Slicing Doughnuts

It is well-known that an ellipse is the locus of all points such that the sum of their distances from two fixed points, the foci, is constant. Thus, a gardener may map out an elliptical flower-bed by driving two stakes into the ground, looping a rope around them and pulling it taut with a pointed stick, tracing out a curve on the ground.

Recreational Mathematics is Fun

We all love music, beautiful paintings and great literature without being trained musicians, talented artists or accomplished writers. It is the same with mathematics: we can enjoy the elegance of brilliant logical arguments and appreciate the beauty of mathematical structures and symmetries without being skilled creators of new theorems. [See TM097, or search for “thatsmaths” at irishtimes.com].

Harding Gallery. Image from Science Museum, London (www.sciencemuseum.org.uk).

A Toy Example of RSA Encryption

The RSA system has been presented many times, following the excellent expository article of Martin Gardner in the August 1977 issue of Scientific American. There is no need for yet another explanation of the system; the essentials are contained in the Wikipedia article RSA (cryptosystem), and in many other articles.

The purpose of this note is to give an example of the method using numbers so small that the computations can easily be carried through by mental arithmetic or with a simple calculator.

Can Mathematics Keep Us Secure?

The National Security Agency is the largest employer of mathematicians in America. Mathematics is a core discipline at NSA and mathematicians work on signals intelligence and information security (US citizenship is a requirement for employment). Why is NSA so interested in mathematics? [See TM096, or search for “thatsmaths” at irishtimes.com].

Flag of the National Security Agency

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.

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 (www.humanware.com)

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 .

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