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Impossible? by Julian Havil

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Chapter 11

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TWO SERIES

As the finite encloses an infinite seriesAnd in the unlimited limits appear,So the soul of immensity dwells in minutiaAnd in narrowest limits no limits inhere.What joy to discern the minute in infinity!The vast to perceive in the small, what divinity!

Jacob Bernoulli

Torricelli’s Tower

In chapter 8 of Nonplussed! we considered the paradoxical solid known (in particular) as Torricelli’s Trumpet. Figure 11.1 shows what this remarkable object looks like. It is formed as the solid of revolution of the curve y = 1 / x for (say) x 1 and calculus was used to show that the trumpet had a finite volume but infinite surface area, the ...

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