In Pursuit of the Unknown

APA Citation:

Stewart, I. (2013). Ghosts of departed quantities. In In pursuit of the unknown: 17 equations that changed the world. New York: Basic Books.

Summary:  

In the late 1600s, Newton in England and Leibniz in Germany developed calculus independently at more or less the same time, Newton is known for using it to explain and understand the universe, Leibniz did little with it.  Newton said “if I have seen a little further, it is because I was standing on the shoulders of giants.” referring to the work, going back to ancient Greeks, that had led up to its discovery. More contemporary influences included Wallis, Fermat, Galileo, and Kepler.

Calculus looked at change over time.  Looking at the speed of an automobile, you can use miles per hour.  You get a closer look at an automobile’s speed than MPH, and split it to more accurate – use smaller intervals of time, Miles/Second.  Which is a pretty close look at speed when driving a car, but for a, “guitar string playing middle C vibrates 440 times every second; average its speed over an entire second and you’ll think it’s standing still.” Galileo conducted experiments on the effects of gravity on objects (balls) as they rolled down an incline.  Studying the speed with smaller and smaller intervals. He noticed that a pattern in regards to a balls speed and distance, regardless of the size of the ball or the incline of the ramp.  Newton used these findings, among others, to form calculus – as the interval continues to get smaller, it becomes nearer to the instantaneous rate of change.

Calculus is applied to helps us understand the world and is applied to concepts ranging from deep outer-space travel to back on our home studies of subduction zones that may create an earthquake.  

Things Learned:

Calculus was discovered at, more or less, the same time by two different mathematicians.  One (Newton) used it to describe the world we live in, the other (Leibniz) did little with it.

My Question:

This answers my question about mathematical thinking by learning about the beginning of calculus and how it was developed through the use of mathematical thinking.  These two mathematicians looked for patterns of objects in the and described how they changed using logic and patterns.