Bent Coins: What are the Odds?

If we toss a `fair’ coin, one for which heads and tails are equally likely, a large number of times, we expect approximately equal numbers of heads and tails. But what is `approximate’ here? How large a deviation from equal values might raise suspicion that the coin is biased? Surely, 12 heads and 8 tails in 20 tosses would not raise any eyebrows; but 18 heads and 2 tails might.

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RT60 and Acoustic Excellence

This week’s That’s Maths column (TM072) [search for “thatsmaths” at irishtimes.com] is about architectural acoustics, and about the remarkable work of Wallace Clement Sabine.

Boston Symphony Hall. Image downloaded from website: http://www.gourmetcaterers.com/exclusive-venues/symphony-hall

Boston Symphony Hall. Image downloaded from BSH.

Continue reading ‘RT60 and Acoustic Excellence’

Fun and Games on a Honeycombed Rhomboard.

Hex is an amusing game for two players, using a board or sheet of paper divided into hexagonal cells like a honeycomb. The playing board is rhomboidal in shape with an equal number of hexagons along each edge. Players take turns placing a counter or stone on a single cell of the board. One uses white stones, the other black. Or red and blue markers can be used on a paper board.

11 x 11 Hex Board. Image from  http://www.iggamecenter.com/

11 x 11 Hex Board. Image from iggamecenter.com

Continue reading ‘Fun and Games on a Honeycombed Rhomboard.’

Pluto’s Unruly Family

An astrodynamical miracle is happening in the sky above. Our ability to launch a space-probe from the revolving Earth to reach a moving target billions of kilometres away almost ten years later with pinpoint accuracy is truly astounding. “New Horizons” promises to enhance our knowledge of the solar system and it may help us to understand our own planet too.

Four tiny moons (on left) orbit the binary system of Pluto (top right) and Charon.

Four tiny moons (on left) orbit the binary system of Pluto (top centre right) and Charon [Image NASA]

[See this week’s That’s Maths column (TM071): search for “thatsmaths” at irishtimes.com].

Continue reading ‘Pluto’s Unruly Family’

Increasingly Abstract Algebra

In the seventeenth century, the algebraic approach to geometry proved to be enormously fruitful. When René Descartes (1596-1650) developed coordinate geometry, the study of equations (algebra) and shapes (geometry) became inextricably interlinked. The move towards greater abstraction can make mathematics appear more abstruse and impenetrable, but it brings greater clarity and power, and can lead to surprising unifications.

Evariste Galois, Sophus Lie and Emmy Noether.

Evariste Galois, Sophus Lie and Emmy Noether.

Continue reading ‘Increasingly Abstract Algebra’

Emmy Noether’s beautiful theorem

The number of women who have excelled in mathematics is lamentably small. Many reasons may be given, foremost being that the rules of society well into the twentieth century debarred women from any leading role in mathematics and indeed in science. But a handful of women broke through the gender barrier and made major contributions. [TM070: search for “thatsmaths” at irishtimes.com ]

Death of the philosopher Hypatia, by Louis Figuier [Wikimedia Commons].

Death of the philosopher Hypatia, by Louis Figuier
[Wikimedia Commons].

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Game Theory & Nash Equilibrium

Game theory deals with mathematical models of situations involving conflict, cooperation and competition. Such situations are central in the social and behavioural sciences. Game Theory is a framework for making rational decisions in many fields: economics, political science, psychology, computer science and biology. It is also used in industry, for decisions on manufacturing, distribution, consumption, pricing, salaries, etc.

Theory of games and economic behavior. Centre: John von Neumann. Right: Oskar Morgenstern.

Theory of Games and Economic Behavior.
Centre: John von Neumann. Right: Oskar Morgenstern.

During the Cold War, Game Theory was the basis for many decisions concerning nuclear strategy that affected the well-being of the entire human race.

Continue reading ‘Game Theory & Nash Equilibrium’


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