Today I learned a really neat (and new to me) basic algebraic technique from Dave Radcliffe on twitter.
This morning James Tanton posed this interesting problem:
I started thinking about it, but work got in the way. Checking back a little later I saw an amazing solution (that fits in a tweet!) from Dave Radcliffe:
Super clever. If you want a circle, you’ll need an equation like and the conditions of the problem essentially allow you to force that equation!
For fun I plugged these three equations into Wolfram Alpha to take a peek at the solution:
(2) , and
The third equation comes from applying Dave’s idea to the first two equations. Sure enough, you get this picture:
The Wolfram Alpha code is here:
Wolfram Alpha code for drawing the above picture
Not every day you learn a new high school algebra technique from a tweet – thanks for posting the cool solution, Dave!
[Post publishing note]
Two great Desmos programs help give you a feel for the problem. First from Chris Lusto:
and second from Justin Lanier:
One thought on “Mad props to Dave Radcliffe”
You might enjoy tinkering around with this slight generalization. Linear combination rocks! https://www.desmos.com/calculator/vkvaesiz8s