Published December 27, 2012
Tags: Geometry, History
The fifth proposition in Book I of Euclid’s Elements states that the two base angles of an isosceles triangle are equal (in the figure below, angles B and C).
For centuries, this result has been known as Pons Asinorum, or the Bridge of Asses, apparently a metaphor for a problem that separates bright sparks from dunces. Euclid proved the proposition by extending the sides AB and AC and drawing lines to form additional triangles. His proof is quite complicated. Continue reading ‘Pons Asinorum’
Published December 20, 2012
Tags: Algorithms, Hamilton
This week’s That’s Maths column ( TM011 ) discusses the challenge faced by Santa Claus: he has about a billion homes to visit in one night, so he needs to be smart in picking his route. The challenge he faces is called the Travelling Salesman Problem, or TSP. Continue reading ‘Santa’s TSP Algorithm’
Published December 13, 2012
Tags: Analysis, Archimedes, Puzzles
Four friends, exhausted after a long hike, stagger into a pub to slake their thirst. But, pooling their funds, they have enough money for only one pint.
Annie drinks first, until the surface of the beer is half way down the side (Fig. 1(A)). Then Barry drinks until the surface touches the bottom corner (Fig. 1(B)). Cathy then takes a sup, leaving the level as in Fig. 1(C), with the surface through the centre of the bottom. Finally, Danny empties the glass.
Question: Do all four friends drink the same amount? If not, who gets most and who gets least? Continue reading ‘Sharing a Pint’
Published December 6, 2012
Tags: Number Theory, Ramanujan
In the Irish Times column this week ( TM010 ), we tell how a collection of papers of Srinivasa Ramanujan turned up in the Wren Library in Cambridge and set the mathematical world ablaze. Continue reading ‘Ramanujan’s Lost Notebook’