Blog Post #3: Mathematics in a story | The King's Chessboard

The book I chose to write about is The King's Chessboard by David Birch, illustrated by Devis Grebu. This book deals with the concept of exponents and exponential growth.

Summary
In David Birch's The King's Chessboard, beautiful illustrations by Devis Grebu tell the tale of a king and a wise man. The king wishes to give the wise man a reward, as the man has performed a great service. While the wise man at first wishes to receive no reward, the king demands he ask for something. Finally, the man figures out his request. Pointing to a chessboard, the man asks that each day, the king give him one grain of rice for every square on the board, doubling in amount each day. So for the first day, he would receive one grain; the second, two; the third, four; the fourth, eight-- and so on. The king, not knowing just how much rice that would amount in and being too prideful to ask, granted his complicated request. Each day, someone was sent to the wise man to deliver the rice. For the first few days, the amount of rice was expectedly little. But soon, the rice started piling up. Before he knew it, the king was sending out tons and tons of rice to the wise man. In disbelief, he called for the royal mathematicians to calculate the number of grains of rice the king had promised-- which turned out to be over 5 billion tons. The king eventually confers with the wise man, and in important lesson is learned about not letting your pride getting the better of you, because even a king can look like a fool. But beyond the moral lesson, there is math to be learned here!

Mathematical Concept
The king wrongly assumed that such little rice could add up to be such an impossible amount. This demonstrates his lack of understanding of exponential growth. As we have learned in class, exponential functions grow much more rapidly than linear ones. Here's an explanation of why:

The equation for a linear function is as follows:

y = mx + b

Because "m" is added an "x" number of times, the repeated sums result in a product.
It could also be written as:

y = b + {m + m + m + m...}

Now, look at the equation for an exponential function:

f(x) = ab^x

Now, "b" is being multiplied an "x" number of times. Which could also look like:

f(x) = a * (b*b*b*b...)

Though it can be a confusing concept at first, it's easy to see that multiplying a number results in a higher product than adding. For the story of The King's Chessboard, the equation would be 2^x, x representing the day. The story explains this complicated concept in a simple manner. This is why literature like this is so important-- and not just for children. Clearly college students can learn from it too!