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A Finite Volume Inside an Infinite Area
A Finite Volume Inside an Infinite Area
Evangelista Torricelli (1608-1647) was an Italian scientist who made relevant contributions in Physics. Fascinated by astronomy, he was a stronger supporter and student of Galileo Galilei. Among his achievements, probably influenced by Galileo, he was the first man to discover the principle of a barometer.
Torricelli's Trumpet
A less well known fact is that in 1641, Torricelli left an imperishable mark on mathematics with important results in the development of calculus. For instance, he discovered a geometric object, today known as Torricelli's trumpet, having the paradoxical property of enclosing a finite volume inside an infinite surface.
Its shape looks like a long, straight horn. So long that it never ends in a mouthpiece. It is also known as Archangel Gabriel's Trumpet. This is a reference to Archangel Gabriel, who will blow a trumpet on Judgement Day.
Torricelli's Trumpet is obtained by rotating the graph of the real function y=1/x (x≥1) around the x-axis.
Torricelli used exhaustion method to prove that this solid has finite volume and infinite surface area. Nowadays, this can be easily verified throught standard integral techniques.
Immediately after its publication in 1644, the result aroused great interest and admiration because it ment totally against the common intuition of the period.
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