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 capabilities:
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.
You can 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 laborious.
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.