# Archimedes the Musical

In 2009, Spiro Liacos wrote and directed a musical called Archimedes. It tells the story of Archimedes’ famous ‘eureka’ moment. In the 3rd-century BC, King Hieron of Syracuse gives his goldsmith a certain amount of gold with which to make a golden crown. Later, a rumour spreads that the crown may not be made of pure gold. The king suspects that the goldsmith has kept some of the gold he was given and has replaced it with an equal weight of silver. The King asks Archimedes, Syracuse’s resident scientific and mathematical genius, to determine whether the crown is in fact made of pure gold or not. This presents a huge problem for Archimedes, because, unbeknown to the King, he is engaged to the goldsmith’s daughter Artemisia…

The show builds in tension from the opening scene to the very end, and entertains all the way with great songs, dazzling colour, and a script that provides the perfect mix of humour and drama. For more information about the musical, visit www.meanttobemusicals.com.au.

Though essentially a comedy-drama musical, Archimedes touches on some very interesting science. Archimedes (the man) invented the compound pulley, the screw (a type of water pump), determined the mathematical principles under which levers and pulleys operate, and built many machines. He is considered to be in the top three mathematicians of all time. He determined that Pi (or ?) was between the values of 3 10/71 and 3 10/70 (or 3 1/7). Our familiar 22/7 is, of course, 3 1/7.

The practical activities below were all used by Cheltenham Secondary College students in Science and Maths classes. The students enjoyed them, learned a lot from them, and, for what it’s worth, were being constantly reminded that the school was putting on a great musical! Many of them kept asking their teachers whether the goldsmith did steal the gold or not, but our answer was simple: “you’ll have to come and see the show”.

PULLEYS

Explores and explains how pulleys work and how they enable us to lift heavy loads. In the opening scene of the musical, Archimedes uses a compound pulley to haul a ship over land, which immediately establishes him as a genius.

Pulleys (pdf)

DENSITY and BUOYANCY

These series of pracs introduce students to the concepts of density and buoyancy. The goldsmith was given a precisely measured mass of gold to make the crown. When the crown was returned, it had the same mass as the gold he was originally given. However, he was suspected of having replaced some of the gold with silver. By completing these pracs, students at your school will learn all about how Archimedes determined the purity of the crown’s gold and his discovery of what we now call, in his honour, the Archimedes Principle.

LEVERS

Though not really a big part of the musical, levers are briefly mentioned. This prac explores the science and maths of levers. Purists, however, may not like this prac because the force is measured in grams! At what age should we start telling kids about Newtons?

First Class Levers (pdf)

CALCULATING Pi (or, more properly, ?)

These three activities get students to calculate ?. The first two are practical activities and are suited to junior classes. The third ideally suits Year 10 or Year 11. Students calculate ? trigonometrically by using circles inscribed and circumscribed with polygons to derive a formula in much the same way as Archimedes did 2,300 years ago (though he used geometry, not trig).

calculating Pi (pdf)

Pi MNEMONICS and PIEMS

We now know that Pi = 3.14159 26535 89793… and the numbers go on and on forever without repeating. So how can we remember the decimal numbers. This fun little activity gets students to write their own Pi mnemonics. For example, the sentence “Now I have a great invention to pacify large and small horsemen” is a Pi mnemonic. If you count the number of letters in each word, and place a decimal point after the first word, you get 3.14159265358; Pi to 11 decimal places!