## Math Help, non-euclidean geometry.

• Ritournelle

Posts: 134
I know there's a few high level physics and math people around here so I though I'd at least give it a shot, I'm stumped and the assignment is late...

So, we have a partition Xbar of the plane X=R^2 consisting of all subsets A (subset of X) of the form

A= I. {(x,y),(-x,y) x=/=0}
OR II. {(0,y)}

Let dbar euclidean (euclidean distance on the partition) be the quotient semi-metric d euclidean ofX=R^2. We want to analyze (XBAR, Dbar euc).

That is the set up.
d. For P, Q ∈ X+, consider a discrete walk w from P ̄ to Q ̄ consisting of the pointsP =P1,Q1 ∼P2,Q2 ∼P3,...,Qn−1 ∼Pn,Qn =QofX. Showthat there is another discrete walk w′ from P ̄ to Q ̄ consisting of points P = P1′, Q′1 =P2′,Q′2 =P3′,...,Q′n−1 =Pn′,Q′n =Q,such that ldeuc(w')<=ldeuc(w) and such that all points Pi′ and Q′i are in X+. Hint: Part c.
e. For the discrete walk w′ of Part d, show that ldeuc(w')=>deuc(P, Q).
I have D by induction, but I'm not totally sure how to get the case in E.

Posts: 3554
What a joke. I can't believe you can't figure that out.
• Ritournelle

Posts: 134
I'm about to cry myself to sleep over it
• Posted by a hidden member.
Math is awesome lol
• danisnotstr8

Posts: 2579
"Blowing in the wind."
• Posted by a hidden member.
why not use the Euclidean space structure to define a metric... this has always been the easiest for me.

