(Crop) Circle Theorems

The more thoroughly you describe,

the more you will confuse.

It is necessary to draw as well as describe.

Leonardo da Vinci

Aims This morning we will use Euclid’s book & crop circles to show;

• The mathematics we see in school wasn’t just handed down in its entirety from antiquity, but has gone through a number of revisions.

• Mathematics provides us with tools which enable us to categorize things such as crop circles.

• Mathematics is a language we can use to describe the design of crop circles; in the break out session later.

• How to make some of the essential shapes found within these circle designs with a piece of string and a marker pen. The essential tools of a circle maker!

• Firstly lets have a look at the most famous book from antiquity; Euclid’s Elements

Euclid’s Elements

The Elements Book 4: Construction of Rectilinear Figures In and Around Circles

The Elements Book 4: Construction of Rectilinear Figures In and Around Circles

The Elements Book 4:

Construction of Rectilinear

Figures In and

Around Circles

plenary

• Euclid’s Elements; the mathematics you

see in school has been handed down and

translated from Greek, to Arabic, to Latin,

into English among other languages.

• Therefore the message in the

mathematics we learn today potentially

could have been lost through the ages.

plenary

• When trying to make sense of the different

types of crop circles we can use

mathematical properties such as

symmetry to help us.

• We can also use polygons to help us

categorise the information you have been

given.

The breakout session

Windmill Hill, Wilts

Aim

• Designing your own crop circles!!!!!

• Watch carefully as I reveal an example of

a crop circle design step by step.

Aim

• Using a string and board marker as a

make shift set of compasses in you pairs

discuss how you would construct the

following;

• 60 degree angle

• Equilateral triangle

• Hexagon

Designing your own crop circles

• What did you notice about the instructions;

• What went well……

• Even better if…….

Now in your pairs

• Create your own crop circle design.

• Think about how you would need to lay

out each stage in your design.

• Write out your instructions on a sheet of

paper, with small sketches to help

describe your design.

• Provide sufficient detail so that another

group could try to replicate your design.

To Conclude

I hope you have enjoyed the session!

Please don’t hesitate to get in touch with me if

you need any further information

gjm@kingswood.bath.sch.uk