This Trumpet is a Mathematical Paradox.

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Infinite shapes typically have infinite volumes, but not Gabriel’s Horn, a fascinating geometric paradox. This infinitely tall trumpet defies expectation with its infinite surface area yet finite volume. While it may seem impossible at first, it stretches our intuition without breaking any mathematical rules. In this video, we’ll explore the peculiar nature of Gabriel’s Horn and uncover the reason behind its paradoxical infinity.

Music and SFX:
https://pixabay.com/sound-effects/

Classical Cello Solo
Rafael Krux

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0:00 Introduction
0:33 What is Gabriel's Horn
1:05 Convergence
1:42 Topology
2:44 Solids of Revolution
5:00 The Paradox of Surface Area
5:50 Black Holes
6:02 Wrap Up
6:22 End Card

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