Posts Tagged 'Time measurement'

Saving Daylight with Hip-hop Time: a Modest Proposal

At 2:00 AM on Sunday 28 October the clocks throughout Europe will be set back one hour, reverting to Standard Time. In many countries, the clocks are put forward one hour in Spring and set back to Standard Time in the Autumn. Daylight saving time gives brighter evenings in Summer.

Hiphop-Time-Banner

In Summer, the mornings are already bright before most of us wake up but, in Winter, the mornings would be too dark unless we reverted to Standard Time.

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Darker Mornings, Brighter Evenings

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].

Sunrise-Newgrange

Sunrise in Newgrange on winter solstice [image from http://www.boynevalleytours.com/

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Modular Arithmetic: from Clock Time to High Tech

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].

Clock-Arithmetic

We use modular arithmetic for timekeeping with a 12-hour clock [Image Wikimedia Commons]

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Pedro Nunes and Solar Retrogression

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.

PedroNunes-Postage-Stamp

Pedro Nunes (1502–1578). Portuguese postage stamp issued in 1978.

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.

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The Great American Eclipse

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 ].

Moon between NASA’s Solar Dynamics Observatory and the Sun, giving a partial solar eclipse from space on Jan. 30, 2014. Image NASA.

Moon between NASA’s Solar Dynamics Observatory and the Sun,
giving a partial solar eclipse from space on Jan. 30, 2014. Image NASA.

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Golden Moments

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.

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When did Hammurabi reign?

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.

Left:  Image of Hammurabi in the US Congress. Right: Part of an inscription of the Code of Hammurabi.

Left: Image of Hammurabi in the US Congress.
Right: Part of an inscription of the Code of Hammurabi.

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