Strange property of physical quantities of some petal shape objects

Abstract

We study various physical quantities of objects with petal shapes. N-petal shapes exhibit N-fold rotational symmetry. Furthermore, they might have an additional characteristic: the equation defining their boundaries could be represented by F(N θ). We will show that physical quantities of objects with these characteristics may show strange properties. By ‘physical quantities’, we refer to aspects such as electric potential and electric field due to a charged petal-shaped plate or cylinder on the rotation axis, their mass and moment of inertia. We are going to show that for such objects, these physical observables do not depend on the number of petals, N. This intriguing result has a simple reason.