Archive for July, 2016

Random Harmonic Series

We consider the convergence of the random harmonic series

\displaystyle R = \sum_{n=1}^{\infty}\frac{\sigma_{n}}{n}

where {\sigma_n\in\{-1,+1\}} is chosen randomly with probability {1/2} of being either plus one or minus one. It follows from the Kolmogorov three-series theorem that the series is “almost surely” convergent.

RandomHarmonicSeriesDistribution

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Computers Speaking in Irish

Most of us use computer terminals, tablets and smart phones, absorbing information quickly and easily. How do the many thousands of Irish people who are blind or visually impaired manage to interact with computers? For them, entering data by keyboard or voice is easy, but special software is needed to convert the text on screen into a form for output to a loudspeaker or headphones, or to drive a refreshable Braille display [TM095, or search for “thatsmaths” at irishtimes.com].

Braille-Display

Braille display (www.humanware.com)

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Squircles

You can put a square peg in a round hole.

Shapes between circles and squares have proved invaluable to engineers and have also found their way onto our dinner tables. A plate in the shape of a `squircle’ is shown in this figure .

Squircle-Plate.jpg

Squircular plate: holds more food and is easier to store.

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Lateral Thinking in Mathematics

Many problems in mathematics that appear difficult to solve turn out to be remarkably simple when looked at from a new perspective. George Pólya, a Hungarian-born mathematician, wrote a popular book, How to Solve It, in which he discussed the benefits of attacking problems from a variety of angles [see TM094, or search for “thatsmaths” at irishtimes.com].

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