The DW Math Thread

Decus - Dreamweaver

Yhumy - Dreamweaver wrote: »

a+b=c
2a-a+2b-b=2c-c
2a+2b-2c=a+b-c
2(a+b-c)=a+b-c
2=1

We cannot divide by zero. I went over a very similar construction in an earlier post.

Yhumy - Dreamweaver wrote: »

Now then, whoever is decent at calculus, derive this:

(∀x)[(∃y)(Kby & Qxy) ⊃(∃z)(~Hz & Qxz)]

From

(∀y)(Kby ⊃~Hy)

Unfortunately, symbolic logic is one area I specifically avoided. Frankly, I was awful at it =/

If you put it into words, I'd be more than willing to give it a shot. b:surrender

MageFizban - Lost City

Decus - Dreamweaver wrote: »

Unfortunately, symbolic logic is one area I specifically avoided. Frankly, I was awful at it =/

If you put it into words, I'd be more than willing to give it a shot. b:surrender

http://en.wikipedia.org/wiki/List_of_mathematical_symbols

Have fun!

Arliana - Dreamweaver

1) (∀y)(Kby ⊃~Hy)
A/
2) ~(∃z)(~Hz & Qiz)
1 ⊃I
3) (∀z) ~(~Hz & Qiz)
2 QN
4) ~(~Hj & Qij)
3 E
5) ~~Hj v ~Qij
4DeM
6) ~Hj ⊃~Qij
5 Impl
7) Kbj ⊃~Hj
1∀ E
8) Kbj ⊃~Qij
6,7 HS
9) ~Kbj v ~Qij
8 Impl
10) ~(Kbj & Qij)
9 DeM
11) (∀y) ~(Kby & Qiy)
10∀ I
12) ~(∃y)(Kby & Qiy)
11 QN
13)~(∃z)(~Hz & Qiz) ⊃~(∃y)(Kby & Qiy)
2-12 ⊃I
14)(∃y)(Kby & Qiy) ⊃(∃z)(~Hz & Qiz)
13 Trans
15)(∀x)[(∃y)(Kby & Qxy) ⊃(∃z)(~Hz & Qxz)]
14∀ I


it doesnt let me do the spacing properly so im putting one line under other

Decus - Dreamweaver

MageFizban - Lost City wrote: »

http://en.wikipedia.org/wiki/List_of_mathematical_symbols

Have fun!

Ugh, I hated that course and always will. >:(

Arliana - Dreamweaver wrote: »

1) (∀y)(Kby ⊃~Hy)
A/
2) ~(∃z)(~Hz & Qiz)
1 ⊃I
3) (∀z) ~(~Hz & Qiz)
2 QN
4) ~(~Hj & Qij)
3 E
5) ~~Hj v ~Qij
4DeM
6) ~Hj ⊃~Qij
5 Impl
7) Kbj ⊃~Hj
1∀ E
8) Kbj ⊃~Qij
6,7 HS
9) ~Kbj v ~Qij
8 Impl
10) ~(Kbj & Qij)
9 DeM
11) (∀y) ~(Kby & Qiy)
10∀ I
12) ~(∃y)(Kby & Qiy)
11 QN
13)~(∃z)(~Hz & Qiz) ⊃~(∃y)(Kby & Qiy)
2-12 ⊃I
14)(∃y)(Kby & Qiy) ⊃(∃z)(~Hz & Qiz)
13 Trans
15)(∀x)[(∃y)(Kby & Qxy) ⊃(∃z)(~Hz & Qxz)]
14∀ I


it doesnt let me do the spacing properly so im putting one line under other

Thanks for saving me Arliana, and for being the third person to participate actively in this thread.

Teppeii - Dreamweaver

Nice to see this thread is booming

Needs some more humor though, don't you think? I do love me some mathematician jokes.

Say; a biologist, physicist, and mathematician observed a couple entering a house. A moment later, they watched as three people exited.

"Ah, it appears they multiplied." said the biologist.
"Ah, it appears I miscalculated." said the physicist.
"Hm, if my calculations are correct, then if one person enters the house, it shall be empty." said the mathematician.

b:cute

MageFizban - Lost City

Teppeii - Dreamweaver wrote: »

Nice to see this thread is booming

Needs some more humor though, don't you think? I do love me some mathematician jokes.

Say; a biologist, physicist, and mathematician observed a couple entering a house. A moment later, they watched as three people exited.

