Scaling the Heights

Programme Outline

The Guard has got his kite stuck in a tree. The Wizard will be happy to sell him a stick with which to retrieve it, but only if he's asked for a specific length of stick. While trying to work out how long a stick is, Lisa and the Guard explore relative lengths, map scales, and 'best buy' scenarios.

Start to 02:20 - Introduction The Guard's kite is stuck up a tree. The Wizard offers to sell him a kite-prodding stick from his timber yard, but only if he's asked for the right length.
02:20 to 04:00 - First steps Lisa reckons that she can work out how long a stick they need, by taking a photograph of the Guard standing under the tree.
04:00 to 04:40 - The Mathematical Encyclopaedia The Encyclopaedia opens to page 1.61803: the Golden Ratio. There follows a brief history of this most aesthetic of numbers.
04:40 to 06:30 - The Wizard's timber yard Lisa's photograph shows that they need a kite-prodding stick twice as long as the Guard's pike. The Wizard has two suitable sticks, one costing 5 florins, and an older one priced at 2 florins per trollurch (an old unit of length no longer in common use).
06:30 to 08:55 - First, find your trollurch rule! To work out how long the second stick is, a trollurch rule is needed. The Wizard keeps his trollurch safe in his maze. Lisa must go in and get it, blindfolded. Luckily, the Guard is given a scale map.
08:55 to 10:00 - Map scales The Wizard describes map scales, and what 'one to twenty-five thousand' really means.
10:00 to 12:45 - Buying the kite-prodding stick The old stick is 3 trollurches long, so it costs 6 florins. Despite the Wizard's protests, the Guard buys the cheaper stick. He heads off to prod his kite, but it all ends in tears.
12:45 to End - A new kite The Wizard decides to leave the lumber business, since it's bad for his back. He makes a presentation to his final customer - a new kite for the Guard!