1 = 2

[ChrisK]

Assume that a = b
Then ab = a^2
Subtract b^2 ab - b^2 = a^2 - b^2
Factor b(a - b) = (a + b)(a - b)
Divide by a - b b = a + b
But a = b
Therefore b = 2b
OR 1 = 2

(I always lie!)

[spitfire23bc]

If a = b

=> (a - b) = 0

Therefore, you are dividing by 0, which gives infinity!

[quarry]

Does that mean the answer is a Black Hole???



But if six turned out to be nine,
I don't mind...

[ChrisK]

If a = b

=> (a - b) = 0

Therefore, you are dividing by 0, which gives infinity!

Very good'ski.

After all:

(I always lie!)

Prove e^(-i*pi) -1=0 (Euler)

re. "i", "j" if'n yer an electron guy.

[RandomHero]

Chris, you're gonna have to come with me. You're under arrest for posessing and misusing weapons of math deduction.

[ChrisK]

Yeth I am!
;D ;D ;D ;D ;D ;D ;D ;D ;D ;D

[spitfire23bc]

At New York's Kennedy airport today, an individual was arrested when he tried to board a flight while in possession of a ruler, a protractor, a setsquare, a slide rule, and a calculator.

At a morning press conference, US Attorney General John Ashcroft said he believes the man is a member of the notorious Al-gebra movement. He is being charged by the FBI with carrying weapons of maths instruction.

“Al-gebra is a fearsome cult,” Ashcroft said. “The cult, whose leader is believed to be a cosine of Osama Bin Laden, is split into several divisions and they are prepared to use a wide variety of means to achieve solutions. The members sometimes go off on tangents in search of absolute values. In addition, they use secret code names like ‘x’ and ’y’ and refer to themselves as "unknowns", but we are positive that they belong to a rather odd common denominator known as the ‘Axis of Even’, with coordinates in many countries.

“As the Greek philanderer Isosceles used to say, there are three sides to every triangle,” Ashcroft declared. When asked to comment on the arrest, President Bush said: “If God had wanted us to have better weapons of maths instruction, He would have given us more fingers and toes.

“I am gratified that our government has given us a sine that it is intent on protracting us from those who are willing to disintegrate us with calculus disregard,” the President said, adding: “Under the circumferences, and factoring in all the variables, we must stand united and draw the line, cos divided we fall.”

President Bush warned: “These weapons of maths instruction have the potential to decimal our society on a scalene never before seen, unless we become exponents of a Higher Power and rid the world of this entirely negative organisation.”

Attorney General Ashcroft concluded: “As our Great Leader would say, read my ellipse. Here is one principle he is uncertainty of: though they continue to multiply, we are circling in ever closer, and their days are numbered as the hypotenuse tightens around their necks.”

[UnklMickey]

Duuuuuuuuuuuuuude!

LSH...


actually it was our Great Leader's daddy who said, "read my ellipse".

but that takes nothing away from that laugh-a-minute post.

thanks.

+1


unk

[spitfire23bc]

I wish I could claim to be the author, but unfortunately that honour goes to an anonymous party.

Genious though! ;D

[UnklMickey]

spitfire23bc said:

I wish I could claim to be the author,...

of course you can!

we have a thread for just that sort of thing.

guitarnuts2.proboards45.com/index.cgi?board=coffee&action=display&thread=1147503801

[spitfire23bc]

LOL!!

;D

[wolf]

ChrisK
I'm surprised no one has responded to your challenge:

Prove e^(-i*pi) -1=0 (Euler)

Well I don't know about raising 'e' to the power of (negative i * pi) and whether that makes the value plus 1.
However, I am familiar with Euler's famous equation:

e^p*i plus 1 = 0

which I think I can prove.

Using DeMoivre's Formula:

e^i*n = cos(n) + i*sin(n)


Substituting the value of pi for n we have:


e^i*p = cos(p) + i*sin(p)


The cosine of p radians is -1 and the sine of p radians is zero. Multiplying zero by 'i', we still get zero and so the equation becomes:

e^p*i = -1 + 0

Or stated another way:


e^p*i +1 = 0


............ and it's just that easy. ;D

[lunaalta]

BEfore reading this thread I thought I had woken up.........

......now I know I'm still asleep, having a nightmare.

[ChrisK]

wolf,

Thanks for reading, thinking, and replying. I'm often guilty of doing only one.

I had stated a formula that combined elements of e^iPi and e^-iPi fully expecting no one to respond.


From "e: The Story of a Number" by Eli Maor.

Euler actually arrived at this equation by yada yada yada arriving at:

e^iX = 1 + iX + (iX)^2/2! - (iX)^3/3!.....
which due to the repetitive powers of i can be written as:

e^iX = 1 + iX + -X^2/2! - iX^3/3! + X^4/4! + ....

By committing what is now known to be a "sin" (separating and collecting real terms from imaginary ones which can cause an infinite series to even become divergent rather than convergent), he arrived at:

e^iX = (1 -X^2/2! + X^4/4! - +...) + i(X - X^3/3!+ X^5/5! - +...)

the two series were known to be the power series for cosX and sinX.

So Euler stated that

e^1X = cosX + sinX,

which at once linked the exponential function (although imaginary) to normal trigonometry. By replacing iX with -iX and using the identities

cos(-X) = cosX, and

sin(-X) = -sinX,

he arrived at e^-iX = cosX - isinX

which led to

cosX = (e^iX + e^-iX)/2, and

sinX = (e^iX - e^-iX)/2.


