Most unlikely LV recording

Shurtagal · Post by **Shurtagal** » July 27th, 2007, 4:52 pm

ceastman wrote:Well, mostly. I believe you're correct with regards to a perfect sphere. The Earth is actually a flattened sphere: the distance between the North and South poles is shorter than the distance between opposite points on the equator. So you'd need the equation for an ellipsoid.

Ok thx, according to Wikipedia, A) Earth is an Oblate Ellipsoid, B)the formula for the volume of an ellipsiod:

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V(Ellipsiod)=4/3pi(a)b(c)

Now the math gets way beyond me but I think that the equation to find two points directly opposite each other on a ellipsiod would be:

ceastman wrote: What would you like to know?

Also, would anyone be interested in having a thread in Off-Topic designated for science-type questions? I know I'm not the only 'professional scientist' here, and it might be fun to have an area for science Q&A.

-Catharine

See above.

Starlite · Post by **Starlite** » July 27th, 2007, 5:13 pm

WOW Zach, you have terrible handwritting.

Shurtagal · Post by **Shurtagal** » July 27th, 2007, 7:51 pm

Yea, I know thats Why I don't handwrite my essays!

Can you make sense of it?

Jc · Post by Jc » July 27th, 2007, 10:35 pm

arrrrgggghhhh!!!! I just had horrible flashbacks of math courses... *runs*

As for the most unlikely LV recording, I think that anything ASL would be pretty hard to put into audio...

(though I wish we could ...)

Shurtagal · Post by **Shurtagal** » July 27th, 2007, 10:49 pm

I'm sorry I happen to love math, and yes ASL would be unlikely!

Jc · Post by Jc » July 28th, 2007, 12:19 am

I always found math way too abstract for me, though I had a math teacher once who was really amazing. He'd go off topic all the time, and he'd start talking about the lives of the mathematicians, or applications of mathematical principles (like the beer foam equation/matrix)

Shurtagal · Post by **Shurtagal** » July 28th, 2007, 12:34 am

JC - thats weird. Its the abstract that is both easiest and funnest for me. it is like I can see the terms independently in my head and move the as though they were on pieces of paper. Such as the equations above which have no real use but are fun to work out. But then there are also equations (or rather systems of them) that help you figure out these general questions too: # The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended?

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Answer:

      a + c = 2200
      4a + 1.5c = 5050

Then solve the system for the number of adults and the number of children:

      a = 2200 – c

      4(2200 – c) + 1.5c = 5050
      8800 – 4c + 1.5c = 5050
      8800 – 2.5c = 5050
      –2.5c = –3750
      c = 1500

      a = 2200 – (1500) = 700

There were 1500 children and 700 adults.

Shurtagal · Post by **Shurtagal** » July 28th, 2007, 12:35 am

But, I digress. Does any one feel like a math thread would be good?

Jc · Post by Jc » July 28th, 2007, 1:06 am

Matrices were fun, but Derivatives and Integrals killed me.

ahab · Post by **ahab** » July 28th, 2007, 8:58 am

Shurtagal wrote:(Question for ceastman, from Shurtagal's handwritten notes:)

"Why is the 'Y' [male] chromosome smaller than the 'X' [female]."

Now, *that's* a question that's *sure* to generate some amusing discussion on LV . . .

ahab · Post by **ahab** » July 28th, 2007, 9:38 am

Shurtagal wrote:
ceastman wrote:Well, mostly. I believe you're correct with regards to a perfect sphere. The Earth is actually a flattened sphere: the distance between the North and South poles is shorter than the distance between opposite points on the equator. So you'd need the equation for an ellipsoid.

Ok thx, according to Wikipedia, A) Earth is an Oblate Ellipsoid, B)the formula for the volume of an ellipsiod:
Code: Select all
V(Ellipsiod)=4/3pi(a)b(c)
Now the math gets way beyond me but I think that the equation to find two points directly opposite each other on a ellipsiod would be:

[cool image of Shurtagal's notes]

Shurtagal, I think your intuition is correct with respect to whether you really need to consider both "A" and "B". If I'm understanding the question you're asking -- the distance between two antipodal points on the Earth, conceived as an oblate ellipsoid of rotation -- the rotational symmetry effectively reduces this to a 2D problem.

