## 24 August 2005## 153If you add up the first 17 positive integers, you end up with 153. (This makes it a "triangular" number; you can arrange 153 widgets in an equilateral triangle, and each side will be 17 widgets long.) Just as straightforward is Carnival of the Vanities #153, hosted this week by Vik Rubenfeld's Woah! Chaz, is that some kind of "new math"? Triangle has 3 sides. Each side 17 widgets long. 3 x 17 = 153? Help! Posted by: Winston at 9:36 PM on 24 August 2005You're forgetting the interior of the triangle. Look at 10 bowling pins. Four on a side — 1-2-4-7, 1-3-6-10, 7-8-9-10 — but there's still 10 pins. And we never mentioned the 5-pin even once. (I once converted a 6-7-10 split, which used up rather a large percentage of my allotment of divine interventions.) You know, I've been watching you post links to CotV pretty much since #1, and keep waiting for you to come up with a blank on the numbers, but I'm thinking now that it just won't happen. My hat is off to you, sir. Posted by: Craig at 5:42 AM on 25 August 2005Well, originally I did riffs on the Carnival itself, or on the format used, or on the name of the blog hosting it, but eventually I got to the point where the numbers themselves became something to play with. Besides, in my younger days as a math geek, I once heard from a teacher that "there are no uninteresting integers." Now's my chance to see for myself. I once converted one too. Too bad it was only in practice and not recorded anywhere! I was actually in a league when I pulled mine off (late 1974); it seriously jeopardized my chances for the Least Improved trophy. Triangular number can be expressed thusly, where
In the case of the pins in bowling, Where
Therefore we get (17 x 18)/2, which according to my calculator works out to (306)/2, or 153. Q.E.D. Posted by: McGehee at 10:42 AM on 26 August 2005 |