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.
Continue reading ‘Topology in the Oval Office’
Published February 16, 2017
Tags: Applied Maths, Mechanics
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.
Continue reading ‘The Spire of Light’
The golden mean occurs repeatedly in the pentagram [image Wikimedia Commons]
Everyone knows about the golden mean. It must be one of the most written-about numbers, certainly in recreational mathematics. It is usually denoted by
and is the positive root of the quadratic equation
with the value
There is no doubt that is significant in many biological contexts and has also been an inspiration for artists. Called the Divine Proportion, it was described in a book of that name by Luca Pacioli, a contemporary and friend of Leonardo da Vinci.
Continue reading ‘Metallic Means’
Published February 2, 2017
Tags: Algorithms, Geometry
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).
Continue reading ‘Voronoi Diagrams: Simple but Powerful’