The desert crossing
bin Hassad, an ancient Arabic mathematician, had to get to the
Great Library at Alexandria in the shortest possible way to deliver
a very important discovery in geometry. In his path at one stage was
a desert of about 800 miles. He was a poor man, only able to afford
to hire one camel for the crossing.
bin Hassad realised that no camel he could afford could go 800 miles without finding extra water in the desert. Of course, he would carry water and the camel would have its own reserves, but still, the limit of travel without finding water would be about 500 miles. There was no limit of water and water bags at the start of the crossing. Clearly, he would have to make a few trips into the desert to set up dumps of water. But a camel was hired on the basis of the distance it travelled. Camel owners were very experienced at judging how far their camels had travelled. The question was what was the least distance that could be travelled to get to to the camel station on the other side of the desert.
He asked the camel hire staff what they thought would be the best way to proceed. "Oh yes", they said, "the best way is to not worry the head at all because this can harm the mind that Allah gave us. Just fill up the camel and these water bags and leave water wherever the camel makes a coughing sound or whenever you feel tired. Come back here and get more water and keep doing this till anyone can see that there is enough water in the desert to cross with a camel. This is the best way"
"Yes!", thought bin Hassad, "Of course! They get more shekels the more their camels travel. But I, a poor man and a mathematician, must work out what the least number of miles are needed to cross".
He concocted a plan on the assumption (correct enough as it happened) that the rough figures above were exact. He crossed the desert and paid all his dues. His feat was the talk of all camel hiring stations in the Arabian Kingdom.