In a nutshell: In web maps, geographical coordinates are projected as if the Earth were a perfect sphere. The results are great for general use but not for high-precision applications. 
Continue reading ‘Maps on the Web’
Archive for May, 2015
Mercator’s Marvellous Map
Published May 21, 2015 Irish Times ClosedTags: Geometry, Geophysics, Spherical Trigonometry
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 irishtimes.com].
![Mercator projection of the Earth, truncated at 75 degrees North and South [Wikimedia Commons, author: Strebe].](https://thatsmaths.files.wordpress.com/2015/05/mercator-projection-75deg.jpg)
Mercator projection of the Earth, truncated at 75 degrees North and South [Wikimedia Commons, author: Strebe].
Suppose six friends visit a pizzeria and have enough cash for just one big pizza. They need to divide it fairly into six equal pieces. That is simple: cut the pizza in the usual way into six equal sectors.
But suppose there is meat in the centre of the pizza and some of the friends are vegetarians. How can we cut the pizza into slices of identical shape and size, some of them not including the central region?
![A pizza with various toppings. Image: Pizza Masetti Craiova, Romania (Flickr) [CC BY 2.0 (http://creativecommons.org/licenses/by/2.0)], via Wikimedia Commons.](https://thatsmaths.files.wordpress.com/2015/05/pizza-with-various-toppings.jpg)
A pizza with various toppings. Image: Pizza Masetti Craiova, Romania (Flickr) [CC BY 2.0 (http://creativecommons.org/licenses/by/2.0)%5D, via Wikimedia Commons.
Modelling the Markets
Published May 7, 2015 Irish Times ClosedTags: Algorithms, Applied Maths, Computer Science
Mathematics now plays a fundamental role in modelling market movements [see this week’s That’s Maths column (TM067) or search for “thatsmaths” at irishtimes.com].
Dow-Jones Industrial Average for the Flash-Crash on 6 May 2010.
Graphic adapted from Sunday Times, 26 April, 2015.
ThatsMaths 