Mandala and 5,6 and 7-fold Division of the Circle

Paul F. Stang
Bridges London: Mathematics, Music, Art, Architecture, Culture (2006)
Pages 645–646


The Compass is perhaps oldest of all the math and drawing tools. When did someone think to put two sticks together, hold one in place and twirl the other, or link two pegs with a rope, pound one in the ground and use the other to draw circles in the dirt? It is commonly known that with only compass, ruler and pencil, a six-fold division of the circle can be made. An amazing array of 2 and 3 dimensional possibilities then follow, to form bridges between Math, Art, History, Culture and Science and even Mythology and Magic! Mathematics is learned through the hands, creativity and social interaction. Further, the compass, when coupled with the phi proportion, can be used to obtain 5 and 7 fold division of the circle. The Initiate, interested in mastering the compass, must begin this journey of exploration by ensuring precision. Often, the compass user grips the device too firmly, pressing harder in an effort to ensure quality. The result of this 'muscling' is often that the point makes an overly large hole in the paper, the compass opens from the pressure, making a spiral, and the paper slips. The proper way to grasp the compass is to twirl the upper post between thumb and index finger, so that it pirouettes. In this way it makes a crisp circle. The image may be faint but we can twirl the compass more times for better definition, rather than pressing harder. With brief explanations, we will now proceed rapidly through a multitude of forms.