How many of you can solve this math equation

[accuscoresucks]

Didn't we say no calculators?

[Ganchrow]

That is Elementary or Intermediate Algebra.

Actually, I believe the correct terminology would be "arithmetic".

For some more complex "arithmetic", calculate this to let's say 6 decimal places:

1 + 2.718282 ^{(√-1 × 3.141593 )}

This, in my opinion, represents perhaps one of the most interesting identities in all of mathematics.

[smitch124]

This is starting to remind me of Good Will Hunting

[Panic]

They lost me at 12(6)

[durito]

i see e and pi and an imaginary number and know i'm done for.

[Ganchrow]

It's just an interesting identity, that's all.

[SBR Lou]

It''s just an interesting identity, that's all ...

In other words, there was a stroke of genius inside my equation?

[smitch124]

Is there an i in the answer?

[Deuce]

Actually, I believe the correct terminology would be "arithmetic".

For some more complex "arithmetic", calculate this to let's say 6 decimal places:

1 + 2.718282 ^{(√-1 × 3.141593 )}

This, in my opinion, represents perhaps one of the most interesting identities in all of mathematics.

1+2.718282 (-3.141593)

3.718282 (-3.141593)

-11.681328

[Deuce]

Actually, I believe the correct terminology would be "arithmetic".

For some more complex "arithmetic", calculate this to let's say 6 decimal places:

1 + 2.718282 ^{(√-1 × 3.141593 )}

This, in my opinion, represents perhaps one of the most interesting identities in all of mathematics.

Why is it interesting? Isn't it perhaps more complex because of the scary decimals and square root?

I classified it as Intermediate or Elementary Algebra because it is an Algebraic equation that is solved uding arithmetic.

[smitch124]

the square root of -1 isn't negative 1 its i...

[Deuce]

the square root of -1 isn't negative 1 its i...

Ahh yes the old imaginary number. Empty set.

I solved accordingly even though it is not correct.

[Ganchrow]

1+2.718282 (-3.141593)

3.718282 (-3.141593)

-11.681328

To 6 decimal places your answer would be off in magnitude from the correct answer by a factor of infinity.

And of couse even if √-1 did equal -1 (which it most decidedly does not), your answer would still be off by quite a bit.

To 6 decimal places:

1 + 2.718282 ^ (-3.141593 ) ≈ 1.043214

[Ganchrow]

Is there an i in the answer?

To 6 decimal places?

That'd be strictly optional.

[Ganchrow]

The answer,. by the way, is that to 6 decimal places

1 + 2.718282 ^{(√-1 × 3.141593)} ≈ 0


e ≈ 2.718282
i = √-1
π ≈ 3.141593

So in other words,

1 + e^{(i × π)} = 0

This is known as Euler's identity and is considered a "beautiful" mathematical equation because it unites probably the 5 most fundamental mathematical constants (e, i, π, 1, and 0) into a single equality, using each of the three basic mathematical operations exactly once.

I don't know ... at least I think it's pretty neat.

[AgainstAllOdds]

I always thought the powers of i were pretty neat...(although probably never needed)

If i remember correctly...

i = √-1

i (squared) = -1
i (cubed) -i
i (to the 4th power) = 1
i (to the 5th power) = i

So if you take this basic list, you can easily find what i(to the 38th) would be or whatever number you may choose. Fun stuff but it gets old quick when you have to keep doing it 100 times in diffrent math homework.

[TodaysAction]

Perenthasis Exponents Multiplication Division Addition Subtraction

Please Excuse My Dear Aunt Sally

From left to right on each side of the operation sign. Then performing the operation.

[max_asdf]

lollll best thread ever

[HedgeHog]

Math problem for Ganch: Post the last digit in pi.

Hint: The first digit is 3.

[Ganchrow]

Math problem for Ganch: Post the last digit in pi.

Hint: The first digit is 3.

As I'm sure you're already aware there is no last digit to the irrational number pi in any number system with a rational base (such as, for example, our familiar base-10).

Although I suppose if you were looking for some tricky-type answer one might attempt to argue that the the last "digit" of the character string "pi" were "i".

[freeVICK]

you gotta be dumb as shit to get that wrong

[HedgeHog]

As I'm sure you're already aware there is no last digit to the irrational number pi in any number system with a rational base (such as, for example, our familiar base-10).Although I suppose if you were looking for some tricky-type answer one might attempt to argue that the the last "digit" of the character string "pi" were "i".

No tricks, and i is not a digit (0-9). How does one prove that pi is infinite?

[bettilimbroke999]

I've got the answer

12 times 6 is 72 5 times 4 is 20 times 4 is 80 72 plus 80=152

[Ganchrow]

No tricks, and i is not a digit (0-9).

One could argue that "i" could be considered a digit depending upon the numerical base which one were using. (0-9 only being the base-10 digits, for example.)

It's not an argument I'd personally make -- but I thought perhaps you were simply posing a trick question because as I'm sure you know that there is no last digit (0-9) to pi in base-10.

How does one prove that pi is infinite?

Pi is not infinite, but rather irrational. Wikipedia details a couple of proofs of this mathematical fact here.

[HedgeHog]

Ganch: If anything is finite, then it has an ending. Because you don't know that exact ending, we call it irrational?

You're saying Pi has an ending but you can't say what it is. Is this a God thing, we just have to believe it's there?

[HedgeHog]

Case in point: My wife is irrational but definitely finite. She may find her ending tonight if she doesn't let up!

[Data]

Math problem for Ganch: Post the last digit in pi.

Hint: The first digit is 3.

There are more then one correct answers. Give us the digit that is next to last.

