Bernstein polynomial

Well, a Bernstein polynomial is like a special kind of math formula that helps us draw shapes or approximate curved lines. It is named after a mathematician named Sergei Bernstein who came up with this idea.

Now, imagine you want to draw a smooth curve, like a circle or a wave. But drawing it by hand can be tricky, so we use maths to help us. A Bernstein polynomial is a clever way of using a formula to create a curve that goes through some points on your shape, and smooths out any bumps in between.

The formula looks a bit complicated, but it's really just a way of adding up lots of little parts, each one with its own power of x and y. So if you have a set of points, like the corners of a polygon, you can plug them into the formula and it will create a curve that passes through all those points.

The cool thing about Bernstein polynomials is that they can make really complex shapes too. By using lots of points and a higher order formula, we can create curves that have lots of twists and turns, like a squiggly line or a spiral.

In summary, a Bernstein polynomial is a fancy maths formula for creating curves and smoothing out shapes. It's named after a clever mathematician and it can help you draw anything from a circle to a squiggly line.