Torricelli’s trumpet

Torricelli’s trumpet is a fictional infinitely long solid of revolution formed when the closed domain

A:={(x,y)2x1, 0y1x}

rotates about the x-axis. It has a finite volume, π volume , but the area of its surface is infinite; in fact even the area of A is infinite, i.e., the improper integral 11x𝑑x is not convergent.

Torricelli’s trumpet is surprising since it can be filled by a finite amount of paint, but this paint can never suffice for painting its surface, no matter how a coat of paint is used!

Title Torricelli’s trumpet
Canonical name TorricellisTrumpet
Date of creation 2013-03-22 17:17:53
Last modified on 2013-03-22 17:17:53
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 14
Author pahio (2872)
Entry type Definition
Classification msc 26A42
Classification msc 26A36
Classification msc 57M20
Classification msc 51M04
Synonym Gabriel’s horn