Now, I am not certain of any of the following, because I'm not a mathematician, but:

(1) Taking the semimajor axis (a) of the Earth to be 6,378,135 m (radius at the equator) and the semiminor axis (b) to be 6,356,750 m (radius at pole), the equation for the the ellipse of rotation becomes:

x^2/(6,378,135)^2 + y^2/(6,356,750)^2 = 1

(2) Now, I'm not completely sure, but I believe that in the polar coordinates version of this equation, x and y can be parameterized according to latitude by the following equations:

x = a cos(L)
y = b sin (L)

where L = the latitude.

(3) Therefore, if you know the latitude of the point on the Earth's surface, you should be able to get the x and y coordinates of the ellipse in Cartesian space

x = 6,378,135 * cos(L)
y = 6,356,750 * sin (L)

(4) At that point, finding the difference between the two antipodes is a straightforward application of the Pythagorean theorem:

Hypotenuse = sqrt(x^2 + y^2)
Distance between antipodal points = 2*hypotenuse

(It would be a lot easier if I could draw it, but I lack the skill . . .)

(5) Example: We stand at 50 deg N latitude, and want to find distance to the antipodal point.

x = 6,378,135 * cos(50) = 4099786 m
y = 6,356,750 * sin (50) = 4869553 m

Hypotenuse = sqrt (4099786^2 + 4869553^2) = 6365594

Distance to antipodal point = 2 * 6365594 = 12731188 m

OK . . . probably I've completely misinterpreted the question being asked, screwed up the math, and given a suspect answer! But hopefully, LV's gently chiding members can give me loving guidance . . .

Shurtagal · Post by **Shurtagal** » July 28th, 2007, 10:55 am

That is so cool!!, I never would have figured it out that far and I think I got a basic understanding of the concepts and processes. (I've only Finished Algebra I, so a bit of that went over my head but I still think I got the jist.) And yes as far as I can tell you made no mistakes and answered the question at hand. So, thanks alot I love to see that kind of stuff worked.

ahab · Post by **ahab** » July 29th, 2007, 6:39 am

Shurtagal wrote:That is so cool!!, I never would have figured it out that far and I think I got a basic understanding of the concepts and processes. (I've only Finished Algebra I, so a bit of that went over my head but I still think I got the jist.) And yes as far as I can tell you made no mistakes and answered the question at hand. So, thanks alot I love to see that kind of stuff worked.

Well, great! Sorry if it was a bit involved; I assumed from your notes, and level of interest, that you were a bit further along . . . either way, it sounds like you have a great math future ahead of you. Enjoy the trip!

ceastman · Post by **ceastman** » July 29th, 2007, 12:10 pm

So ahab's going to go start a Science Thread! yay ahab!

Meanwhile, a brief answer to the question I think you were asking:

You asked:

(1) Why do genes get small as you move from 1 to 23?

Clarification: I'm pretty certain you mean chromosomes, not genes.

Humans have 23 pairs of chromosomes, within which reside many thousands of genes. Answer to your question in a moment.

(2) Why is the Y chromosome smaller than the X?

The answer to both of these is really more historical than scientific. I'm having trouble finding a good reference, but the folks who (presumably) invented karyotyping (a method to separate and visualize the chromosomes of a cell) found that there were 23 different chromosome lengths (22 identical-length pair-sets (e.g. the two copies of chromosome 1 were identical in length, ditto chromosome 2, 3... all the way to 22), and a 23rd set where the lengths were identical in a female and different in a male). Those folks arbitrarily decided that they would call the longest one chromosome 1, the next-longest chromsome 2, etc. down to 22.

With the X and Y chromosomes, they don't really fit the length pattern. They're sometimes designated chromosome pair 23, though that's pretty rare. They were given letter codes rather than number codes because they have different lengths. It's just the way that the folks who first saw it decided to organize them, and that organization has stuck.

Does this answer your question, or should I try to explain in another way?

Now, because the Y chromsome doesn't match the X chromosome, you can get what are called X-linked disorders in human males, which I'll be happy to talk about elsewhere if you're interested.

Once ahab's created the science thread, we can re-post all this discussion there.

-Catharine

magtutudlo · Post by **magtutudlo** » July 30th, 2007, 9:09 am

This is why I choose English and history.

I'll leave the math and science to others.