Archimedes' use of infinitesimals

Hey kiddo, do you remember when we talked about Archimedes? He was a really smart guy who lived a long time ago in Ancient Greece. Archimedes had many famous discoveries and one of them was his use of infinitesimals.

Infinitesimals are really tiny numbers. They are so small that we can't even write them down using regular numbers. Archimedes used these tiny numbers to figure out really big and complicated problems, especially those related to geometry and mathematics.

For example, he wanted to find out how much space there was inside a circle. Now, we know that a circle is round and has no straight lines, so how do we measure its area? Archimedes came up with a clever idea. He divided the circle into tiny slices, like a pizza. But instead of cutting it into an even number of slices, he made the slices smaller and smaller until they were infinitesimally small.

Then, he figured out how much space there was in each tiny slice using a mathematical formula. Finally, he added up all those tiny slices to get the total area of the circle! It was a really clever way to solve a really tricky problem.

So you see, Archimedes was a genius who used really tiny numbers to solve really big problems. It's like using a magnifying glass to look at something really small or a telescope to look at something really far away. Just like how we use different tools to solve different problems, Archimedes used infinitesimals to solve his.