Geometry Online  Introduction  Distances  Midpoints 

Think of a city's streets as a huge square grid. No city is really laid out in exact squares. There are curves, diagonals, deadends, and oneway streets. Our schoolbus geometry is what mathematicians call an idealized model. We're considering city streets as if they were a perfect square grid, but we know they're not exactly.

 
Put an X on all the points on the grid that are 4 blocks away from Point A. Remember this is schoolbus geometry, and you have to stay on the streets, no cutting across corners.
The definition of a circle is all the points in a plane a given distance from a given point. You just found all the points 4 units from Point A. So could we say this is what a circle looks like in our schoolbus geometry? Wow, that's a circle! 
See the SchoolBus Geometry circle You'll have to hit back on your browser to return to this page. 

Algebra Connection: While we're talking about circles, let's go back to Euclidean Geometry and look at our familiar circles. The equation of a circle centered at the origin in Euclidean geometry is

Can you see from the second figure why that is? (Think Pythagorus.)
Challenge Questions:

Geometry Online  Introduction  Distances  Midpoints 