## Categories

The bulk of my articles will probably continue to be on the subjects of ** Mathematics** and

*and are marked with those categories.*

**Subversion**I have tried to keep to purely technical matters. Occasionally I might express an opinion or a personal preference; I try to mark such material with the category ** Subjective**. When I write about software or documents that I think are useful, these are instead marked with

*.*

**References**Much of what I write is a clarification or re-organisation of well-known material. When I have written about something new, however trivial or otherwise, I have used the ** Research** category; it is unlikely that this material is ground-breaking or previously unknown, but it is original

*to me*.

When an post is intended to be a memory aid, or a method to help check a half-remembered fact or formula, I use the * Mnemonics* category.

The * Example* category is used for posts containing only a worked example, perhaps with a link to another post.

When an article contains a query regarding something about which I have not been able to find out, or a problem that I have only been able partially to solve, then it is marked with the * Question / Unsolved* category.

Many of my categories have finer subcategories. (I may not break Mathematics into further subcategories, as much of what I write about is algebraic, combinatorial or other formal manipulation.)

Some of my categories are rather broad. For example, I just lump *Astronomy* in with * Cosmology*.

Wednesday, 8 May 2013 at 22:19 |

Hi- have a question that might be right up your alley- I’m interested in summed pairs of triangular numbers where you can define them as pairs of every Nth triangular. Obviously every 1st will be squares, but what about every 2nd, 3rd and so on. I’ve found these in mathematical work on atomic nuclei, in relation to so-called ‘magic’ numbers. Thanks. Jess Tauber

Thursday, 9 May 2013 at 23:55 |

see https://rhubbarb.wordpress.com/2009/04/23/hypertetrahedral-polytopic-roots/

Write T(n) = n(n+1)/2 for the n^th triangular number.

Then T(n) + T(n-1) = n(n+1)/2 + n(n-1)/2 = n^2.

Is this what you mean by “2nd”?:

T(n) + T(n-2) = n(n+1)/2 + (n-1)(n-2)/2 = (1/2) [n^2 + n + n^2 – 3n + 2] = n^2 – (n-1)

which might be pictured as an n × n square with an off-diagonal missing. I can’t see a simpler geometric interpretation for such numbers.