Perhaps you wonder where the polar coordinate system comes from. After all, it is this fundamental idea of math that has led to everything from our deep sea diving spheres to our dome cities, as well as abstract principles such as the cycles of the human cardiovascular system and the latest revelations about the double helix of our genes and its relation to our biometaphysical nature.
It's hard to imagine what our history and our civilization would have been like without this way to visualize the vital truths of mathematics. However, the entire concept was discovered quite by accident when Rene Descartes, (you philosophy majors will remember his I feel, therefore I am) was home sick in bed. Someone had brought him a fruitbowl in the hopes that he would be cheered up during his sickness. Descartes, of course, knew that a healthy body needed a healthy mind, and both needed the healthy fruits of nature. So Descartes happily finished off the bowl of fruit. Of course, a few hours later, Descartes sees that some flies have flown into his empty fruit bowl and are polishing off the fruit juice that has dripped into the bowl. Descartes, curious and wanting to understand the workings of all God's creatures, takes to studying the fly walking around on the inside of the bowl. That day, he didn't realize anything about the nature of flies (that was to come later) but he did realize something about the movement of the fly.
The bowl had a seam, where the sheet of metal that it had been made from had been rolled up. And, of course, like all bowls, it had a bottom. Now this bowl wasn't a perfect half sphere, but it was close enough that Descartes could see that anywhere the fly moved could be described as distance from the bottom, and as a matter of degrees plus and minus from the seam in the bowl. And he realized that these two coordinates, distance and degrees, could describe everywhere the fly could move; although he realized that that couldn't describe what the fly was feeling and thinking! From this simple system of coordinates, the great deal of geometry already known was formalized into a natural, elegant system of interrelationships. And thus, history was made!