Today is the winter solstice, the shortest day of the year. We might expect that the latest sunrise and earliest sunset also occur today. In fact, the earliest sunset, the darkest day of the year, was on 13 December, over a week ago, and the latest sunrise is still more than a week away. This curious behaviour is due to the unsteady path of the Earth around the Sun. Our clocks, which run regularly at what is called mean time, move in and out of synchronization with solar time [TM129 or search for “thatsmaths” at irishtimes.com].

## Posts Tagged 'Time measurement'

### Darker Mornings, Brighter Evenings

Published December 21, 2017 Irish Times Leave a CommentTags: Astronomy, Time measurement

### Modular Arithmetic: from Clock Time to High Tech

Published November 2, 2017 Irish Times Leave a CommentTags: Arithmetic, Time measurement

You may never have heard of *modular arithmetic*, but you use it every day without the slightest difficulty. In this system, numbers wrap around when they reach a certain size called the modulus; it is the arithmetic of remainders [TM126 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Modular Arithmetic: from Clock Time to High Tech’

### Pedro Nunes and Solar Retrogression

Published October 12, 2017 Occasional Leave a CommentTags: Astronomy, Time measurement

In northern latitudes we are used to the Sun rising in the East, following a smooth and even course through the southern sky and setting in the West. The idea that the compass bearing of the Sun might reverse seems fanciful. But in 1537 Portuguese mathematician Pedro Nunes showed that the shadow cast by the gnomon of a sun dial can move backwards.

Nunes’ prediction was counter-intuitive. It came long before Newton, Galileo and Kepler, and Copernicus’ heliocentric theory had not yet been published. The retrogression was a remarkable example of the power of mathematics to predict physical behaviour.

### The Great American Eclipse

Published August 20, 2015 Irish Times Leave a CommentTags: Astronomy, Time measurement

Just two years from now, on Monday, August 21, 2017, the Moon’s shadow will sweep across the United States at a speed of over 2,000 km/hr. The Great American Eclipse of 2017 will generate a frenzy of activity. [TM074: search for “thatsmaths” at irishtimes.com ].

### Golden Moments

Published March 26, 2015 Occasional Leave a CommentTags: Recreational Maths, Time measurement

Suppose a circle is divided by two radii and the two arcs *a* and *b* are in the golden ratio:

*b* / *a* = ( *a + b *) / *b* = *φ* ≈ 1.618

Then the smaller angle formed by the radii is called the golden angle. It is equal to about 137.5° or 2.4 radians. We will denote the golden angle by *γ*. Its exact value, as a fraction of a complete circle, is ( 3 – √5 ) / 2 ≈ 0.382 cycles.

### When did Hammurabi reign?

Published June 19, 2014 Irish Times Leave a CommentTags: Astronomy, History, Time measurement

The consequences of the Earth’s changing climate may be very grave. It is essential to understand past climate change so that we can anticipate future changes. This week, *That’s Maths* in *The Irish Times* ( TM047 ) is about the chronology of the Middle East. Surprisingly, this has important implications for our understanding of climate change.

### The Antikythera Mechanism

Published November 21, 2013 Irish Times 1 CommentTags: Archimedes, Mechanics, Time measurement

The article in this week’s *That’s Maths* column in the* Irish Times* ( TM033 ) is about the Antikythera Mechanism, which might be called the First Computer.

**Two Storms**

Two storms, separated by 2000 years, resulted in the loss and the recovery of one of the most amazing mechanical devices made in the ancient world. The first storm, around 65 BC, wrecked a Roman vessel bringing home loot from Asia Minor. The ship went down near the island of Antikythera, between the Greek mainland and Crete. Continue reading ‘The Antikythera Mechanism’