Chebyshev form

Chebyshev form is a mathematical way to describe a type of curve. It's named after a man called Pafnuty Chebyshev who was a very clever mathematician from Russia. The curve that Chebyshev form describes is wiggly and bumpy but still looks smooth.

Imagine drawing a line on a graph that goes up and down lots of times but always stays within a certain distance from the middle. The middle could be a straight line or another curve that is smoother. This distance is called the "tolerance limit," and it means how much the line can stray from the middle before it's too far away.

Chebyshev form is cool because it lets us describe this wiggly line with just a few numbers. These numbers tell us how many times the line goes up and down and how much it can stray from the middle. We can use this formula to make all kinds of different wiggly lines, like ones that wiggle less or more or ones that wiggle in different ways. It's like having a recipe for making wiggly lines!