Archive for August, 2013

A Hole through the Earth

“I wonder if I shall fall right through the earth”, thought Alice as she fell down the rabbit hole, “and come out in the antipathies”. In addition to the author of the “Alice” books, Lewis Carroll – in real life the mathematician Charles L. Dodgson – many famous thinkers have asked what would happen if one fell down a hole right through the earth’s centre.

Galileo gave the answer to this question: an object dropped down a hole piercing the earth diametrically would fall with increasing speed until the centre, where it would be moving at about 8 km per second, after which it would slow down until reaching the other end, where it would fall back again, oscillating repeatedly between the two ends.
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Ternary Variations

Georg Cantor (1845-1918) was led, through his study of trigonometric series, to distinguish between denumerably infinite sets like the rationals and uncountable sets like the reals. He introduced a set that is an abstract form of what we now call Cantor’s Ternary Set. In fact, the ternary set had been studied some ten years earlier by the Dublin-born mathematician Henry Smith and, independently, by the Italian Vito Volterra. General sets of this form are now called Smith-Volterra-Cantor sets (SVC sets).
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The Atmospheric Railway

Atmospheric pressure acting on a surface the size of a large dinner-plate exerts a force sufficient to propel a ten ton train! The That’s Maths column ( TM027 ) in the Irish Times this week is about the atmospheric railway.
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The remarkable BBP Formula

Information that is declared to be forever inaccessible is sometimes revealed within a short period. Until recently, it seemed impossible that we would ever know the value of the quintillionth decimal digit of pi. But a remarkable formula has been found that allows the computation of binary digits starting from an arbitrary  position without the need to compute earlier digits. This is known as the BBP formula.
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Admirably Appropriate

The topic of the That’s Maths column ( TM026 ) in the Irish Times this week is the surprising and delightful way in which mathematics developed for its own sake turns out to be eminently suited for solving practical problems.

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