The Painter’s Paradox comparative analysis of Gabriel’s Horn and triangular pipe with Koch’s Fractal shaped cross section

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. 119-122. ISSN 2582-1873

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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.

Item Type: Articles in APF Magazines
Authors: Suraiya Khan, Rida
Document Language:
Language
English
Uncontrolled Keywords: Paradox, Geometric progression, Infinite series
Subjects: Natural Sciences > Mathematics
Divisions: Azim Premji University > University Publications > At Right Angles
Full Text Status: Public
URI: http://publications.azimpremjifoundation.org/id/eprint/3347
Publisher URL:

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