Ratio and Proportion





Long ago, in an oasis in the desert of Arabia, lived an old man called Abdullah. Right in front of his tiny hut was a tall date tree, laden with the juiciest dates one could ever have seen. One hot day, a traveler named Karim stopped at this oasis and walked up to Abdullah’s hut. Abdullah offered him some water. Karim received it graciously. When Karim saw the juicy dates, he wished he could have some. Sensing what was on in Karim’s mind, Abdullah said “I wish I could give you some dates, but alas, I am cursed.” “Cursed? By whom and why?” asked Karim. “Well, there is a spirit who lives in this tree and he says I can have the dates only if I can tell the height of the tree. Now tell me, how can I get a measuring tape so long as to measure the height of this tree? Besides, do you think at my age it is possible to risk climbing the tree?” Karim said “But you don’t need any tape to measure the height of this tree. Just get me a small measuring tape and I can do it for you in minutes.” Abdullah got him a metre scale. Karim fixed his own walking stick next to the tree. The Sun was not yet above their heads and it cast two shadows on the ground, one shadow was that of the tree and the other was that of the stick. Karim measured the lengths of both the shadows. He said “This stick is 60cm long and its shadow is 12 cm. The length of the shadow is one fifth the actual length of the stick. Now the length of the shadow of the tree is one metre, so the actual height of the tree is five times this length. That is the tree is five metres tall.” Abdullah shouted out to the tree “the tree is five metres tall”. Immediately the tree bent down and said “Well done! Take as many dates as you wish”. So Abdullah and Karim picked up some juicy dates. You see Mathematics can be fun and has many practical applications as well.