Abstract
This paper presents the Painter’s Paradox—a highly counterintuitive situation where a painter is able to fill a certain 3-dimensional object with paint but is unable to fully paint the surface of that object.
Mathematically, this paradox illustrates that a 3-dimensional object can have a finite volume while having an infinite surface area. A well-known object like Gabriel’s Horn is a classic example used to illustrate this paradox. To study it, we require a basic understanding of integral calculus and the concepts of surface area and volume.
However, one can construct other objects that illustrate the same paradox, using only high school geometry and geometric series. At the heart of this paradox lies the counterintuitive nature of infinite series.
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