"Ah, it appears they multiplied." said the biologist.
"Ah, it appears I miscalculated." said the physicist.
"Hm, if my calculations are correct, then if one person enters the house, it shall be empty." said the mathematician.

b:cute

That joke always makes me smile. Anyway. . . :

"What is Pi?"
A mathematician: "Pi is the ratio of the circumference of a circle to its diameter."
A computer programmer: "Pi is 3.141592653589 in double precision."
A physicist: "Pi is 3.14159 plus or minus 0.000005."
An engineer: "Pi is about 22/7."
A nutritionist: "Pie is something that will make you fat!"

Decus - Dreamweaver

MageFizban - Lost City wrote: »

That joke always makes me smile. Anyway. . . :

"What is Pi?"
A mathematician: "Pi is the ratio of the circumference of a circle to its diameter."
A computer programmer: "Pi is 3.141592653589 in double precision."
A physicist: "Pi is 3.14159 plus or minus 0.000005."
An engineer: "Pi is about 22/7."
A nutritionist: "Pie is something that will make you fat!"

Q. What do you get when you cross an anopheles mosquito with a mountain climber?
A: Nothing: you can't cross a vector with a scaler.

Teppeii - Dreamweaver

A mathematician and an engineer are on desert island. They find two palm trees with one coconut each. The engineer climbs up one tree, gets the coconut and eats. The mathematician climbs up the other tree, gets the coconut, climbs down, climbs the other tree and puts it there.
The mathematician explains: "Now we've reduced it to a problem we know how to solve."

grimreaperhc

Is this why the mathematicians are starving, Teppna? b:chuckle

If you don't bother with math, you wont be hungry.

Teppeii - Dreamweaver

GrimReaperHC wrote: »

Is this why the mathematicians are starving, Teppna? b:chuckle

If you don't bother with math, you wont be hungry.

No, the reason mathematicians are starving is because a degree in mathematics has far less of a chance of feeding a family of four than, say, a single coconut.b:chuckle

Decus - Dreamweaver

Hey again ladies and gentlemen! New week; new problem(s)!

This week, as I will from now on do, I am giving TWO problems. One of them is more challenging than the other, purely to diversify the responses we get. You are only allowed to solve one. (No alt posting either, please! Give others a chance.)

Here's numero uno:

Approximate a solution to this equation on the interval (0,1) that is correct to nine decimal places. You may use whatever method you wish so long as you do not just use any kind of program or calculator to do all the work for you. ('Cause that's lame. When I mean "method," I mean mathematical method!) You must show your work...

And numero dos:

A certain six-digit number is split into two parts; the first three digits and the last three digits are added (as 3-digit numbers), the resulting sum is squared, and the answer is the original 6-digit number! What was the number?


(EDIT: #2 has potentially many numbers, just fyi.)


Avast ye mathies!

Teppeii - Dreamweaver

Decus - Dreamweaver wrote: »

A certain six-digit number is split into two parts; the first three digits and the last three digits are added (as 3-digit numbers), the resulting sum is squared, and the answer is the original 6-digit number! What was the number?

I got 494,209.

494 + 209 = 703
703^2 = 494,209

I'd do the first one, but I'm currently analyzing Dante's Inferno in original middle-English translation for my literature class. I'll just do it later and not share the answer I suppose.b:sad

MageFizban - Lost City

PWI physics problem:

http://i38.tinypic.com/2dk0j9g.jpg

Teppeii - Dreamweaver

Decus - Dreamweaver wrote: »

Approximate a solution to this equation on the interval (0,1) that is correct to nine decimal places. You may use whatever method you wish so long as you do not just use any kind of program or calculator to do all the work for you. ('Cause that's lame. When I mean "method," I mean mathematical method!) You must show your work...

By the way; Decus, forgive me if i'm wrong, but isn't y = x^3 a homeomorphism of the real line? And in turn homeomorphic to the open interval (0,1)?

I may be incredibly off base. I'm probably thinking in a completely different branch of mathematics here. But when I see that equation I immediately think topology.b:surrender

/Hysteria/ - Dreamweaver

ugh im all mathed out, just had an exam in math and logic today, pretty sure i aced it though!!!!!b:victory

Decus - Dreamweaver

Teppeii - Dreamweaver wrote: »

By the way; Decus, forgive me if i'm wrong, but isn't y = x^3 a homeomorphism of the real line? And in turn homeomorphic to the open interval (0,1)?

I may be incredibly off base. I'm probably thinking in a completely different branch of mathematics here. But when I see that equation I immediately think topology.b:surrender

Very true, kōhai. To be fair, any strictly one-to-one, continuous function (with a continuous inverse!) is a homeomorphism of the real line. So the function I gave is no different from, say y= 3x. In topological terms, we'd call y=x^3 bicontinuous, but I intend to avoid jargon in this thread as much as possible.

