Talk:Prime spiral (Ulam spiral)

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Revision as of 15:05, 11 June 2010 by Iris (Talk | contribs)
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Abram, 6/9: I notice that the page has been revision since our meeting on 6/8, but I haven't yet had a chance to review these revisions. My comments dated 6/8 are from a discussion on 6/8, but were not posted on the discussion page until the evening of 6/9. Clearly, some of them have already been addressed.

Active Comments

Things that are great about this page

  • Great brief intro to the spiral. The context in which it was invented and the description of how we don't know formulas for prime numbers really help make the page seem relevant.
  • Good use of examples in the quadratic polynomials section
  • Sentence like, "It might seem strange that..." do a good job guiding the reader through the content
Abram, 6/9

Reframe the description of quadratic polynomials along diagonals

All entries along a diagonal can be described with quadratics that have a leading coefficient of 4, not just the prime entries. Rephrase this section to make that more clear. (Abram, 6/8)

--I rephrased the section so that any diagonals can be described through quadratics. pf. Maurer and I talked, and it turns out that there are some exceptions, so I'll have to fix that point. (IRis, 6/11)

Also, it would be good to include a proof of this fact, rather than simply an example. A proof that this is true along the main diagonals (that go through entry number 1) won't be too ugly. We haven't yet figured out if doing a proof along other diagonals is or is not nasty. (Abram, 6/8)

--I provided the proof with the small animation. (Iris, 6/11)

Elaborate on the Euler section

Does this section generalize in any way to work with numbers other than 41? Does the fact that there are 40 consecutive prime diagonal entries give a hint of some larger pattern, or is it just an isolated curiosity? In general, make the significance of this material (and whether or not it is even seen as significant) a little clearer. (Abram, 6/8)

Add A "Why It's Interesting" section

We have discussed that this spiral is not something mathematicians have studied seriously, but on the other that the patterns you describe are not just people's minds trying to find patterns, which indicates the spiral could be significant. Having a section about this could be interesting. (Abram, 6/8)

--I have added a "Why its interesting" section. I actually addressed the problem of people's mind trying to find patterns in the more mathematical section where I compare the Ulam spiral for prime numbers and random numbers. I'm not sure whether I should move this section (Iris, 6/11)

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