Posts Tagged 'Spherical Trigonometry'

Mercator’s Marvellous Map

Try to wrap a football in aluminium foil and you will discover that you have to crumple up the foil to make it fit snugly to the ball. In the same way, it is impossible to represent the curved surface of the Earth on a flat plane without some distortion.  [See this week’s That’s Maths column (TM068):  search for “thatsmaths” at].

Mercator projection of the Earth, truncated at 75 degrees North and South [Wikimedia Commons, author: Strebe].

Mercator projection of the Earth, truncated at 75 degrees North and South [Wikimedia Commons, author: Strebe].

Continue reading ‘Mercator’s Marvellous Map’

Fermat’s Christmas Theorem

Albert Girard (1595-1632) was a French-born mathematician who studied at the University of Leiden. He was the first to use the abbreviations ‘sin’, ‘cos’ and ‘tan’ for the trigonometric functions.

Left: Albert Girard (1595-1632). Right: Pierre de Fermat (1601-1665)

Left: Albert Girard (1595-1632). Right: Pierre de Fermat (1601-1665)

Continue reading ‘Fermat’s Christmas Theorem’

Pythagoras goes Global

Spherical trigonometry has all the qualities we expect of the best mathematics: it is beautiful, useful and fun. It played an enormously important role in science for thousands of years. It was crucial for astronomy, and essential for global navigation. Yet, it has fallen out of fashion, and is almost completely ignored in modern education.
Continue reading ‘Pythagoras goes Global’

Shackleton’s spectacular boat-trip

A little mathematics goes a long, long way; in the adventure recounted below, elementary geometry brought an intrepid band of six men 800 sea miles across the treacherous Southern Ocean, and led to the saving of 28 lives. Continue reading ‘Shackleton’s spectacular boat-trip’

Carving up the Globe

This week, That’s Maths (TM007) describes various ways of dividing up the sphere. This is an important problem in geometry, biology, chemistry, astronomy, meteorology and climate modelling. Continue reading ‘Carving up the Globe’

Analemmatic Sundials

This week’s That’s Maths article, TM003, describes the analemmatic sundial on the East Pier in Dun Laoghaire.

An article in Plus Magazine, by Chris Sangwin and Chris Budd, gives a description of  the theory of these sundials and instructions on how to build one.

A script to design an analemmatic sundial, written by  Alexander R. Pruss, is available here.  To run it, just enter the width of the sundial, the latitude and longitude, and the timezone. The script will generate all the required dimensions.

Here is a technical article, The Equation of Time and the Analemma (PDF), submitted to the Bulletin of the Irish Mathematical Society.

Napier’s Nifty Rules

Spherical trigonometry is not in vogue. A century ago, a Tripos student might resolve a half-dozen spherical triangles before breakfast. Today, even the basics of the subject are unknown to many students of mathematics. That is a pity, because there are many elegant and surprising results in spherical trigonometry. For example, two spherical triangles that are similar – having corresponding angles equal – have the same area. This contrasts sharply with the situation for plane geometry. Continue reading ‘Napier’s Nifty Rules’

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