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#1 2006-03-01 05:12:33

ryos
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Registered: 2005-08-04
Posts: 394

Pascal's triangle strikes again

So, I'm sitting (lying, actually) peacefully, studying H NMR spectroscopy for my Organic Chemistry class, when I come to the topic of splitting. Basically, NMR spectrometers apply a magnetic field to the substance under study, and different hydrogens emit peaks of RF radiations at slightly different frequencies based on the structure of the molecule; this lets us infer a lot of information about the a molecule's structure.

Anyway, hydrogens that are vicinal to each other split the peaks of their neighbors. The "mini-peaks" are not the same height as each other, but rather are governed by a ratio of heights. Here are the height ratios listed in a table of my book for multiplets from a doublet to a septet:

       1:1
      1:2:1
     1:3:3:1
    1:4:6:4:1
  1:5:10:10:5:1
1:6:15:20:15:6:1

Does that look familiar to anyone else? Score one for Pascal!


El que pega primero pega dos veces.

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#2 2006-03-01 05:17:03

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Re: Pascal's triangle strikes again

Wanna know something other?
Pascal's Δ

Last edited by krassi_holmz (2006-03-01 05:17:49)


IPBLE:  Increasing Performance By Lowering Expectations.

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#3 2006-03-01 08:47:42

MathsIsFun
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Registered: 2005-01-21
Posts: 7,534

Re: Pascal's triangle strikes again

Or my version: Pascal's Triangle


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#4 2006-03-01 13:43:44

John E. Franklin
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Registered: 2005-08-29
Posts: 3,561

Re: Pascal's triangle strikes again

On the web page krassi h. pointed out, their is a mistake in the diagram of pascal's triangle.  The 186 in the bottom row should be a 286 I think.


igloo myrtilles fourmis

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#5 2006-03-01 13:56:10

John E. Franklin
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Registered: 2005-08-29
Posts: 3,561

Re: Pascal's triangle strikes again

I really enjoyed MIF's pages on Pascal's triangle!  My favorite part was the picture of the marbles in a tetrahedron.  Wonderful implications, how the diagonal rows are possibly for each successive dimension that we cannot visualize in our 3-D world, at least that's what we can see with our eyes.   
Diagonal rows:
1.  all ones (0-D ?)
2. 1-D (counting numbers along a line)
3. 2-D triangle (like bowling pins)
4. 3-D triangle (like the marbles MIF has depicted)
5. 4-D triangle I am guessing, how could we prove this?????


igloo myrtilles fourmis

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#6 2006-03-01 13:59:46

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,561

Re: Pascal's triangle strikes again

What is vicinal hydrogens??  Is it in close proximity to each other??


igloo myrtilles fourmis

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#7 2006-03-01 14:21:31

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,561

Re: Pascal's triangle strikes again

I found this, but wish it explained more.
http://www.wfu.edu/~ylwong/chem/nmr/h1/splitting.html


igloo myrtilles fourmis

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#8 2006-03-01 14:56:17

John E. Franklin
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Registered: 2005-08-29
Posts: 3,561

Re: Pascal's triangle strikes again


igloo myrtilles fourmis

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#9 2006-03-01 16:42:04

ryos
Member
Registered: 2005-08-04
Posts: 394

Re: Pascal's triangle strikes again

"Vicinal" hydrogens are separated by three bonds. So, in this structure: H3--C--C--H3 (ethane), 3 hydrogens are vicinal to three others.

So yes, they're close together, but not so much in space as in bonds (though it usually means in space, too).


El que pega primero pega dos veces.

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#10 2006-03-01 17:40:30

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,561

Re: Pascal's triangle strikes again

Thanks for the info, ryos, and Boy, this chemistry reading is really fascinating. 
And difficult.


igloo myrtilles fourmis

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#11 2006-03-01 17:43:35

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Re: Pascal's triangle strikes again

Ya, It's difficult-not so easy as math!!!


IPBLE:  Increasing Performance By Lowering Expectations.

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