there stalks with nodes
bent in some special manner?).In
the dizzying discussions that go on about the topic, a distinction between
these different causes could just help to clarify things.
 It
was fortunate that 'The Hidden Form' was published in 2002, because what
I am here calling 'Hypermaths' had mainly appeared by then. The forms since
that statement have tended to be somewhat complex for a school classroom.
The majestic logic of the phenomenon has unfolded over about one decade,
geo-metry
in
the most literal sense (from Greek geo-Earth,
metros - measure)
- to the accompaniment of media scorn, derision and silence. The phenomenon
has been, as John Michell so rightly observed, 'the best show in England'.
In struggling to discern the patterns that were developing, the gentle,
sage council of the late Gerald Hawkins, the astronomer, helped to guide
us: www.lovely.clara.net/hawkins.htmlHe
showed how the phenomenon expressed musical-harmonic ratios. My approach
has been slightly different, and I describe the way it has manifested in
whole-number patterns.
For companion reading, I recommend all
the Yearbooks by Karen Douglas and Steve Alexander,
www.temporarytemples.co.uk/shop/yearbooks.html,
Vital
Signs by Andy Thomas www.vitalsignspublishing.co.uk/
and The Hypnotic Power of Crop Circles by Bert Janssen as basic
texts. www.cropcircleconnector.com
is the essential web picture-gallery, but one needs a subscription to access
earlier years.
I have to put my hand on my heart and
say that using these designs in the classroom will not cost a mathematics
teacher their job: in fact, it cannot fail to enhance student interest
in the subject.
|
Welcome
to this 'Hypermaths' Website, concerning the geometry of crop circles.
It is designed for school maths teachers who wish to bring a bit of inspiration
into their lessons; to bring out the Harry Potter in their pupils, as it
were.
