Happy pi day 2020!
Since pi is the number of round things, we devote this year's pi day celebrations to...curvature!
Not only does curvature lend beauty to the world we live in (it would be awful if all lines were straight), it also is crucial in our understanding of it. The following articles look at how curvature can be described using maths and explore how those mathematical notions are important in physics and cosmology. From Einstein's theory of gravity to the ultimate fate of the Universe, curvature is key!
Kissing the curve — From a smile to a line drawing by Picasso, curves bring great beauty to our world. But how curvy is a curve?
Kissing the curve: Manifolds in many dimensions — Following on from our previous article about curvature of lines and surfaces, we now move up to curvature of their higher dimensional equivalent – manifolds.
Maths in a minute: Osculating the curve — We are very pleased with our toy demonstrating the curvature of any smooth function. Try it out!
Maths in a minute: Not always 180 — What happens when the angles of a triangle don't add up to 180 degrees? You get positive or negative curvature!
Maths in a minute: Einstein's general theory of relativity — Find out how curvature is key in Einstein's hugely successful theory of gravity.
Maths in a minute: Black holes — When the curvature of spacetime becomes extreme you get what is called a black hole. Find out more about these fascinating objects here.
The shape and fate of the Universe — How will the Universe end? In a big crunch? Or a big freeze? It all depends on its curvature.
Hidden dimensions — String theory says that the world has many more dimensions than those we can perceive. So where are the others? curvature provides some answers.