Suraiya Khan, Rida
(2022)
The Painter’s Paradox comparative analysis of Gabriel’s Horn and triangular pipe with Koch’s Fractal shaped cross section.
At Right Angles (12).
pp. 119122.
ISSN 25821873
Abstract
This paper presents the Painter’s Paradox—a highly counterintuitive situation where a painter is able to fill a certain 3dimensional object with paint but is unable to fully paint the surface of that object. Mathematically, this paradox illustrates that a 3dimensional object can have a finite volume while having an infinite surface area. A wellknown 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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