# Math and Campus Maps

It’s been a few days since I’ve posted as I’ve been pretty busy with frosh week events here at Waterloo. Since I’m going into software engineering, I’m technically part of both the engineering faculty and math faculty and therefore participate in events from both faculties. At this point, all “softies” have earned their engineering hard hats and pink math ties:

The other night, one of the Comp Sci guys on my floor came to my room with a pretty cool math problem that would have fit well on Project Euler. It basically wanted to know how many downward-pointing triangles were present in a pyramid made of triangles. Of course, these downward-pointing triangles could be built from multiple triangles; for 4 layers of pyramid the answer is 7 because of one bigger multi-triangle:

Arriving at a computer-friendly answer is very easy, and requires a simple nested for-loop. I also found a slightly more elegant solution with only a single for-loop, but again this solution was fairly easy to come by. The hard part began when a few more CS/Eng students arrived and asked if we could find a single equation that would work for all cases that was “calculator-friendly”, i.e. without any looping. This was tougher.

We worked for several hours that night and didn’t really produce any solid results. I decided to try again earlier this morning and I’ve finally come up with an extremely ugly solution for cases were the number of layers (n) is greater than 4:

I’m still not satisfied, but I’m putting it away because I’ve already put way too much time into it.

The second item I mentioned in my title is an idea for an app I’ve started working on. I used my iPhone + Google Maps to get around campus for the first few days, but this required some looking back/forth between the phone and the actual campus map. I think it would be handy to have a campus map super imposed onto Google Maps. In addition this map could take building names as start/end locations and plot the optimal route. I’m hoping to have this done by the time class starts on Monday. 😛

T