Sunday, December 19, 2010

Year-End Note

It is that time of the year again.

We heard a call from South,

saying, "Come - whoever you are!"
"Poor or rich"
"Full or null"
"Up or down"
"Live or dull"
"Come, just hear my cry!"

It was not the ears heard the call,
But the heart trembled with it.
How can one remain unconscious to this call?

So my friend,
never reject a good call.
Shine with your mercy
upon everyone.

Break your daily routine,

Do things out of the box.

Search the good in bad,
And never give up thinking.

--- Polar Fox

Sunday, December 12, 2010

Fox 323

Polar Fox:
Hey Red, these points seem to have identity issues. Are they black or white?

Red Fox: An obvious illusion! They are white for sure.

Polar Fox: So what I perceive is not the exact reality?

Red Fox: This is just a simple game of colors playing on your retina. It is perfectly explainable and part of the reality.

Polar Fox: Yes, most definitely. But, can this be an artful clue of an even bigger reality that there is truth beyond what you see?

Red Fox: Here we go again!

Polar Fox: A brush mark from a picture? A letter from a book? A note from a symphony?

Red Fox: And who is the artist, juggling with colors to deceive our perception?

Polar Fox: Deceive? I am not so sure. But looks like someone who knows us inside and out. And I think he wants to talk.

Red Fox: Why me? Why me?

Polar Fox: Yep, and you have bigger ears than mine.

Friday, December 10, 2010

Fox 316 and 318 - Solutions

Both solutions to 316 and 318 are by Bleaug. Also César Lozada has commented out a very similar solution to 316. Obviously, the maximum area is achieved when P is the mid-point, which is also the case for 321. But for Fox 322, it is not that obvious. That's why it still remains as unsolved. Thank you all for the good work.

Fox 316 Solution:
"I couldn't get a pure geometric demonstration of these two problems. At best, with some lazy observations you are able to show that for both #316 and #318, maximum area is achieved for P midpoint of BC:
a) angle(QPR) in P remains constant when P varies
b) PR/PB is constant
c) PQ/PC is constantHence area(PQR) is proportional to PB.PC which is maximized when P is the midpoint of BC.
The rest is obtained by calculus."

Fox 318 Solution:

Monday, December 6, 2010