I was reading the math book i borrowed., Mathematical Journeys. Very interesting and it starts everything from the beginning and gets each chapter up to Olympiad-like standard. There was this simple game mentioned, Nim. Fun game, isn't so mathematical, but if you want to win, you'll be need to express the numbers using binary representation (And I'm not going to tell you more).

Next i found some stuff that I've been looking for, mainly the paper in which i copied down some math stuff at nyjc library, the day before GP paper. I remember that i was just browsing through this mathematical gazette magazine while i came across this article talking about whether e^pi or pi^e was bigger. I had noted down the major parts of the proof at that time, but only managed to find that paper today as i was flipping through one of my memo pads. Here's the full version of the proof:

Also, i went cycling today, saw my teacher along the way. Today was quite adventurous, there were some parts where i got to drive at high speeds. It was better that the previous downhill since this one was longer. I also went to explore this park near potong pasir station and found many runners there, it's a good place to run. Only thing is that it's not sheltered (it's a park, remember?). Then there was this time when i got onto a raised platform at a high speed; my water bottle flew out of the basket infront (and due to faulty breaks, it took me about 40m to stop). I tried it again with some strategy and this time, my bottle did the jump but landed back in. Cool huh?