Would you have allowed this?

[Felnar]

magic ruins a DM's best laid plans...

I wouldve handled the situation differenty.
The Intellegence stat is not how smart your character is.

Intellegence determines how well your character learns and reasons.

Intellegent characters are "smarter" because they get more skill points (which could go into knowledge skills). If your character didnt train in mathematics, he doesnt know it (maybe you could argue that your intellegent character could reason it though ). Also, remember that a raise in Intellegence is not retroactive.
It shouldve required some sort of knowledge check. Does your DM let you make untrained knowledge checks normally? ("what your character knows" isnt handled all that well in the core rules. For example, you have to buy Knowledge(local). My group house ruled getting some free knowledge type skills at character creation.)
The Souljourner brings up a good point too, how did you measure the angles? I would say its fairly easy with improvised tools tho (using a weighted string).

I'd have you make a check for each angle measured (fail and your measurement is off), then if your character did know trigonometry i'd do a Knowledge(math) check DC 15 (basic question) to calculate where you think the Big Bad is, then let you attempt the DDoor.

Reading the Locate Creature spell, it seems like it was only designed for 2-D top-down use, because it's blocked by "running water". To me this feels similar to the vampire weakness "unable to cross running water".

Now that i've shat all over everything... I would like to applaud your clever thinking (even if it was a tad meta-game) . After you beat the Big Bad, did you remember to proceed backward through his lair and ambush all his guardians from behind?
- Felnar

Funny, the Geometer PrC (CArcane) doesnt even require Knowledge(mathematics).

 

[Jeff Wilder]

Funny, the Geometer PrC (CArcane) doesnt even require Knowledge(mathematics).

That's because there's no such skill.

My necrotheurge (the character in question) has at least 6 ranks in every RAW Knowledge skill except (nature) and (dungeoneering). If he can build a bridge (architecture and engineering), he can measure angles and knows trigonometry.

(I disagree that it was metagaming, BTW. I have a very high IQ, and a very good education, and my PC is both smarter and better educated than I am.)

Oh, and for those who were wondering, the 250 foot drop was a shaft, straight down. That's why I figgered it was at least possible to do the calculations on the fly.

 

[Jeff Wilder]

The Intellegence stat is not how smart your character is [but rather how well he learns and reasons].

Just out of curiosity, just how do you define "smartness" if not by how well someone "learns and reasons"?

 

[Felnar]

That's because there's no such skill.

My necrotheurge (the character in question) has at least 6 ranks in every RAW Knowledge skill except (nature) and (dungeoneering). If he can build a bridge (architecture and engineering), he can measure angles and knows trigonometry.

(I disagree that it was metagaming, BTW. I have a very high IQ, and a very good education, and my PC is both smarter and better educated than I am.)

Oh, and for those who were wondering, the 250 foot drop was a shaft, straight down. That's why I figgered it was at least possible to do the calculations on the fly.

Knowledge(mathematics) is in Sword and Fist.
The list in the PHB is not an exhaustive list. Every knowledge skill description says you can create more areas of knowledge with DM approval.
Assuming only Core-Listed skills, K(architecture and engineering) was the only one I would say could cover Trig. I checked Survival to see it it had anything in it about orienteering, but it doesnt. Still, any way you look at it, it's a knowledge check, not a Intellegence check. And you do have knowledge skills, so you're good to go. The check DC25 was too high, i'd go DC 15 (basic question) in whatever knowledge skill you thought covered trig.
And i said "even if it was a tad meta-game", because i didnt know if it was or not. You only described your character as having 22 int.

- Felnar

 

[Felnar]

Just out of curiosity, just how do you define "smartness" if not by how well someone "learns and reasons"?

maybe smart isnt the right word.
but Intellegence is not what you know, its how well (fast/accurate) you learn.
High Intellegence gives bonus skill points because you pick-up and understand things better than the average individual.

- Felnar

 

[helium3]

I'm not really a simulationist DM, but I insist that if my players are going to use the "my character is smart enough to know that" card, they should have spent some role-playing time earlier in the game in fact showing that their character knows what the player claims it knows. IE, the character studies with some sage or engineer for a month, learning astronomical techniques for determing when the next lunar eclipse will be or how to build a tunnel through a mountain by starting at both ends and meeting in the middle.

If they had knowledge (mathematics) I would certainly allow allow it.

I wouldn't let players suddenly discover that their characters knew trig, nor would I allow a character to sit down and "figure it out" simply because they had a high intelligence score. It took a large number of highly intelligent people several thousand years to get to trig, and even then it wasn't really as sophisticated as our modern understanding of it.

 

[Patryn of Elvenshae]

I'm not really a simulationist DM, but I insist that if my players are going to use the "my character is smart enough to know that" card, they should have spent some role-playing time earlier in the game in fact showing that their character knows what the player claims it knows.

Because all character background and downtime activities must be explicitly told to the DM months in advance of them possibly being used? Nah, I don't think so. That seems overly ... restrictive ... to me.

IE, the character studies with some sage or engineer for a month, learning astronomical techniques for determing when the next lunar eclipse will be

Given that the character in question is an engineer and a wizard, I'd say he's covered.

 

[Jeff Wilder]

maybe smart isnt the right word.
but Intellegence is not what you know, its how well (fast/accurate) you learn.

And -- you quoted it yourself -- how well you reason. Mathematics is nothing if not starting with propositions and reasoning to conclusions, right?

Personally, BTW, I think Knowledge (mathematics) is way too limited a skill, which is why it didn't make it into 3.5. The Knowledge skills are all very broad. (You simply cannot be an engineer without a knowledge of higher mathematics, you know?)

 

[helium3]

Because all character background and downtime activities must be explicitly told to the DM months in advance of them possibly being used? Nah, I don't think so. That seems overly ... restrictive ... to me.

Overly restrictive or not, that's how I run the game. Deciding that your character has an interest in mathematics is not exactly a minor detail, especially in a medieval setting. Some people might think it is, but my opinion on that matter folds in with my complaints regarding the "I'm playing a game that takes place in a medieval period but I'm going to pull modern concepts out of my arse whenever necessary" style of game play. It's an incredibly pernicious and difficult to handle form of meta-gaming.

Given that the character in question is an engineer and a wizard, I'd say he's covered.

I agree. I would probably allow it with a skill check, which is apparently what happened in this case.

 

[Jeff Wilder]

I agree. I would probably allow it with a skill check, which is apparently what happened in this case.

If I'd thought of it, that's what I would have suggested. Instead, we went with an Intelligence check.