[HedgeHog]

There are more then one correct answers. Give us the digit that is next to last.

Data:

I did half the work. Ok, I'll start you off with 3.14....; but you'll have to do the rest.

Seriously, why is Pi finite when no one knows its exact ending?

[SBR Lou]

Hedge, I'm quite frankly amazed the genius equation I wrote in page one is being ignored. I'd at least like some props from a man of your mental stature so I can sleep well tonight. In case you missed the math heavy equation which I somehow fired up after really honing in on all my education, feast your eyes (and Texas Instruments calc.) on this--

(12)6+5(4)4=

[HedgeHog]

Hedge, I'm quite frankly amazed the genius equation I wrote in page one is being ignored. I'd at least like some props from a man of your mental stature so I can sleep well tonight. In case you missed the math heavy equation which I somehow fired up after really honing in on all my education, feast your eyes (and Texas Instruments calc.) on this--

(12)6+5(4)4=

I thought you accepted 152 as the correct answer as many had it and Ganch didn't correct it.

[SBR Lou]

I thought you accepted 152 as the correct answer as many had it and Ganch didn't correct it.

Sounds like I may have stumped Ganch.

I'll make another one.

a(d^2y/(dx)^2 + b(dy/dx) + cy = f(x)

[HedgeHog]

Crazyl:

If I read the original equation right, I come up with 1352.

4 to the 4th power is 256 x5 is 1280 and add 72 (12x6) is 1352.

[Data]

Data:

I did half the work. Ok, I'll start you off with 3.14....; but you'll have to do the rest.

OK, 159.

Seriously, why is Pi finite when no one knows its exact ending?

Pi is finite because it is between two numbers that are known to be finite, 3 and 4, 1 and 100 are the examples of that. However, the decimal representation of that constant consists of infinite number of non-recurring digits.

[HedgeHog]

So pi is a finite number in an infinite range between 3 and 4?

PS I get it finally. 3 and 4 are finite numbers and the answer is somewhere in between w/o pinpoint accuracy.

[Ganchrow]

So pi is a finite number in an infinite range between 3 and 4?

PS I get it finally. 3 and 4 are finite numbers and the answer is somewhere in between w/o pinpoint accuracy.

No, it does have pinpoint accuracy. It just can't be expressed as a finite series of base-10 integer digits. The same is true for many rational numbers as well.

For example 1 7 can't be expressed as a finite series of base-10 integer digits. 1 7 = 0.142857142857 (the overline means that the numbers beneath repeat indefinitely). It still has pinpoint accuracy ... it just can't be expressed as a finite series of base-10 digits. (It could be expressed as finite series of base-7 digits, hwowver, 1 7 = 0.1 in base 7.)

One of the many things that's special aboiut irrational numbers (numbers such as π, e, or √2 to enumerate but three) is that they can't be expressed as a finite series of digits in any integer base (also implying that they can't be expressed as an infinitely repeating pattern of digits (such as in the case of 1 7 ).

Now this doesn't mean we can't calculate π to arbitrary precision.

One of of the most well known representations of π, for example is

[nbtable][tr][td]π = 2*[/td][td][/td][td] n! (2n+1)!! [/td][/tr][/nbtable]
(where Z!! is the double factorial of integer Z equaling X * (Z-2)!! for Z ≥ 2, and 1 for Z = 0 or Z = 1)

Hence:

π = 2 * ( 1 (1) + 1 (1*3) + (1*2) (1*3*5) + (1*2*3) (1*3*5*7) + (1*2*3*4) (1*3*5*7*9) + ... )

which after 47 terms converges to the same precision as Excel 2003 on my 32-bit Vista (3.14159265358979) machine.

There are other (more quickly converging) algorithms which can be used to calculate to π arbitrary precision, this just happens to be one of the simplest.

Remember ... the sum of an infinite series of positive numbers need not be infinite. One commonly cited example of this (frequently known as the "Achilles and the Tortoise" paradox -- although it's in no way really a paradox) is that the infinite series:

1 2 + 1 4 + 1 8 + 1 16 + 1 32 + 1 64 + ...

in fact isn't infinite in value at all but in fact totals to exactly 1.

This can be easily seen with the following proof:

Let X = 1 2 + 1 4 + 1 8 + 1 16 + 1 32 + 1 64 + ...

so

2*X = 2 2 + 2 4 + 2 8 + 2 16 + 2 32 + 2 64 + 2 128 + ...

2*X = 1 + 1 2 + 1 4 + 1 8 + 1 16 + 1 32 + 1 64 + ...

subtracting X = 1 2 + 1 4 + 1 8 + 1 16 + 1 32 + 1 64 + ... from both sides then yields:

X = 1


QED

A similar proof can be used to show that 0.99999 = 1.

So it's not that we don't know the last digit of π, it's that there is no last digit of π. This doesn't make the value of π any more infinite than the value of 1 7 or the infinite series 1 2 + 1 4 + 1 8 + 1 16 + 1 32 + 1 64 + ... above.

Anyway, my apologies for the diversion.

a(d^2y/(dx)^2 + b(dy/dx) + cy = f(x)

a * d²y/dx² + b * dy/dx + c * y = f(x)

You're looking for a general form solution to a 2^nd order inhomogeneous differential equation. None exists.

There are, nevertheless, established methods for determining solutions given specified values (of value ranges) for a, b, and c, as well as a definition for the function f(x). If you're genuinely interested in this (and already understand the concepts underpinning calculus in general and differential equations in particular) then you should first see this page (which describes the methodology for solving 2^nd order homogeneous differential equations, that is where f(x) = 0), and then see this page, which describes the more general solution where f(x) ≠ 0.

Have fun.