In this page you need to make a number of choices for the set up of the
exercise. If you ever want to come back and change those options you can follow
the link at the bottom of the next page.
The first thing you need to do is choose the open set you want to work with.
Click on the button for the shape of set you want (the default is
Or you can choose from this list to work with one of the same shapes, but in a larger size:
There are two modes you can run this demo in. In regular mode you see the open
set, you click on a point in it, and then the computer draws an open ball around your
point. In battleships mode, you never actually see the open set. You click
blindly on the image, and the computer draws in your open disk. You get to see all
your previous disks, so by doing this repeatedly, you see the open set you selected
filling out. (This illustrates the principle that an open set can always be expressed
as the union of (possibly infinitely many) open disks.)
There are three ways that you can select the size of the open balls you use.
You can opt to input the radius you want in an input box (first, click on the
set to select the point you're interested in, and then you'll be prompted for the
Alternatively, you can have the computer choose a radius for you, and that can be
either some random radius (random, but small enough to fit in the set), or it
can be that largest, or optimal, radius that will fit in the set.
Now choose the method you want to use to find the radius:
When you're happy with your choices, press:
At any time you can return to this page by following one of the links at the bottom
of the subsequent pages.