Also, the inverse of the given function in the problem is impossible (as far as I know) to write out.

That being said, it doesn't mean a solution doesn't exist. b:quiet

/Hysteria/ - Dreamweaver wrote: »

ugh im all mathed out, just had an exam in math and logic today, pretty sure i aced it though!!!!!b:victory

Way to go! Keep it up!

Luckycat - Dreamweaver

Approximate a solution to this equation on the interval (0,1) that is correct to nine decimal places. You may use whatever method you wish so long as you do not just use any kind of program or calculator to do all the work for you. ('Cause that's lame. When I mean "method," I mean mathematical method!) You must show your work...

~

Not sure if this is right but I'll give it a shot

f(x) = cos(x) - x^3 = 0


Using Newton's method to approximate root to 9 decimal places

Xn+1 = Xn - f(Xn)/f'(Xn)

for the interval [0,1]
f(0) = cos(0) - 0 = 1 > 0
f(1) = cos(1) - 1^3 = -0.4597 <0

Since root lies somewhere between 1 and -0.4597, pick estimation of 0.5 for x0

X1 = X0 - f(X0)/f'(X0)

f(x) = cos(x) - x^3
f'(x) = -sin(x) - 3x^2

X1 = 0.5 - 0.75258/-1.229425
= 1.11214

and so on...

so the roots are approx.

X0 = 0.5
X1 = 1.11214
X2 = 0.909672693
X3 = 0.867263818
X4 = 0.865477135
X5 = 0.865474033
...

the later approx. till X9 are the same so I'll use 0.865474033

ya and I found a sketch of the function to see if the root is somewhat accurate

http://i52.tinypic.com/2mmaagw.png

/Hysteria/ - Dreamweaver

Decus - Dreamweaver wrote: »

Very true, kōhai. To be fair, any strictly one-to-one, continuous function (with a continuous inverse!) is a homeomorphism of the real line. So the function I gave is no different from, say y= 3x. In topological terms, we'd call y=x^3 bicontinuous, but I intend to avoid jargon in this thread as much as possible.

Also, the inverse of the given function in the problem is impossible (as far as I know) to write out.

That being said, it doesn't mean a solution doesn't exist. b:quiet




Way to go! Keep it up!

ty ty xD, im actually pretty happy about it cuz im horribad at math <.<

Decus - Dreamweaver

Luckycat - Dreamweaver wrote: »

~

Not sure if this is right but I'll give it a shot

f(x) = cos(x) - x^3 = 0


Using Newton's method to approximate root to 9 decimal places

Xn+1 = Xn - f(Xn)/f'(Xn)

for the interval [0,1]
f(0) = cos(0) - 0 = 1 > 0
f(1) = cos(1) - 1^3 = -0.4597 <0

Since root lies somewhere between 1 and -0.4597, pick estimation of 0.5 for x0

X1 = X0 - f(X0)/f'(X0)

f(x) = cos(x) - x^3
f'(x) = -sin(x) - 3x^2

X1 = 0.5 - 0.75258/-1.229425
= 1.11214

and so on...

so the roots are approx.

X0 = 0.5
X1 = 1.11214
X2 = 0.909672693
X3 = 0.867263818
X4 = 0.865477135
X5 = 0.865474033
...

the later approx. till X9 are the same so I'll use 0.865474033

ya and I found a sketch of the function to see if the root is somewhat accurate

http://i52.tinypic.com/2mmaagw.png

Way to go Luckycat!

Glad to see people still use Newton's method! b:victory

Teppeii - Dreamweaver

Luckycat - Dreamweaver wrote: »

~

Not sure if this is right but I'll give it a shot

f(x) = cos(x) - x^3 = 0


Using Newton's method to approximate root to 9 decimal places

Xn+1 = Xn - f(Xn)/f'(Xn)

for the interval [0,1]
f(0) = cos(0) - 0 = 1 > 0
f(1) = cos(1) - 1^3 = -0.4597 <0

Since root lies somewhere between 1 and -0.4597, pick estimation of 0.5 for x0

X1 = X0 - f(X0)/f'(X0)

f(x) = cos(x) - x^3
f'(x) = -sin(x) - 3x^2

X1 = 0.5 - 0.75258/-1.229425
= 1.11214

and so on...

so the roots are approx.

X0 = 0.5
X1 = 1.11214
X2 = 0.909672693
X3 = 0.867263818
X4 = 0.865477135
X5 = 0.865474033
...

the later approx. till X9 are the same so I'll use 0.865474033

ya and I found a sketch of the function to see if the root is somewhat accurate

http://i52.tinypic.com/2mmaagw.png

Yeah...uh...that's totally what I got too....

