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Imagine a room – the Oval Office for example – that has three electrical appliances:
• An air-conditioner ( a ) with an American plug socket ( A ),
• A boiler ( b ) with a British plug socket ( B ),
• A coffee-maker ( c ) with a Continental plug socket ( C ).
The problem is to connect each appliance to the correct socket, avoiding any crossings of the connecting wires.
Fig. 1: Positions of appliances and sockets for Problem 1.
Towering over O’Connell Street in Dublin, the Spire of Light, at 120 metres, is about three times the height of its predecessor [TM109 or search for “thatsmaths” at irishtimes.com]. The Spire was erected in 2003, filling the void left by the destruction in 1966 of Nelson’s Pillar. The needle-like structure is a slender cone of stainless steel, the diameter tapering from 3 metres at the base to 15 cm at its apex. The illumination from the top section shines like a beacon throughout the city.
The golden mean occurs repeatedly in the pentagram [image Wikimedia Commons]
and is the positive root of the quadratic equation
with the value
There is no doubt that
We frequently need to find the nearest hospital, surgery or supermarket. A map divided into cells, each cell covering the region closest to a particular centre, can assist us in our quest. Such a map is called a Voronoi diagram, named for Georgy Voronoi, a mathematician born in Ukraine in 1868. He is remembered today mostly for his diagram, also known as a Voronoi tessellation, decomposition, or partition. [TM108 or search for “thatsmaths” at irishtimes.com].
Voronoi diagram drawn using the applet of Paul Chew (see Sources below).
ThatsMaths 