CHRONOCROSSSSSSSS!!!!

[cosmicpanda]

This is SG. We like crazy stuff.

 

What is the area of a circle with radius i?

[eclipse0]

 

Since i is  √(-1), then I'd have to say that the circle does not exist.  However, since the area of a circle is πr² and {√(-1)}² = -1, then -1 * π = -π.

 

The answer is negative pi...

 

That can't be true, pi is always positive!

 

*implodes due to paradox*

[Dunbar]

*dies a little inside*

 

: p

 

Anyhoo!

 

WHAT IS THE MASS OF A SATELLITE MOVING IN A PERFECTLY CIRCULAR ORBIT 1600 km ABOVE EARTH, USING 2 days 34 minutes and 16 seconds TO COMPLETE A FULL LAP!?

 

I LIKE PHYSICS

[eclipse0]

That would be the moon?

[Dunbar]

Didn't consider that xd But the height would make sense

 

But the moon isn't a mass!

[eclipse0]

I didn't answer your question, I asked one of my own...

 

[cosmicpanda]

well, pointsies to 'clipse. And none to CCS. >:(

[ChronoCrosS]

Due to my lack of attendance in new threads since all I usually do is look at "New replies to you posts" I request a new question to be asked. Ask away and ye shall be answered. Can anyone tell me what is the Laplace Transform of sin(-5t)?

[Dunbar]

I didn't answer your question, I asked one of my own...

 

 

Ah, you're far too clever for me

 

[ChronoCrosS]

What? no answer for my question Demi, where is Eclipse?

[Dunbar]

I'm sorry, but I have no idea what a Laplace Transform is

 

I can derive or integrate it if you'd like : p

 

Oy, wikipedia tells me it's an integral transform!

 

Which would make the answer (1/5)cos(-5t) + C

 

I loves the maths

[ChronoCrosS]

Nope, anyone else. Good try though.

[cosmicpanda]

how about we up the stakes?

 

10 points to the person who can get CCS's question right. I'll rely on him to judge since I can't do it  :D

 

 

Oh, and CCS, a question just for you:

 

Look at this number:

 

1.0136432647705078125

 

Identify it and explain how it affects music. You may use google.

 

I don't think it's a hard question, but 10 points if you get it right as well  :D

[Dunbar]

Bah humbug, I thought it was an integral :(

 

NOW I DON'T KNOW WHAT TO BELIEVE

 

 

[ChronoCrosS]

I think that my question is fairly difficult, unless you have taken calculus in University.

 

For your question Pandy, I looked it up and found that this number is sometimes known as the Pythagorean comma, or ditonic comma, which is precisely equal to the ratio 531441/524288 or 23.46 (music) cents (where 1200 cents make up an octave on a logarithmic scale). Though I am no expert or even knowledgeable in music, I'll try to explain as best I can. This number arises from the concept of scales and of Pythagorean tuning. This method of musical tuning involves different note frequencies where each are based on the relationship 3/2 and powers of two and three. 

 

The exact definition of the Pythagorean comma is the difference (expressed as a ratio) between the Pythagorean apotome and lemma:

 

apotome/lemma = 3¹²/2¹⁹ = 531441/524288

 

So, all you folks (cept' Pandy  :D) may be wondering, what the $%&*@ is a apotome and lemma? To answer that question I'll tell you a some info about Pythagorean tuning.

 

The following ratios are in terms of hertz (frequency)

For example if I say 2/1 that means that one note beats twice for every single beat of the latter note. Note that lower frequency notes sound lower to our ears.

 

The basic intervals of Pythagorean tuning are the superparticular ratios: (i.e. numbers of the form (n+1)/n where n is any integer) 2/1, 3/2 and 4/3. The first number, 2/1 is an octave, the second is a perfect fifth and is the musical interval between a note and the note seven semitones (smallest musical interval that is commonly used) above it. The final ratio of 4/3 is a perfect fourth and consists of a note and the note five semitones above it.

 

The difference between the perfect fourth and the perfect fifth is the tone, or major second with a ratio of 9/8.

 

Now that that is over with, two tones make a ditone, one known as a major third (ratio of 81/64) and as minor third or semiditone (ratio 32/27). The difference between the minor third and the tone is the minor semitone (lemma) and the difference between the lemma and the tone is the major semitone (apotome). Although the apotome and lemma are equal on something like a piano (i.e. like A flat and G sharp), they are NOT equal in Pythagorean tuning. Ignoring this difference leads to the enharmonic change, which I will not get into. Final note, the Pythagorean interval is so small that we can't tell the difference between an apotome and a lemma.

 

There, I hope that is a good enough answer. I could go on about this for a lot longer but I thought it best to stop there.

 

For my question, try a google search of "table of laplace transforms". Compare the equation I gave to the one in the table. That is the best hint I can give.  ;D

[cosmicpanda]

Heh, nice effort. I'll give you the points.

 

I was hoping that you would mention that it was the difference between 12 fifths and 7 octaves, and also how piano tuners deal with it, but I can handle it.  :D

 

Just one note: if two notes an octave apart are perfectly tuned, you shouldn't hear any beating.

[Dunbar]

The amount of intelligence presented in these boards sometimes has the ability to completely take me by surprise xd

[ChronoCrosS]

Ya, that stuff is actually pretty cool, it's like the fusion of math and music. Or you could argue that music is simply creative math...  :D

 

Sorry I didn't say the answer you wanted, but I did my best. I thought is wasn't bad for being completely oblivious to the subject before you mentioned it.  ;D

 

Anyone got the answer to my Q yet?

[Dunbar]

I'm out : p

[ChronoCrosS]

Of your pants? Well I know THAT!

[Dunbar]

*rimshot*

 

*audience hoots and hollers*