Mathematicians have traditionally dealt with convergent series and shunned divergent ones. But, long ago, astronomers found that divergent expansions yield valuable results. If these so-called asymptotic expansions are truncated, the error is bounded by the first term omitted. Thus, by stopping just before the smallest term, excellent approximations may be obtained. Astronomical Series Many of … Continue reading Divergent Series Yield Valuable Results
Month: December 2019
Having your Christmas Cake and Eating it
As Christmas approaches, the question of fair sharing comes into focus. Readers can rejoice that there has been a recent breakthrough in cake-cutting theory. Cake cutting may sound limited, but it is important for many practical problems. A cake is a metaphor for a parcel of land to be divided, broadcast frequencies to be allocated, … Continue reading Having your Christmas Cake and Eating it
The Intermediate Axis Theorem
In 1985, cosmonaut Vladimir Dzhanibekov commanded a mission to repair the space station Salyut-7. During the operation, he flicked a wing-nut to remove it. As it left the end of the bolt, the nut continued to spin in space, but every few seconds, it turned over through $latex {180^\circ}&fg=000000$. Although the angular momentum did not … Continue reading The Intermediate Axis Theorem
A New Mathematical Discovery from Neutrino Physics
Although abstract in character, mathematics has concrete origins: the greatest advances have been inspired by the natural world. Recently, a new result in linear algebra was discovered by three physicists trying to understand the behaviour of neutrinos [TM176 or search for “thatsmaths” at irishtimes.com]. Neutrinos are sub-atomic particles that interact only weakly with matter, so that they … Continue reading A New Mathematical Discovery from Neutrino Physics
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