Shoemaker's Knife

Steve Phelps


  • 1. The Shoemaker's Knife
  • 2. Pappus' Chain of Inscribed Circles
  • 3. Figure 5.4.1
  • 4. Cadena de Pappus
  • 5. empirical approach to the Ancient Pappus Theorem

1.

The Shoemaker's Knife

The area enclosed by the semi-circles centred O, X and Y and on the same diameter is called the Shoemaker's Knife. The radii of the two smaller semi-circles are variable. This is illustrated in the diagram below.

Prove that the area of the circle which has the radical axis as diameter is equal to the area of the Shoemaker's Knife.
– Nikky Vanderhout

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