Curse

Quizzical · May 17, 2007, 06:28 AM // 06:28

I was reading some Sylvester for my research the other day when I came across this table:

Code:

       Triangle of Obliteration.
1 1 1  1   1      1           1 ......
  2 3  4   5      6           7 ......
    6 15  29     49          76 ......
      36 210    804        2449 ......
         876  24570      401134 ......
             408696   246382080 ......
                    83762796636 ......

Note the caption there: "Triangle of Obliteration". Upon reading that, it occurred to me that this might be the best name in the whole history of mathematics. And the name was given not by some punk grad student, but by the great mathematician James Joseph Sylvester.

And then it occurred to me that this deserved to be an epic something or other in a video game. A quick check of Google shows that this is not already the case.

It's not like the artifacts already in Guild Wars are particularly intimidating. Stormcaller is great if your enemies happen to dissolve in water, unlike every single mob in the game. The Urn of Saint Viktor? Careful, or someone will plant a flower in it. And what's the Scepter of Orr supposed to do? Fix misspelled logic gates?

The Triangle of Obliteration, on the other hand, has exactly the sort of intimidating name that you want on a powerful weapon. In fact, I'll bet that if Shiro and Abaddon knew that you were coming after them with a Triangle of Obliteration, they'd be so scared that they'd surrender without a fight.

Could there be a more fitting tribute to Sylvester than to put his Triangle of Obliteration into an online game that didn't exist until more than a century after his death? Please, ArenaNet, make it so!

References:

J. Sylvester, On the so-called Tschirnhausen transformation, Crelle's Journal für die reine und angewandte Mathematik, 1887.

bilateralrope · May 17, 2007, 06:55 AM // 06:55

Ok, what exactly is the pattern in that triangle ?

JeniM · May 17, 2007, 07:24 AM // 07:24

I can't see any pattern at all

Quizzical · May 17, 2007, 07:38 AM // 07:38

The recursion is hideous, but I just thought it was a cool name.

Quote:

Originally Posted by J. Sylvester

Continuing this process of reduction until the first index is reduced to zero a very easy calculation leads to the formula of obliteration
[p, q, r, s, ... theta] = p + [q1, r1, s1, ... theta1],
where
q1 = p(p+1)/2 + q,
r1 = p(p+1)(2p+1)/6 + pq + r,
s1 = p(p+1)(p+2)(3p+1)/24 + p(p+1)q/2 + pr + s,
.................................................. .................................................. ..
theta1 = p(p+1)...(p+i-1)(ip+1)/(1.2.3...(i+1)) + p(p+1)...(p+i-2)q/(1.2.3...(i-1)) + ... + theta.

See also http://www.research.att.com/~njas/sequences/A001660

bilateralrope · May 17, 2007, 08:59 AM // 08:59

So we have a bunch of numbers with no visible pattern, a quote that looks like its part of the algorithm used to generate something (but I'm not sure its to do with the op) and a link doesn't make much sense either except for referring to a textbook.

Kale Ironfist · May 17, 2007, 09:22 AM // 09:22

EVERYTHING but the name should be thrown out the window, since that's got nothing to do with what he's suggesting. What he IS suggesting is putting in a quest item named "Triangle of Obliteration" similar to the quest item "Rune of DOOM".

I think that's what you're trying to get across, right?

JeniM · May 17, 2007, 11:16 AM // 11:16

sure name a quest that but i don't get the actual stuff even after doing Alevel maths and computing

FelixCarter · May 17, 2007, 11:26 AM // 11:26

Quote:

Originally Posted by bilateralrope

So we have a bunch of numbers with no visible pattern, a quote that looks like its part of the algorithm used to generate something (but I'm not sure its to do with the op) and a link doesn't make much sense either except for referring to a textbook.

HURRAY! All signs point to a great idea! Print it, slap a trademark on it, and sell it for 100k+80lp. We'll make millions.

JeniM · May 17, 2007, 11:38 AM // 11:38

As the Norn sound like they kill anything a three sided fight would be easly done (three side --> triangle referance)

Dougal Kronik · May 17, 2007, 11:40 AM // 11:40

Quote:

Originally Posted by Quizzical

Triangle of Obliteration
It's not like the artifacts already in Guild Wars are particularly intimidating. Stormcaller is great if your enemies happen to dissolve in water, unlike every single mob in the game. The Urn of Saint Viktor? Careful, or someone will plant a flower in it. And what's the Scepter of Orr supposed to do? Fix misspelled logic gates?

The Triangle of Obliteration, on the other hand, has exactly the sort of intimidating name that you want on a powerful weapon. In fact, I'll bet that if Shiro and Abaddon knew that you were coming after them with a Triangle of Obliteration, they'd be so scared that they'd surrender without a fight.

Fixed.

/signed for this item to be added.

Amon Warrior · May 17, 2007, 03:17 PM // 15:17

Somehow the words Triangle and Obliteration don't add up...

Regardless of its origins, it's not really that catchy, is it? But I like the word OBLITERATION!

Sword of Obliteration anyone? Now that one for my warrior would be super!

SotiCoto · May 17, 2007, 04:26 PM // 16:26

...... Triangle of Obliteration failz versus Shriek function.

MithranArkanere · May 17, 2007, 04:41 PM // 16:41

I don't think monsters would fear somebody pointing a set square or something like that at them...

tenshi_strife · May 17, 2007, 05:48 PM // 17:48

Tenshi Strife:I'm weilding a Triangle of Obliteration and a Text book!

lol sure why not

Quizzical · May 18, 2007, 05:12 AM // 05:12

What I had in mind was perhaps a green off-hand item.

The reference in the original post was to a journal article, not a textbook. The link gave a bit of information about the numbers along the diagonal of the triangle, but was pretty sparce. Another article that I didn't give a reference to is a little clearer, but written in French.

Sylvester originally used the Triangle of Obliteration to answer a question of what could be done with a method of Tschirnhaus that Tschirnhaus had (mistakenly) believed could solve polynomials of all degrees. It also comes up in characterizing when the bounds of the Kruskal-Katona theorem can be attained by a clique complex of a graph, and has a related simplicial complex interpretation.

Though as applications go, I'd be happy with +12 energy (req 9 domination magic), half skill recharge domination (20% chance), +1 domination magic (20% chance).

Bankai · May 18, 2007, 07:55 AM // 07:55

I'd make it a trio of bosses. Warrior, Monk, Elementalist or something. Which obliterate everything in their path.

legion_rat · May 18, 2007, 11:58 AM // 11:58

octagon of flatulence

not nearly as scary but shiro wouldnt wanna hang out long around you with this either.

~the rat~

Sidheyuna Aetheris · May 18, 2007, 06:30 PM // 18:30

Um, did anyone else have a mental picture involving a triangle (musical instrument) with the destructive power of a ginormous hydrogen bomb?

One *ting* and THE WORLD ENDS!! Bwahahaaaa

PS..Sorry Quizzical, it's not that I'm not taking your idea seriously. It was just your comment about the "Urn of Saint Viktor" that started my brain along a similar path.

manitoba1073 · May 18, 2007, 08:31 PM // 20:31

its already ingame. its just called loot scaling

Guardian of the Light · May 18, 2007, 10:57 PM // 22:57

Hmm that pattern is hard to find (tried a few patterns and it didn't work all the way) but overall I like the idea.