Contact geometry

Contact geometry is like how your hands and skin work together. Your hands touch things all the time, right? But your skin stops your hands from sinking into things or just passing right through them. That's what contact geometry is all about - when two things touch each other, there's an invisible layer of space that stops them from just blending together.

There is this thing called a manifold when we talk about geometry, which is like an invisible world that we can study. In this world, we can talk about shapes like squares, circles, and triangles even if we can't see them in the real world. If we think about a square, for example, it has four sides that come together at right angles. But some shapes have weird angles and curves that meet at strange angles. Imagine you have a toy airplane and touch its wings with your fingers. Even though both the airplane's wings and your fingers are smooth, they touch at an angle, and there is an invisible line that runs between them. This invisible line is a bit like a character in a book that we can't see but is important. It's called the contact structure!

Contact geometry helps us understand these strange shapes that touch at odd angles. It's like a special tool that helps us see the invisible contact structure and how it affects the way shapes move and interact with each other. Scientists and mathematicians use contact geometry to help them explore the untouchable world of abstract shapes and spaces. That's why it's so essential!