Imagine you are playing with play-doh and you make a big ball. Now, you want to put some lines on the ball to make it look cool. The lines can go up and down or side to side, but they have to stick to the ball. That's kind of what the Beltrami equation is like.
The Beltrami equation is a way to describe how lines change when you bend or twist something. It's like if you had a piece of paper with lines on it, and you crumpled it up. The lines would still be there, but they would be all twisted and bent.
Mathematicians use the Beltrami equation in lots of different ways. They might use it to study how materials like rubber or clay bend and change when you pull or twist them. They might also use it in studies of fluid dynamics, which is how liquids and gases move around.
The equation is named after Eugenio Beltrami, an Italian mathematician who came up with it in the 1800s. Even though it's a little tricky to understand, it has helped scientists and mathematicians understand some really cool things about the world around us.