Math, and other games
Things that were fun about today:
1) I wore my favourite shirt--it's black and it says "Start a revolution... stop hating your body", and it magically makes me feel awesome--and my favourite underwear.
2) I woke up early to go grocery shopping and got to take a lovely walk though my quaint neighborhood in the early-morning autumn air.
3) I figured out the answer to a ridiculous math problem that I'd previously had no idea how to do. Then I went to ask my teacher if it was right, and I got to go in the very fast elevator in the math building. I love very fast elevators; they will never stop being exciting. You can feel yourself getting heavier as they accelerate upwards, because guess why? GENERAL RELATIVITY, that's why.
4) It was show-and-tell day in my Physics of Music class.
5) I was practicing the piano for a bit and I finally got the Arpeggio of Ridiculousness in Fur Elise to sound okay. We'll see if it sticks.
6) It was lighting levels day for the play I'm working on. Lighting levels is where you sit in the theatre in the dark and decide how the lights should look for each scene. It takes a really long time, but omg the lights are going to be SO PRETTY. The designer did a fantastic job with everything, and to be honest I'm a bit jealous, but this is supposed to be a list of positive things, undertaken specifically, in fact, to take my mind off this, so I'll try not to think about it anymore.
7) I was told on two different occasions that I'm a good stage manager and coach. I sure hope those people weren't just being polite.
The other part of this post is a math question. I have to prove that any prime besides 2 that's the sum of two squares is congruent to 1 modulo 4 (in other words, ∀x[Px ∧ x = y2 + z2 --> x = 2 ∨ ∃q(x = 4q + 1)], where Px means x is prime). I HAVE NO IDEA WHY THIS IS. Do you?
EDIT: I got it. Here's why:
If x and y are both even, then the sum of their squares is even and therefore not a prime except maybe 2.
If x and y are both odd, then the sum of their squares is still even and not a prime, either.
If x is even and y is odd, then x=2m and y=2n+1, so x2 = 4m2 and y2 = 4n2+4n+1, so their sum is one more than a multiple of 4.
1) I wore my favourite shirt--it's black and it says "Start a revolution... stop hating your body", and it magically makes me feel awesome--and my favourite underwear.
2) I woke up early to go grocery shopping and got to take a lovely walk though my quaint neighborhood in the early-morning autumn air.
3) I figured out the answer to a ridiculous math problem that I'd previously had no idea how to do. Then I went to ask my teacher if it was right, and I got to go in the very fast elevator in the math building. I love very fast elevators; they will never stop being exciting. You can feel yourself getting heavier as they accelerate upwards, because guess why? GENERAL RELATIVITY, that's why.
4) It was show-and-tell day in my Physics of Music class.
5) I was practicing the piano for a bit and I finally got the Arpeggio of Ridiculousness in Fur Elise to sound okay. We'll see if it sticks.
6) It was lighting levels day for the play I'm working on. Lighting levels is where you sit in the theatre in the dark and decide how the lights should look for each scene. It takes a really long time, but omg the lights are going to be SO PRETTY. The designer did a fantastic job with everything, and to be honest I'm a bit jealous, but this is supposed to be a list of positive things, undertaken specifically, in fact, to take my mind off this, so I'll try not to think about it anymore.
7) I was told on two different occasions that I'm a good stage manager and coach. I sure hope those people weren't just being polite.
The other part of this post is a math question. I have to prove that any prime besides 2 that's the sum of two squares is congruent to 1 modulo 4 (in other words, ∀x[Px ∧ x = y2 + z2 --> x = 2 ∨ ∃q(x = 4q + 1)], where Px means x is prime). I HAVE NO IDEA WHY THIS IS. Do you?
EDIT: I got it. Here's why:
If x and y are both even, then the sum of their squares is even and therefore not a prime except maybe 2.
If x and y are both odd, then the sum of their squares is still even and not a prime, either.
If x is even and y is odd, then x=2m and y=2n+1, so x2 = 4m2 and y2 = 4n2+4n+1, so their sum is one more than a multiple of 4.