Newton's theorem about ovals
Newton's theorem about ovals is a fancy way of explaining how ovals are made. Imagine you have a string and you tie the ends together to form a loop. Now, you grab two points on the string and pull them away from each other, making the string loose.
If you move those points around the loop, you'll notice that the length of the string between those points always stays the same. This is called the constant sum property.
Newton's theorem says that if you draw two lines through the center of the loop and the points where the string is being pulled, the lines will always intersect at a right angle. This is true for all ovals, whether they're stretched out like an egg or squished like a circle.
So, basically, Newton figured out that if you stretch a looped string out and move two points around, the length between those points stays the same and the lines through the center and the points always intersect at a right angle. Cool, huh?
If you move those points around the loop, you'll notice that the length of the string between those points always stays the same. This is called the constant sum property.
Newton's theorem says that if you draw two lines through the center of the loop and the points where the string is being pulled, the lines will always intersect at a right angle. This is true for all ovals, whether they're stretched out like an egg or squished like a circle.
So, basically, Newton figured out that if you stretch a looped string out and move two points around, the length between those points stays the same and the lines through the center and the points always intersect at a right angle. Cool, huh?