Norton's dome

Norton's Dome is a very big hill that is shaped like a dome, just like the top of a bubble or a ball. Imagine if you took a big scoop of ice cream and put it upside down on a table, that's what Norton's Dome looks like.

Now, if you were to put a ball on top of Norton's Dome, it would stay there without rolling off. This might seem strange because if you put a ball on a hill, it usually rolls down, right? But not on Norton's Dome!

The reason for this is that Norton's Dome is a very special shape. It's what we call a "mathematical surface," which means that it obeys certain rules and formulas that mathematicians have figured out.

One of these rules is that any object placed on top of Norton's Dome will stay in place because the surface is perfectly symmetrical. This means that no matter which way you look at Norton's Dome, it will always look the same.

Another interesting thing about Norton's Dome is that if you were to roll a ball down from the very top, it would slow down and stop at a particular point before rolling back up again. This is because of a concept called "conservation of energy," which is like a rule that says energy can't be created or destroyed, only transferred from one thing to another.

So, the ball starts off with a lot of energy at the top of the dome, but as it rolls down, some of that energy gets turned into heat and friction with the surface of the dome. Eventually, the ball reaches a point where it has given up all of its energy, so it stops moving. At this point, it starts rolling back up the dome because of gravity, and the process starts all over again!

In summary, Norton's Dome is a big hill that looks like an upside-down scoop of ice cream, and any object placed on it will stay in place because of its symmetrical shape. If you roll a ball down the dome, it will slow down and stop at a certain point before rolling back up again because of the rules of energy conservation.