Mad props to Dave Radcliffe

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 x^2 + y^2 = r^2 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:

(1) y = x^2 + x - 10,

(2) x = y^2 + 3y- 4, and

(3) x^2 + (y+ 1)^2 = 15.

The third equation comes from applying Dave’s idea to the first two equations. Sure enough, you get this picture:

WolframAlpha Image

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:

Chris Lusto’s Desmos Program

and second from Justin Lanier:

Justin Lanier’s Desmos Program

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Comments

One Comment so far. Leave a comment below.
  1. You might enjoy tinkering around with this slight generalization. Linear combination rocks! https://www.desmos.com/calculator/vkvaesiz8s

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