Claw Calculator

Name: Claw - Geometry Calculator
Author: Jürgen Kummer

Calculations at a claw. Here, claw is the name of a form made of two circles, where the smaller circle touches the larger inside and is removed from that. Then it is halfed through both centers and the intersection. The result looks like a cat's claw.
Enter both radiuses, choose the number of decimal places, then click Calculate.

Formulas:

l = 2 \cdot (R - r)

p = π \cdot (R + r) + l

A = \frac{π \cdot (R^{2} - r^{2})}{2}

pi:

π = 3.141592653589793 ...

Radius, lengths and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).

This shape has three vertices, two with a right angle and one with an angle of zero degrees. Consequently, the sum of its angles is 180 degrees, the same as that of a triangle. Nevertheless, such a claw shape, as well as any shape with curved sides, is not classified as a triangle in Euclidean geometry. Triangles are polygons and must therefore consist solely of straight sides.

Claw is not a formal geometric term but rather a descriptive one borrowed from outside geometry that fits this shape quite well. Of course, other claw-like shapes can also be created. Another potentially suitable name would be hook.
This claw shape represents an intermediate stage in the construction of an arbelos from a semicircle, specifically, the point after one small semicircle has been removed from the edge but before the second has been removed. If the radius of the small circle is half that of the large circle, this claw can be extended into a half Yin-Yang by attaching the previously removed small semicircle to the straight side.

A claw shape of this kind possesses no symmetries. It is chiral, meaning there are two distinct versions that are mirror images of each other and cannot be mapped onto one another through rotation ans translation. Compared to the shape shown above, the other version of the claw has its tip and small arc on the right, with the two right angles positioned on the left.

↑ up