Warp wrote:
>   Geometry, trigonometry and in some cases even calculus has been quite
> useful in graphical-heavy and game programming.

But in a sense, that's because you're simulating physics. None of those 
apply to programming a board game, for example.

-- 
Darren New, San Diego CA, USA (PST)
   Serving Suggestion:
     "Don't serve this any more. It's awful."

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Mike Raiford <"m[raiford]!at"@gmail.com> wrote:
> http://www.maa.org/devlin/LockhartsLament.pdf

tl;tr all yet.

but this:



someday."

seems to describe very well a serialist composer working on the sheet alone...
:)

yes, perfect analogy to math education today.

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clipka <ano### [at] anonymousorg> wrote:
> Am 09.12.2010 21:29, schrieb Kevin Wampler:
>
> >> That reminds me vividly of something which I have noticed and realized
> >> all by myself: I have never seen *anywhere* the *logical* explanation of
> >> how you can easily calculate, for example, the sum of all the integers
> >> from 1 to 100. It's *always* just the raw and sterile formula, and that's
> >> it. No explanation, no intuitive nor logical way of deducing it. Just the
> >> formula and that's it.
> >
> > I can't say I've had the same experience. I've seen plenty of
> > explanations of that formula, probably more so than any equation other
> > than the Pythagorean theorem.
>
> Same here. Maybe I was lucky in having maths teachers who loved maths
> just as much as I do; maybe it's the difference in educative system;
> maybe it has changed over time.
>
> In my case, our teacher did...
>
> - show us how to deduce the formula for that sum;
>
> - give us historical background of how the basic idea behind the formula
> was discovered by later mathematician Carl Friedrich Gauss when he was a
> kid, to the surprise of the teacher who had thought he had found a way
> to keep his pupils busy; and
>
> - use it as an introductory example for mathematical induction, which
> they then trained us to apply to other problems (and by that I mean
> types of problems, not just the same problem with different parameters).
>
> So I think I did get a truly mathematical education. I might add that
> this was German Gymnasium in the 80's. I'm pretty sure pupils at
> Hauptschule weren't that lucky; maybe even today's Gymnasium pupils
> aren't either, but I hope things haven't changed that dramatically.

Precisely my same experience, the Gauss story and all.  Perhaps the education
system just needs more such motivated teachers.

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Darren New <dne### [at] sanrrcom> wrote:
> And while I took and understood a great deal of math, it wasn't until
> physics class that I suddenly said "Oh, *that* is what an integral is for!"

indeed application should come before ready-given formulas...

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Darren New <dne### [at] sanrrcom> wrote:
> Warp wrote:
> >   Geometry, trigonometry and in some cases even calculus has been quite
> > useful in graphical-heavy and game programming.
>
> But in a sense, that's because you're simulating physics. None of those
> apply to programming a board game, for example.

they do for your game interface, unless you go for 70's ASCII interface. :)

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nemesis wrote:
> Darren New <dne### [at] sanrrcom> wrote:
>> Warp wrote:
>>>   Geometry, trigonometry and in some cases even calculus has been quite
>>> useful in graphical-heavy and game programming.
>> But in a sense, that's because you're simulating physics. None of those
>> apply to programming a board game, for example.
> 
> they do for your game interface, unless you go for 70's ASCII interface. :)

I didn't use any of those for my puzzle game. Sure, the graphics card was 
doing that stuff, but that's only because it's doing 2D with a 3D engine. 
Mostly you don't really need that sort of thing outside of simulating 
(however approximately) physics, methinks.

-- 
Darren New, San Diego CA, USA (PST)
   Serving Suggestion:
     "Don't serve this any more. It's awful."

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Darren New <dne### [at] sanrrcom> wrote:
> Warp wrote:
> >   Geometry, trigonometry and in some cases even calculus has been quite
> > useful in graphical-heavy and game programming.

> But in a sense, that's because you're simulating physics.

  I'm not so sure I would call, for example, the problem "is this point
inside this polygon?" a problem of physics. It sounds mostly a problem
of pure mathematics.

> None of those 
> apply to programming a board game, for example.

  If you need to program an AI opponent for such a board game, it certainly
requires knowledge on several sub-branches of mathematics. Perhaps not eg.
trigonometry (unless the board game is more heavily based on the actual
geometry of the board), but certainly others.

-- 
                                                          - Warp

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On 09/12/2010 07:50 PM, Warp wrote:

>    That reminds me vividly of something which I have noticed and realized
> all by myself: I have never seen *anywhere* the *logical* explanation of
> how you can easily calculate, for example, the sum of all the integers
> from 1 to 100. It's *always* just the raw and sterile formula, and that's
> it. No explanation, no intuitive nor logical way of deducing it. Just the
> formula and that's it.
>
>    The raw formula is rather useless by itself when you don't understand
> where it's coming from.

I do recall seeing in my sister's maths book the infamous quadratic 
solution formula. The book then went on to explain how to derive it...

...by starting with the quadratic equation and applying a seemingly 
arbitrary sequence of exotic algebraic manipulations to it. Sure enough, 
the final result *is* the standard formula. But surely no person would 
have thought of plucking this exact random series of transformations out 
of thin air.

In other words, it demonstrates that the formula *works*, but offers no 
intuitive insight into *why* it works. I got /that/ a bit later that 
day, after I discovered something called "factorisation"...

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On 09/12/2010 09:37 PM, andrel wrote:

> mildly related http://www.cs.utexas.edu/users/EWD/ewd05xx/EWD538.PDF

You can't tile this room because there are more black squares than white 
squares, and every tile covers one black and one white square.

Genius!

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On 09/12/2010 09:35 PM, Darren New wrote:

> And while I took and understood a great deal of math, it wasn't until
> physics class that I suddenly said "Oh, *that* is what an integral is for!"

I read my dad's "elementary calculus" textbook when I was a teenager. 
The only thing I discovered was Pythagoras' theorem (which, 
astonishingly, I had never even heard of before). The rest of the book 
made absolutely no sense to me at all. It talked a lot, and it had some 
formulas that gradually got more and more complicated, but I had no idea 
what the hell it was trying to *do*.

Fast forward a few years to a quants ("quantitative methods") class some 
day at college. (I'm not exactly sure what this has to do with 
"computing", but anyway...) We were working on graphing the income, 
profit, etc. of a fictional company. Rather than invent some fictional 
data, DKJ invented some low-degree polynomial that was supposed to 
represent income, and another that represented costs, and we were 
sitting there computing this stuff with pencil and paper.

I don't know if you've ever tried it, but tabulating even a low-degree 
polynomial by hand is tedious, even with a calculator. You tabulate the 
income polynomial, tabulate the cost polynomial, subtract one column 
from the other, and that gives you monthly profit. You then compute a 
running total of that to determine how much money in total this company 
has made or lost.

I figured out that we only actually *need* the final column. Well, you 
can subtract one polynomial from the other and do some simplifications. 
That enables you to compute the profit with fewer operations. But now 
how the hell do you compute the running total? By observing the general 
shape of the graph I was plotting (with pencil and paper, mind you), I 
was able to fit a polynomial to it. And you know, it's the damnedest 
thing... the coefficients seemed to be somehow *related* to the original 
polynomial.

At this point DKJ peered over my shoulder, and pointed out that what I 
had just done was "integral calculus", and some guy called Laplace had 
invented it 200 years ago. He showed me the general formula for 
integrating a polynomial. I was kind of suspicious at the exact integral 
coefficients; of all the possible real numbers in existence, that seems 
like a rather large coincidence. None the less, I went home and managed 
to find my dad's old calculus book.

Now it actually made perfect sense. :-P

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