Geek Challenge Results: Define the Doodling Curve

Last month’s Geek Challenge was to find the limiting curve created by drawing lines on graph paper in a certain pattern.  

The correct answer is C, and the values for the constants were 1, 2, and 1.

These three people answered the question correctly: Andrea Gotti of Milan Polytechnic, Adnaan Velji of DMC, and Dan Freve of DMC. Of these, the winner is Andrea Gotti. Andrea solved the problem as follows:

Each line of the paper doodle passes through two points. Those points will be called P and Q: 

While Dan’s and Andrea’s answers are very similar, Andrea gets top honors for his rigor in demonstrating that the stationary point is a maximum with the second derivative method, and supplying a more complete diagram.

Adnaan demonstrated that in mathematics there is usually more than one way to skin a cat. He used the formula for the intersection of two lines to calculate the limit of where the consecutive two lines would intersect as the distance between their endpoints on the axis approaches zero. The author used a similar method when formulating the problem. 

We each filled a couple of pages with equations to arrive at the same conclusion that Dan and Andrea reached in a few short steps.

Submit your comments to geekchallenge@dmcinfo.com.