User:Astrachan

Plustorial is like factorial, but applies to sums rather than to products. The precise derivation of the term has been verified as due to Tom Rice, a teacher at East Tipp Middle School in North Lafayette Indiana. In email correspondence verifying that he did coin the term he writes:

One of the conditions of use, however, was to realize that no one outside of our Indiana cornfield would know what in the world it meant.

Reader's Note: although I cannot prove it, I've been aware of (and called it such) "plustorial" since I was in junior high school (1972/1973/1974). We used a '+' instead of the dot in the exclamation mark to denote such. IIRC, it was Mrs Ross at Jordan Junior High School in Palo Alto.

It is much easier to say "five plustorial" than to say (equivalently) "the 5th triangle number (or triangular number)".

Five plustorial is $$1+2+3+4+5 = 15$$ and in general N-plustorial is the sum of the numbers from 1 to N.


 * $$1 + 2 + 3 + \cdots + N $$

This is Mrs. Ross. I never told this guy that. He's wierd

The Exclamation_mark is commonly used for factorial, e.g., five factorial is written as follows:


 * $$5! = 1 \times 2 \times 3 \times 4 \times 5$$

There is no recognized symbol for plustorial. In popularizing the term we suggest using two plus signs aligned vertically. The double_dagger &Dagger; math symbol may serve for this purpose:


 * $$5\ddagger = 1 + 2 + 3 + 4 + 5 = 15$$

In one likely apocryphal story Carl Gauss is said to have figured out the formula for 100&Dagger; noting that there at 50 pairs of numbers summing to 101, e.g.,


 * $$\underbrace{(1+100) + (2 + 99) + \cdots + (49 + 52) + (50 + 51)}_{\mbox{50 occurrences}} = 5050

$$

The story appears to have been discredited, but in any case plustorial didn't emerge as a conventional term in the early 1780's when Gauss would have figured out the formula if the story was verifiable.

A simple proof by induction shows that N&Dagger; is given by the formula below which is a generalization of the formula "discovered" by Gauss.



N\ddagger = \sum_{i=1}^N i = 1 + 2 + \cdots + N = \frac{N(N+1)}{2} $$

The word frindle is an underused synonym for pen (as well as a popular children's book) because of constant usage in a fictional story. By capitalizing on popular usage, we hope plustorial will become a recognized term in a similar way.