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The Arbelos: The Shoemaker's Knife and Kissing Circles

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With thanks to Ray Cross, for pointing me in this direction     Arbelos is an old Greek name for a shoemaker's knife. The curved blade with points at each end is an ideal shape for cutting leather precisely, and so has been a shoemakers' tool for centuries. Mathematically, the Arbelos has some lovely properties that have made it worthy of study for millenia. It is often referred to as the Arbelos of Archimedes. The Arbelos is made up of three semi-circles with centres on the same interval. Two of these are contained exactly within the third larger circle, and so all three 'kiss', just like the Farey Numbers and Ford Circles! In the task, we will explore some of these properties using a dynamic Geometry Expressions model, built upon a unit circle. Feel free to explore further...

Giant Arbelos sculpture in the Netherlands

Try building your own Arbelos model using GXweb and use it to explore both the geometry and the algebra involved.

 

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