Blog Post 3 -->Jonathan Lencki

Blog post #3

Jonathan Lencki

The Kings Chessboard by David Birch

Part A:

         A Wiseman does a favor for the king and the king gives the Wiseman a reward for his favor. At first the Wiseman doesn’t want anything for his favor until the king persists to return the favor threatening him that if he doesn’t ask for anything he will wish he had. The Wiseman then looks towards the kings chessboard and decides on his favor. He asks that the king give him a grain of rice for the first square on his chessboard, the next day he asks for 2 grains for the next square, the next day, four grains and to double the amount of rice everyday for every square for all of the Kings 64 chess square. The king begins to think to himself how many grains of rice he would have to emit by the time the favor is over and he is totally unsure, being custom to only giving pounds of rice. The queen then suggests to the King to simply ask the Wiseman how much rice that is. Being a proud man, the King refuses to show the rest of his chamber that he cannot count deciding to not ask the Wiseman the question. The king finally grants the Wiseman his requests and his councilors erupt in laughter at the Wiseman’s strange request. The Wiseman then bows and leaves quietly. Later in the day the Wiseman is given his first grain of rice by a Kings servant in splendid dress, after receiving it he places it on the first square of his chessboard. The King, hearing of the Wiseman’s action, then places a square of rice on his chessboard. The Wiseman continues to receive the increasing grains of rice everyday until on the eighth day, instead of receiving rice from a Kings Servant, a normal rice worker appears, delivering the Wiseman’s 128 grains of rice. The King soon forgets about the Wiseman and his rice leaving the counting and distribution of rice to the Weigher of The King’s Grain: 256 grains of rice and then 512 and then 1024. The Weigher of The King’s Grain now has to spend his whole day counting rice so he begins sending the Wiseman an Ounce of rice. Four days later the Wiseman receives only 16 ounces, he takes one grain of rice for his chessboard and gives the rest to a beggar. Soon the Grain Weigher realizes that everyday he will continue to lose half as much rise as he had the following day, ultimately going to The Grand Superintendent of The King’s Granaries; when he gets there however he panics’ and is unable to tell the superintendent of the extreme loss of grain. Nine days later the superintendent sees men carrying four sacks of rice to the Wiseman’s house. Realizing how much rice is being given away he rushes to the King’s palace. The King however is away on a hunting trip so he is unable to order the discontinuation of the deliveries. Soon, the Wiseman is receiving tons of rice everyday. When the King returns he hears cheering from the town and sees full carts of his rice being taken away. The king calls the royal mathematicians to his chamber and is told that the total amount of rice after the 64 days is Five hundred forty nine billion seven hundred fifty five million eight hundred thirty thousand eight hundred eighty seven tons. Appalled by the Wiseman he demands him to make a new request because the Kings doesn’t have enough rice to get through this 64 days. The Wiseman is satisfied with his plan and then asked the King a strange question: “are you satisfied”. Seeing all the happy people in the town the King happily answers that he is in fact satisfied. The Wiseman continued to serve the King many times again but never for reward.

Part B:

Clearly this elaborate story details the function of Exponential Growth. The King doesn’t even think about how every day he would have to double the amount of rice from the last day and ultimately makes the mistake of being mathematically short sited. Through the reading of this story you gain a great perspective of the pure mass exponential numbers have especially when given such a large window of growth (64 days). The expression the represents this growth pattern is N^2 where N represents the grains of rice being doubled from the day before.

Part C:

By explaining a fundamentally challenging concept through a very basic story, the reader is able to grapple with the concept of doubling more fully then if he or she were to be simply lectured about exponents. Through the readers engagement with the story they are able to see how the mathematical concepts can function in real life, while also getting some great morals along the way.