Some mysteries solved as history of maths puzzles discussed

MATHS PUZZLES and challenges have been with us always it seems, with societies at least as far back as the Babylonians creating them. Ancient Egyptians and the Chinese too have very early examples of mathematical conundrums.

The history of maths ideas, puzzles and games was the subject under discussion last night at the Chester Beatty Library in Dublin in a talk given by Prof David Singmaster as part of Maths Week.

The Rhind Mathematical Papyrus dating to 1650BC provides proof of their interest, he said, although the Egyptians were not central to the advance of mathematics in the wider world.

Prof Singmaster specialises in trying to understand the intent behind old mathematical puzzles, which can represent a considerable challenge. Many old puzzles do not have an explanation so it is up to the researcher to “try to understand what the person is trying to achieve”, he said.

Ireland’s greatest mathematician, William Rowan Hamilton, was deeply interested in maths-based puzzles and some now carry his name, including the the Hamilton Circuit, he said.

The object is to establish a path along a circuit, for example a geometric shape, and visit each corner or junction only once. A square or a hexagon provide no challenge but try this with a dodecahedron as Hamilton did and it is a different matter.

See mathsweek.iefor details of events this weekend. Maths Week ends on Sunday.

Maths Week Puzzle 5

The Simpsons, the long-running TV cartoon series, has many mathematical jokes.

Many of the writers have maths, computing or science degrees, including chief writer Al Jean, who has a maths degree from Harvard. In one episode Lisa teaches Bart how to win at mini-golf and Bart remarks, “I can’t believe it. You’ve actually found a practical use for geometry!” The joke is that geometry is very useful and trigonometry, that branch which allows us to calculate angles, lengths of lines and areas, is one area of maths that finds use in everyday activities.

How much of your trigonometry can you remember?

The accompanying diagram shows an ornamental flower bed shaped as a regular five-pointed star. Somebody was sent to measure it and found that their tape was only three metres long and so unimaginatively came back with only one measurement: the distance between two adjacent inside corners (marked here as A and B), which was exactly three metres. Can you calculate the area? See page 9 for solution