The King's Chessboard

1. I contemplated the stories my parents read to me as a child and really struggled to find one that not only pertained to math, but more specifically the mathematical concepts we have recently studied. Thus, I decided use one of your examples and read The King's Chessboard for the first time. This story is apparently quite ancient and goes under many different titles, yet the moral of the story remains the same. The story I read was originally published in January 1988, thus I'm guessing a retelling of the old tale, and was written by David Burch; it had intensely colorful images of a world set in the past in a desert like setting. In this story a wise man refuses to accept a reward for his duties from the King, however the King insists so the wiseman decides to use this opportunity to try to outsmart the King using math. The wiseman asks the King to place grains of rice on a chessboard starting with 1 grain on the first square, and 2 on the second square, 4 on the third etc. However, by the 41st square the King realizes he is in over his head and cannot afford to give this much rice to anyone, nonetheless a commoner. The King realizes he has been tricked, and decides to trick the wiseman back by giving him a bag of rice and asks him to count every single grain within the bag, if he can do so he can have all the rice; this is in fact an impossible task due to the time the task would require. The wiseman realizes the King had tricked him back and neither give or receive any rice. Thus, one could infer it is a story of karma or the King's power or simply of greed, either way it is intellectually stimulating and interesting.

2. This story is a fascinating way to explain exponential growth. Each square the King must place rice on the grains are to be doubled. Thus, by the end of the first row of the Chessboard the King has placed 128 grains. He must do this for all 64 squares on the board, therefore by the 41st square he was to owe over a trillion grains of rice. The book is demonstrating how quickly exponential growth can occur and how easily the numbers will become increasingly larger. The author is cleverly explaining doubling and is highlighting how quickly numbers increase when doubling is involved, therefore it was inevitable, if you understand the growth pattern of 2n where n is greater than or equal to zero, that the King was to owe more grains than he possessed. This story is a perfect example of exponential growth as there is a constant increase in quantity according to the law, in this situation the wiseman's rule of doubling the grains to be placed on each square. Also, it is exponential growth, not exponential decay, because the initial value (b) is a whole number; the King must start by placing 1 grain of rice on square one thus the initial value was a whole number. Overall, the way the book intertwines exponential growth with a clever story is fascinating, yet at the same time it is written in a way that aids the reader in understanding exponential growth in a way a basic math class may not be able to provide.

3. I believe literature is an effective way to teach mathematical concepts, despite the common thought that the two are quite contradictory. I think it is valid, as many people learn in different ways, thus explaining a mathematical concept with a story could aid some in grasping the concept as words for some are easier understood than numbers, also it gives people an easy example to remember when they are applying the concept in the future. I think before I had written this post I may have argued differently, especially due to the fact I had never had a teacher read me a story in a math lesson before this class, however the story allowed me to learn about exponential growth in a different way than we had learned in class and this really helped me grasp the fundamentals. I believe it is the way the math is intertwined with a real life example that helped me to understand, therefore I think using literature to teach certain mathematical concepts is extremely useful and should be used more often.