Talk:Square pyramidal number/GA1

Latest comment: 2 years ago by Olivaw-Daneel in topic GA Review

GA Review

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The following discussion is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.


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Reviewer: Olivaw-Daneel (talk · contribs) 01:45, 18 December 2021 (UTC)Reply

Good Article review progress box
Criteria: 1a. prose ( ) 1b. MoS ( ) 2a. ref layout ( ) 2b. cites WP:RS ( ) 2c. no WP:OR ( ) 2d. no WP:CV ( )
3a. broadness ( ) 3b. focus ( ) 4. neutral ( ) 5. stable ( ) 6a. free or tagged images ( ) 6b. pics relevant ( )
Note: this represents where the article stands relative to the Good Article criteria. Criteria marked   are unassessed

Interested in reviewing this. I'll have comments up in a couple days. Olivaw-Daneel (talk) 01:45, 18 December 2021 (UTC)Reply

The article is well-illustrated, but I think it covers the material a bit too tersely – some further elucidation would greatly help. Specific suggestions below.

Lead

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  • Currently the first sentence requires the reader to know what a figurate number is – suggest postponing the mention of figurate numbers to a separate sentence that hints at their definition. (Perhaps something like "It can be generalized to a broader category of numbers that are known as figurate numbers...")

Formula

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  • There seem to be two competing definitions here – algebraic and geometric – and I'm not sure which of them is more primary. Since the lead starts out with the geometric version, suggest doing the same here. (It may also be logical to rename this section to Definition).
    • It really was intended as a formula solving the question "how many points are in a pyramid" rather than a definition "these numbers are the values of a cubic polynomial". I rewrote to suggest that ordering more strongly. —David Eppstein (talk) 07:26, 22 December 2021 (UTC)Reply
      • I like the new version. A few comments: the sphere interpretation is not mentioned in ref #1 (suggest adding ref #10 Beiler); numbers of points should be numbers of spheres; height probably refers to the number of layers but could be clearer.
  • The lead hints at a historical perspective – The study of these numbers goes back to Archimedes and Fibonacci – that one would expect to be covered here. (E.g. When and for what purpose this was studied.)
  • The mention of figurate numbers appears all of a sudden; as in the lead, it would be helpful to gloss them before use.
  • The more general statements about Erhart polynomials are uncited (ref #5 Beck only talks about polytopes with integer vertices)

Geometric enumeration

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Relations to other figurate numbers

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  • In the first sentence, it should be made more clear that the pyramid is made of cannonballs.
  • This fact was proven by G. N. Watson in 1918 – I'm not sure if Watson deserves sole credit. Ref #9 Anglin says that he filled gaps in earlier drafts by Moret-Blanc (1876) and Lucas (1877).
  • The sum of binomials equation is not cited (suggest adding ref #11 Caglayan)
    • Since Caglayan phrases this as a problem rather than a statement, I used two other references, Conway & Guy's Book of Numbers and a paper by Grassl. Grassl explicitly uses the binomial coefficient description of this formula rather than calling them tetrahedral numbers as the other sources do. —David Eppstein (talk) 22:43, 24 December 2021 (UTC)Reply
  • In ref #10 Beiler: pp. 194 → pp. 194–195
  • Last paragraph: a single tetrahedron of slightly more than twice the edge length – why is the length slightly more than twice? (The source says: "Four times the nth square pyramidal number is the (2n)th tetrahedral number".)
    • The edge length of   is  . The edge length of   is  , slightly more than twice. Edge length is off by one from the index in the sequence of these numbers. —David Eppstein (talk) 22:10, 24 December 2021 (UTC)Reply
      • Ah I see, so that's based on an "edge" as a line connecting the centers of the spheres – do sources define it this way? It seems at odds with the last figure which says   has side 24. Olivaw-Daneel (talk) 00:01, 25 December 2021 (UTC)Reply

Other properties

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  • Suggest expanding a little to avoid a single-sentence section. Some possibilities: the connection to Archimedes' approximation for π (22/7) mentioned in the ref; some background on the Leibniz formula.
    • I found a connection to approximation theory and added it. While searching for material for this expansion, I also found additional material on the history of these numbers (now split off into a separate history section) and on using them to count certain integer matrices (added to the end of the enumeration section). —David Eppstein (talk) 23:24, 24 December 2021 (UTC)Reply

Placing it   on hold; please ping when you're done. Thanks. Olivaw-Daneel (talk) 09:47, 24 December 2021 (UTC)Reply

@Olivaw-Daneel: All comments addressed; I think it's now ready for a second look. —David Eppstein (talk) 23:24, 24 December 2021 (UTC)Reply

Just one last comment above about edge length. The article looks great; I really like the history section. Olivaw-Daneel (talk) 00:01, 25 December 2021 (UTC)Reply
Ok, changed to "points along each edge" rather than edge length to avoid that ambiguity. —David Eppstein (talk) 00:11, 25 December 2021 (UTC)Reply
Great, congrats on the GA. Olivaw-Daneel (talk) 00:23, 25 December 2021 (UTC)Reply
The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.