On December 25th, Julian Calendar, Isaac Newton was born in the countyside of Lincolnshire. His mother wanted him to become a farmer, but he had greater aspirations. Whilst the school taught the ideas of Aristotle, he learned about the works of modern thinkers such as Rene Descartes, Galileo Galilei, and Johannes Kepler.
Newton soon became curious about mathematics and science. According to legend, his ideas came when an apple fell on his head. But that was not how the story actually go. In August 1665, Cambridge university temporarily closed and Newton went out to his farm. Whilst there, he thought about the behavior of an apple falling and related it to the movement of the moon and realized the connection between them. To understand his ideas, let's explore some of them.
The Derivative
So you are watching a ball rolling down a hill right now. That ball is rolling faster and faster. We have some sense of how fast it's going right now, but what does that mean? Many scholars at the time look at the distance an object travels over a given time interval, that's the average speed. But the ball's speed is constantly changing, so how do we describe the speed at that moment?
The answer is a derivative. Let's say we wanted to know how fast something went right now. Our tools are this: We know the formula for speed is distance divided by time, we can plot out a graph that tells us distance versus time, the formula for slope is (y2-y1)/(x2-x1), and we have something called limits. Limits look at function as they approach a certain number. Say for example, we have y=1/x. What if we wanted to know what happen when x is infinite. Wait, that isn't allowed in math. But we would expect it would be zero because as we divide by larger and larger numbers, the amount gets smaller and smaller. So we actually say the limit as x approaches infinity of 1/x, is equal to 0. Now using these tools, let's observe the slope as the amount of time passed is equal to zero. As you can see in this animation, we could get better and better approximation of the slope.
The Intergral:
Suppose this time, you know the speed and how it changes over time. Suppose you wanted to find the distance you traveled. How would you do that? We now have the derivative to work with. We know the speed is distance divided by time, and we know the time. Dimensional analysis can tell us based off of average speed and the time it took, we can figure out the distance by multiplying them. But what is the exact answer? Turns out this question could also be phrased as: What is the area underneath a curve? The answer, like before is to look at limits. Multiplying average speed by time is just like finding the area of a rectangle, where the base is the time and the height is the speed. Imagine looking at tinier and tinker time intervals, and adding up these tiny rectangles up. Like this:
Gravity:
Many people would attribute Newton to gravity and his laws of physic, and even memorize what his three laws are (often followed by a cringy pun). I won't write out the full reasoning, but here's how he reasoned gravity: If I drop an apple, it will fall. If I threw an apple, it makes a curved path. The Earth is round, so what if I threw the apple fast enough that by the time the apple is suppose to hit the ground, it completely misses the ground? That's what the moon is doing!
Optics:
Newton was less known for his works in optics, but he showed white light contained all the color of a rainbow. Newton also invented his Newton telescope.
Isaac Newton would spend his later year serving as President of the Royal Society and died at the age of 84.
That is why during this holiday, thank Isaac Newton for the stuff you have today because without his contributions to math and science, where would we be?
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