• Ritournelle

Posts: 134
The metric is already defined... It's euclidean, and it's 2-dimensional, but that's irrelevant anyways. I already used transitivity and induction to demonstrate part D (also before that, I know that because we have a space of a folded euclidean plane, (X+), the reverse triangle inequality including proof by the Taylor-Schwarz inequality definitely proves that dbar is deuc(P, Q), then I believe it must imply a strict equality (or at least an iff statement) for d euc (P,Q)= d euc (P',Q')
• Posted by a hidden member.
LOVALOT said *<|=^D ▁▂▃▄ l|̲̅̅●̲̅̅|̲̅̅=̲̅̅|̅●̲̅̅| ▄▃▂▁ १|˚-˚|५ !!!!!!!˚∆˚!!!!!!! ☀‿☀♫ ˙❤‿❤˙˙❤‿❤˙˙❤‿❤˙˙❤‿❤˙ ◠◡◠|〇◡〇|◠◡◠ ✌ { ◕ ‿ ◕ } ✌ ༗_ゝ༗ [◠し_◠ฺ ] ☛｀ิิ‿ゝ´ิ ☛ ªʘ̀‿‿ʘ̀ª |'L'| •❐_❑• ✌▓▒░ ❤‿‿❤░▒▓✌ ✌⊂(✰‿✰)つ✌ ☜Ҩ.¬_¬.Ҩ☞ *<|=^D ▁▂▃▄ l|̲̅̅●̲̅̅|̲̅̅=̲̅̅|̅●̲̅̅| ▄▃▂▁ १|˚-˚|५ !!!!!!!˚∆˚!!!!!!! ☀‿☀♫ ˙❤‿❤˙˙❤‿❤˙˙❤ *<|=^D ▁▂▃▄ l|̲̅̅●̲̅̅|̲̅̅=̲̅̅|̅●̲̅̅| ▄▃▂▁ १|˚-˚|५ !!!!!!!˚∆˚!!!!!!! ☀‿☀♫ ˙❤‿❤˙˙❤‿❤˙˙❤‿❤˙˙❤‿❤˙ ◠◡◠|〇◡〇|◠◡◠ ✌ { ◕ ‿ ◕ } ✌ ༗_ゝ༗ [◠し_◠ฺ ] ☛｀ิิ‿ゝ *<|=^D ▁▂▃▄ l|̲̅̅●̲̅̅|̲̅̅=̲̅̅|̅●̲̅̅| ▄▃▂▁ १|˚-˚|५ !!!!!!!˚∆˚!!!!!!! ☀‿☀♫ ˙❤‿❤˙˙❤‿ *<|=^D ▁▂▃▄ l|̲̅̅●̲̅̅|̲̅̅=̲̅̅|̅●̲̅̅| ▄▃▂▁ १|˚-˚|५ !!!!!!!˚∆˚!!!!!!! ☀‿☀♫ ˙❤‿❤˙˙❤‿❤˙˙❤‿❤˙˙❤‿❤˙ ◠◡◠|〇◡〇|◠◡◠ ✌ { ◕ ‿ ◕ } ✌ ༗_ゝ༗ [◠し_◠ฺ ] ☛｀ิิ‿ゝ´ิ ☛ ªʘ̀‿‿ʘ̀ª |'L'| •❐_❑• ✌▓▒░ ❤‿‿❤░▒▓✌ ✌⊂(✰‿✰)つ✌ ☜Ҩ.¬_¬.Ҩ☞ ❤˙˙❤‿❤˙˙❤‿❤˙ ◠◡◠|〇◡〇|◠◡◠ ✌ { ◕ ‿ ◕ } ✌ ༗_ゝ༗ [◠し_◠ฺ ] ☛｀ิิ‿ゝ´ิ ☛ ªʘ̀‿‿ʘ̀ª |'L'| •❐_❑• ✌▓▒░ ❤‿‿❤░▒▓✌ ✌⊂(✰‿✰)つ✌ ☜Ҩ.¬_¬.Ҩ☞ ´ิ ☛ ªʘ̀‿‿ʘ̀ª |'L'| •❐_❑• ✌▓▒░ ❤‿‿❤░▒▓✌ ✌⊂(✰‿✰)つ✌ ☜Ҩ.¬_¬.Ҩ☞ ‿❤˙˙❤‿❤˙ ◠◡◠|〇◡〇|◠◡◠ ✌ { ◕ ‿ ◕ } ✌ ༗_ゝ༗ [ *<|=^D ▁▂▃▄ l|̲̅̅●̲̅̅|̲̅̅=̲̅̅|̅●̲̅̅| ▄▃▂▁ १|˚-˚|५ !!!!!!!˚∆˚!!!!!!! ☀‿☀♫ ˙❤‿❤˙˙❤‿❤˙˙❤‿❤˙˙❤‿❤˙ ◠◡◠|〇◡〇|◠◡◠ ✌ { ◕ ‿ ◕ } ✌ ༗_ゝ༗ [◠し_◠ฺ ] ☛｀ิิ‿ゝ´ิ ☛ ªʘ̀‿‿ʘ̀ª |'L'| • *<|=^D ▁▂▃▄ l|̲̅̅●̲̅̅|̲̅̅=̲̅̅|̅●̲̅̅| ▄▃▂▁ १|˚-˚|५ !!!!!!!˚∆˚!!!!!!! ☀‿☀♫ ˙❤‿❤˙˙❤‿❤˙˙❤‿❤˙˙❤‿❤˙ ◠◡◠|〇◡〇|◠◡◠ ✌ { ◕ ‿ ◕ } ✌ ༗_ゝ༗ [◠し_◠ฺ *<|=^D ▁▂▃▄ l|̲̅̅●̲̅̅|̲̅̅=̲̅̅|̅●̲̅̅| ▄▃▂▁ १|˚-˚|५ !!!!!!!˚∆˚!!!!!!! ☀‿☀♫ ˙❤‿❤˙˙❤‿❤˙˙❤‿❤˙˙❤‿❤˙ ◠◡◠|〇◡〇|◠◡◠ ✌ { ◕ ‿ ◕ } ✌ ༗_ゝ༗ [◠し_◠ฺ ] ☛｀ิิ‿ゝ´ิ ☛ ªʘ̀‿‿ʘ̀ª |'L'| •❐_❑• ✌▓▒░ ❤‿‿❤░▒▓✌ ✌⊂(✰‿✰)つ✌ ☜Ҩ.¬_¬.Ҩ☞ ] ☛｀ิิ‿ゝ´ิ ☛ ªʘ̀‿‿ʘ̀ª |'L'| •❐_❑• ✌▓▒░ ❤‿‿❤░▒▓✌ *<|=^D ▁▂▃▄ l|̲̅̅●̲̅̅|̲̅̅=̲̅̅|̅●̲̅̅| ▄▃▂▁ १|˚-˚|५ !!!!!!!˚∆˚!!!!!!! ☀‿☀♫ ˙❤‿❤˙˙❤‿❤˙˙❤‿❤˙˙❤‿❤˙ ◠◡◠|〇◡〇|◠◡◠ ✌ { ◕ ‿ ◕ } ✌ ༗_ゝ༗ [◠し_◠ฺ ] ☛｀ิิ‿ゝ´ิ ☛ ªʘ̀‿‿ʘ̀ª |'L'| •❐_❑• ✌▓▒░ ❤‿‿❤░▒▓✌ ✌⊂(✰‿✰)つ✌ ☜Ҩ.¬_¬.Ҩ☞ ✌⊂(✰‿✰)つ✌ ☜Ҩ.¬_¬.Ҩ☞ ❐_❑• ✌▓▒░ ❤‿‿❤░▒▓✌ ✌⊂(✰‿✰)つ✌ ☜Ҩ.¬_¬.Ҩ☞ ◠

I disagree with your Mel Gibson statements.
• ursa_minor

Posts: 566
what planet are you from?

my brain hurts
• Posted by a hidden member.
What was part c? Hint might be useful.

edit: nvm, just saw that you already got d
• Posted by a hidden member.
Wow this thread seriously turns me on.

Next semester I will be covering these subjects in an advanced modern physics class--I've seen problems like this before but do not yet know how to solve them.

Sorry but I have to go jack off now! lol
• cromi

Posts: 489
i consider myself as an ok pure math student and judging by the question... i think ur... screwed lol.

• Ritournelle

Posts: 134
Ugh, I didn't finish the assignment, but I got a little bit further!
• Posted by a hidden member.