Maps on the Web

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. WM-vs-Merc-Detail Continue reading ‘Maps on the Web’

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 irishtimes.com].

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’

Eccentric Pizza Slices

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.

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.

Have a think about this before reading on. There is more than one solution.

Continue reading ‘Eccentric Pizza Slices’

Modelling the Markets

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 Aversge for 6 May 2010. Graphic adapted from Sunday Times, 26 April, 2015.

Dow-Jones Industrial Average for the Flash-Crash on 6 May 2010.
Graphic adapted from Sunday Times, 26 April, 2015.

Continue reading ‘Modelling the Markets’

Brouwer’s Fixed-Point Theorem

A climber sets out at 8 a.m. from sea-level, reaching his goal, a 2,000 metre peak, ten hours later. He camps at the summit and starts his return the next morning at 8 a.m. After a leisurely descent, he is back at sea-level ten hours later.

Climber-Up-Then-DownIs there some time of day at which his altitude is identical on both days? Try to answer this before reading on.
Continue reading ‘Brouwer’s Fixed-Point Theorem’

Tap-tap-tap the Cosine Button

Tap any number into your calculator. Yes, any number at all, plus or minus, big or small. Now tap the cosine button. You will get a number in the range [ -1, +1 ]. Now tap “cos” again and again, and keep tapping it repeatedly (make sure that angles are set to radians and not degrees). The result is a sequence of numbers that converge towards the value 0.739085 … .

CosCosCos Continue reading ‘Tap-tap-tap the Cosine Button’

For Good Comms, Leaky Cables are Best

A counter-intuitive result of Oliver Heaviside showed how telegraph cables should be designed [see this week’s That’s Maths column (TM066) or search for “thatsmaths” at irishtimes.com].

Atlantic-Telegraph-Map Continue reading ‘For Good Comms, Leaky Cables are Best’


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