What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Can Jo make a gym bag for her trainers from the piece of fabric she has?
Published May 2001,February 2011.
It is a new geometrical instrument and a toy with 3 basic
The disk spins around a steel pin through its centre and has 100
holes arranged along a spiral. Each one is 1 mm further from the
centre than the last. The protractor scale around the edge measures
its rotation from alignment with one line to alignment with
another. Circle Scribe claims that the disk compass is the most
significant step in geometrical instrumentation since Thales of
Miletus returned to Greece after his studies with the Pyramid
builders of Egypt 500 BC. Visit www.treasure-troves.com/bios/Thales.html
You can buy one from their website www.circlescribe.com or make your
own by printing out a spiral onto an overhead transparency. Use
Excel or some other spreadsheet to create the spiral. Excel's radar
graph plots points increasing from 0.1 to 10.0 with increments of
0.1 and laid out in 10 columns of 10 rows of the spreadsheet. Once
you have printed the spiral you can make holes with a drawing pin
which will later form the centre pin. The protractor scale can be
copied from a large 360 protractor in pen although this is
The disk compass enables you to accurately and quickly draw many
fascinating diagrams and constructions and Circle Scribe has
included many in their book Fun Art and Geometry. The by product is
a deeper understanding of and confidence in the basic concepts and
theorems of Geometry like angle, radius, diameter, curvature,
centre, symmetry, etc etc.
One activity which straddles the divide between Maths and Art is
the Cardioid: this is a fascinating and very ancient drawing whose
name is derived from its appearance as 3 dimensional heart shape.
It is based on a ring of 36 dots evenly spaced around a circle at
10 degree intervals. Each circle has its centre on one of the dots
and its circumference passes through the top dot. The envelope is
also the locus of a point on the circumference of a circle rolling
around another of the same radius.
There are several similar diagrams based on the ring of dots and
the nephroid shown here is named after its kidney shape. In this
diagram a vertical diameter is drawn through the ring of dots. Each
circle is again centred on a dot but this time the constraint is
that they must touch the diameter. There are many lessons about
tangents to be learned from constructing this diagram.
Using the coordinate system it is possible to accurately and
quickly construct many fascinating diagrams such as the sine wave,
the conic sections (parabola, hyperbola, and ellipse) with
reference to their directrix and focus.
Their most recent addition is Sierpinski's triangle - a simple
fractal which can be drawn very accurately and very quickly. Visit
www.fractalus.com to see
some computer generated fractals.
Visit www.circlescribe.com for some
more ideas about the use of the disk compass. Dialogue from
children parents teachers and students is always welcome.