And difficult.]]>

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

]]>http://www.wfu.edu/~ylwong/chem/nmr/h1/splitting.html]]>

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?????]]>

Pascal's Δ]]>

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!

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