# User:Nfgdayton/sandbox

## History

Let's pretend that you are the person that invented agriculture.

Let's say that you figured out that when you put seeds in the ground in a square plot that is 10 paces by 10 paces you find that you have enough wheat to keep yourself fed while the next crop grows. Having done this you find that you have lots of time on your hands so you start thinking. Pretty soon you've discovered how to catch live wild birds. You find that if you feed your birds some of your grain they lay eggs for you which go nicely with the wheat that you've been eating. Unfortunately since you didn't increase the amount of wheat that you planted you find that you come up a little short at the end of the season and have to eat your birds. Since you're no dummy (you invented agriculture didn't you!) you land on the idea of using stones to keep track of the wheat you eat, and the amount of wheat a single bird eats. The next season you decide to plant wheat in a plot that is 11 X 11 paces. Your stones tell you that you eat 10 times as much wheat as your birds, and you have some wheat left over.

We know that the area of land to grow the amount of wheat you need is ${\displaystyle x^{2}}$. We know that the amount of wheat that a bird needs is 1/10th what you need or 1/10 ${\displaystyle x^{2}}$.

The amount of wheat you need is equal to 100 square paces. So ${\displaystyle x^{2}=100.}$

Plugging that into the equation we get:

${\displaystyle 100+(1/10*100)=s}$ where s=the square paces you need for you and your bird.

${\displaystyle 110=s}$

Since your last field of wheat was 11 x 11 square paces or 121 square paces you have 11 square paces worth of wheat left over. So you catch another bird.

Why did we use the the terms ${\displaystyle x^{2}}$ and ${\displaystyle 1/10x^{2}}$ above? ${\displaystyle x^{2}}$ is the term that we use to figure out the amount of land we need, but since our point of view is currently ourselves we can use variables like h for human, b for bird. In fact in the exercises below we will figure out values for other variables. Following the exercises we will change our point of view, and see how this change led to considerations like what are shown in the diagram on the right.