I just, uh, put my notes and work in this here Klein bottle, and then I couldn't find them later.b:cry

Luckycat - Dreamweaver

Decus - Dreamweaver wrote: »

Glad to see people still use Newton's method! b:victory

glad to know I learnt something in ap calc b:chuckle

MageFizban - Lost City

Teppeii - Dreamweaver wrote: »

Yeah...uh...that's totally what I got too....

I just, uh, put my notes and work in this here Klein bottle, and then I couldn't find them later.b:cry

If you happen to find my 4d hypercube in there, pls tell me.

Decus - Dreamweaver

I'm putting them up early because I probably won't put them up till Wednesday otherwise:

New week (not really, but go with it!); new problems!

I'll even throw in a fun algebra problem for the younger readers! So you get the normal two plus a bonus. Cookies to whoever solves the challenging one this week, it's frustratingly annoying

Eins:

Solve this indefinite integral. No online integrators, calculators, or google-ing! Do your own work! :<
It's not easy, but it isn't impossible; and far more rewarding if you figure out a creative way to do it.

Zwei:

Prove there are no rational numbers x, y such that 2x^2 - 3y^2 = 1
but that there are infinitely many rational x, y such that 2x^2 - 3y^2 = -1
As always, show your work

Drei:

Find all positive real numbers n such that this is an integer. No google-ing necessary, it's pretty easy to do. Just try it!

Enjoy mathies, and good luck!

Teppeii - Dreamweaver

Decus - Dreamweaver wrote: »

Solve this indefinite integral. No online integrators, calculators, or google-ing! Do your own work! :<
It's not easy, but it isn't impossible; and far more rewarding if you figure out a creative way to do it.

I got maybe halfway through this. And I feel like a champ for getting that far.

Seriously. **** this integral.b:surrender

Decus - Dreamweaver

Teppeii - Dreamweaver wrote: »

I got maybe halfway through this. And I feel like a champ for getting that far.

Seriously. **** this integral.b:surrender

Try another then, I said you could only post one solution, but that doesn't mean you can't try the others

grimreaperhc

Ewww math ... b:avoid b:cute

Tearle - Dreamweaver

GrimReaperHC wrote: »

Ewww math ... b:avoid b:cute

+1 :<

Dsholder - Dreamweaver

Calculator to Calculate:

• Effective Health
• PvP Damage Done to Opponent
• Damage per Second Delivered PvP

I'm trying to figure out the chances are of my Barbarian surviving against certain classes and I'm stuck on the Effective Health formula provided by PWpedia; it says:

Effective Health = health / (1 - defense / (40 * attacker level + defense))
I'm confused here, I don't understand who's defense they are implying I use and I also don't know if I should turn the defense level into a percentage or keep as whole number.

I'm trying to figure out Damage dealt in PvP also, but the formula wording posted confuses me a bit:

damage dealt = skill damage dealt * PvP damage delivered * air to ground delivered * level delivered * bless delivered


Question: What number do skills use as the Base Damage? When using physical attacks do I round my high-end with my low-end to calculate a physical attack average as well?


Another set of Formulas that confuse me, based off wording. I don't understand weather I use whole numbers for the attack level and defense level. Also for physical defense, I'm guessing I use mine there, as a percent or as a whole number?:

Defense and resistance work by lowering damage according to the following formula.
physical reduction % = physical defense / (40 * attacker level + physical defense)
magical reduction % = magic resistance / (40 * attacker level + magical resistance)
damage delivered = damage dealt * ( 1 - reduction % )


If people could place their character builds with a PWI Calculator to let me practice testing the math behind these formulas that'd be appreciated as well. I'm interested in Cheze's sin, Fizzy's Psychic, and also Interested in Azzazin's sin for the most part, but I'd like others to participate as well XD

Teppeii - Dreamweaver

Decus - Dreamweaver wrote: »

Try another then, I said you could only post one solution, but that doesn't mean you can't try the others

But I already got the other two and checked my work for good measure. I decided not to post any solutions on the chance that I eventually get this one. I keep coming back to it. I really, really wanna figure it v.v

Decus - Dreamweaver

Dsholder - Dreamweaver wrote: »

If people could place their character builds with a PWI Calculator to let me practice testing the math behind these formulas that'd be appreciated as well. I'm interested in Cheze's sin, Fizzy's Psychic, and also Interested in Azzazin's sin for the most part, but I'd like others to participate as well XD

You are welcomed to debate formulae, just please keep this thread about math and not posting builds to test them. Let them send you those in PMs or something else.