By replacing X with Pi, and knowing that cosPi = -1 and sinPi = 0, Euler obtained the formula

e^iPi = -1

By rewriting we obtain

e^iPi + 1 = 0

Which connects the five most important constants in math and the three operations of addition, multiplication, and exponentiation. They symbolize the four major branches of math; arithmetic, algebra, geometry, and analysis.


BTW,

Roger Cotes (1682 - 1716) stated

log (cosX + isinX) = iX.

DeMoivre (1667 - 1754) discovered that

(cosX + isinX)^N = cosNX + isinNX, which in light of Euler's formula becomes the identity

(e^iX)^N = e^iXN


It's now safe to wake up......................

[quarry]

Uh, why did the chicken cross the Möbius strip?

[ChrisK]

Because he could(n't).

I love uncle Moby's strip..

If one takes a Mobius strip and cuts it exactly down the center line, one gets a strip twice as long with 4 half-twists (the Mobius strip has one half-twist, one side, and one edge) and having TWO sides and edges (even number of half-twists).

If one takes the above resulting strip and cuts it exactly down the center line, one gets two strips of the same starting length with 4 half-twists and having TWO sides and edges (even number of half-twists) each. These are double looped with each other.


If one takes a Mobius strip and cuts it exactly 1/3rd of the way parallel to the edge, one gets a strip twice as long with 4 half-twists and having TWO sides and edges (even number of half-twists); AND a separate Mobius strip looped thru the former.

If one takes a Mobius strip and cuts it exactly 1/4th of the way parallel to the edge, one gets a strip twice as long with 4 half-twists and having TWO sides and edges (even number of half-twists); AND a separate Mobius strip looped thru the former.

If one takes the prior example's resulting Mobius strip and cuts it 1/3rd of the way parallel to the edge, one gets yet another strip twice as long with 4 half-twists and having TWO sides and edges (even number of half-twists); AND again a separate Mobius strip, all three being inter-looped.


If one takes a three half-twist strip (still having one side and one edge) and cuts it exactly down the center line, one gets a strip twice as long with 8 half-twists and having TWO sides and edges (even number of half-twists), inter-looped with itself.


While the resulting strip topology seems to get rapidly boring, the inter-looping may well be an interesting knot theory study (knot them there Boy Scout nots). ;D

[fobits]

Hey, this is fun...

e^ip + 1 = 0

e^ip = -1

sqroot( e^ip ) = sqroot( -1 )

So if a pickup is mounted sqroot( e^ip ) radians from the bridge, it will produce only imaginary sounds.

Cool.

[ChrisK]

Well, maybe ;D

If a pickup is mounted "whatever" radians from the bridge, the results will be somewhat indeterminate since a radian is an angular notation and the pickup (at least its center of rotation) will still be on the bridge.

Those poles forward toward the neck may pick up something, while those aft will just "track yer watch".


If yer talking aboot the angular rotation of the string frequency. I 'll see you in St. Louis and help you install the pickup there (in St. Louis, not in yer guitar). ;D

[quarry]

"Film is one of the three universal languages, the other two: mathematics and music.”
- Frank Capra, film director

[fobits]

If a pickup is mounted "whatever" radians from the bridge, the results will be somewhat indeterminate since a radian is an angular notation and the pickup (at least its center of rotation) will still be on the bridge.

The center may be on the bridge, but if it's rotated through an imaginary angle, the rest of it will be hard to see.

Jimi Hendrix had one of those. He pretended to play with his teeth, but actually the strings were plucked by leprechauns in the seventh dimension.

Oh, radians. I meant to say furlongs.

[ChrisK]

As in furlongs per forte-night?

[pollyshero]

WTF!!!

I take some time off and look what's going on? MATH! It's just wrong...

Sometimes you smart people really tick me off.

PH

[UnklMickey]

quarry said:

"Film is one of the three universal languages, the other two: mathematics and music.”
- Frank Capra, film director

i think this thread might be considered math pornography.

[wolf]

In answer to Quarry's riddle:

Why did the chicken cross the Möbius strip?

To get to the same side. ;D

*******************************************
By the way, is that avatar from a Captain Beyond album?

[quarry]

wolf said:

By the way, is that avatar from a Captain Beyond album?

Yes, it is. And, no, I'm not a raving CB fan; I do enjoy their music (especially from the album the art is from), but I simply liked the image as an avatar...

In an attempt to keep this post on topic:

In an insane asylum, three patients are up for release. The Doctor decides to give them an intelligence test. He turns to the first man and asks, "What is three times three?"

"274," he replies.

The Doctor asks the second man, "What is three times three?"

"Tuesday," replies the second man.

The Doctor turns to the third man, "Okay, your turn. What's three times three?"

"Nine," says the third man proudly.

"That's great!" says the doctor. "How did you arrive at that?"

"Simple," says the third man. "I subtracted 274 from Tuesday."

[UnklMickey]

quarry said:

...In an attempt to keep this post on topic:

In an insane asylum...

it's even more appropriate, taken out of context.

[ChrisK]

So a guy gets a flat tire next to a fence at an insane asylum.

While changing the tire, he inadvertently knocks the 5 lug nuts down a sewer.

While pondering his dilemma, an observing inmate inside the fence says" Take one lug nut off of each of the other three wheels and drive to a store and buy more lug nuts."

The guy says "Wow, since you're so smart, what are you doing in there?"

The inmate says " I may be crazy, but I'm not stupid!"


Evaluate iⁱ

[lunaalta]

Of course.........
I never did wake up............
Thank goodness for that!

[ChrisK]

"goodness" ani't gonna help ya,

You DID wake up!

And you're being simulated.

[UnklMickey]

pollyshero said:

....Sometimes you smart people really tick me off....

according to my ex, only part of me is smart.