This Problem has Bamboozled Me! - DPChallenge Forums

10/19/2009 02:09:09 AM · #1

Originally posted by zxaar:

Originally posted by Spazmo99:
whatever.

maths is beyond you.
Try something simpler.

:-D

Can I try you? You're simple.

10/19/2009 01:43:30 AM · #2

Originally posted by Spazmo99:

whatever.

maths is beyond you.
Try something simpler.

:-D

10/19/2009 01:34:02 AM · #3

Originally posted by zxaar:

never mind.

I never mind any of your posts anyway.

10/19/2009 01:33:29 AM · #4

whatever.

Originally posted by zxaar:

Originally posted by Spazmo99:

wrong.

please see Eratosthenes

i have seen it.
Here is a link about what he did.

//en.wikipedia.org/wiki/File:Eratosthenes.svg

here is explaination of what he did.

//farm3.static.flickr.com/2526/4024204482_473235bb89_o.jpg

He assumed the third angle , which is at sun (Sun_A) equal to 0. Which makes his solution an approaximation and not true solution to problem.

And here is how you got to that assumption:

Originally posted by zxaar:

Originally posted by ErikV:
The arc difference between the two cities is 13 degrees (90-77). 13 degrees = 13/360 of the total circumference and also equals 1500 miles. Therefore the circumference = 1500 miles x 360/13 = 41538.46 km.

if the definition of angle of altitude given here is correct:

//susdesign.com/popups/sunangle/altitude.php

then above solution has to be wrong.

here is why.

consider triangle formed by three points
sun'c center
earth's center
observer's position.

Lets call angles at these corners as
Sun_A, Earth_A, Ob_A

We know that

Sun_A + Earth_A + Ob_A = 180.

Now this page says altitude of sun is angle with HORIZONTAL plane.
This horizontal plane has to be tangent to earth surface.
Which means that

Ob_A = 90 + 77 (altitude angle + plane's angle 90).

it implies that Earth_A + Sun_A = 180 - (90 - 77 ) = 13.

it means that Earth_A < 13.

in the solution that you guys have presented so far, Earth_A = 13, which is simply not possible. (because Sun_A > 0 ).

10/18/2009 09:39:58 PM · #5

For anyone interested in history, this is good read:

//galileoandeinstein.physics.virginia.edu/lectures/gkastr1.html

10/18/2009 07:05:55 PM · #6

Originally posted by Spazmo99:

wrong.

please see Eratosthenes

i have seen it.
Here is a link about what he did.

//en.wikipedia.org/wiki/File:Eratosthenes.svg

here is explaination of what he did.

//farm3.static.flickr.com/2526/4024204482_473235bb89_o.jpg

He assumed the third angle , which is at sun (Sun_A) equal to 0. Which makes his solution an approaximation and not true solution to problem.

And here is how you got to that assumption:

Originally posted by zxaar:

Originally posted by ErikV:
The arc difference between the two cities is 13 degrees (90-77). 13 degrees = 13/360 of the total circumference and also equals 1500 miles. Therefore the circumference = 1500 miles x 360/13 = 41538.46 km.

if the definition of angle of altitude given here is correct:

//susdesign.com/popups/sunangle/altitude.php

then above solution has to be wrong.

here is why.

consider triangle formed by three points
sun'c center
earth's center
observer's position.

Lets call angles at these corners as
Sun_A, Earth_A, Ob_A

We know that

Sun_A + Earth_A + Ob_A = 180.

Now this page says altitude of sun is angle with HORIZONTAL plane.
This horizontal plane has to be tangent to earth surface.
Which means that

Ob_A = 90 + 77 (altitude angle + plane's angle 90).

it implies that Earth_A + Sun_A = 180 - (90 - 77 ) = 13.

it means that Earth_A < 13.

in the solution that you guys have presented so far, Earth_A = 13, which is simply not possible. (because Sun_A > 0 ).

Message edited by author 2009-10-18 19:06:43.

10/18/2009 06:25:49 PM · #7

never mind.

Message edited by author 2009-10-18 18:32:32.

Canon EF-S 18-135mm f/3.5-5.6 IS

10/18/2009 05:32:57 PM · #8

Originally posted by SteveJ:

I make it 41,538.46677766655555 kilometres, but then I don't really do kilometres, only miles:))

I *knew* I should have rounded up, danggit!

R.

SteveJ

Canon EOS-7D

10/18/2009 04:14:42 PM · #9

Wow, have they discovered a new planet called Nearth? Almost the same name as ours!!

It amazes me what these astrognomers find out there every night, all I see a lots of tiny holes in the big black sheet that covers the blue sky, so it can be called night.

I make it 41,538.46677766655555 kilometres, but then I don't really do kilometres, only miles:))

Nikon AF Zoom-Nikkor 70-200mm f/2.8 VR DG IF-ED

10/18/2009 03:44:17 PM · #10

Originally posted by ErikV:

Originally posted by Bear_Music:
It seems to me that if there's a 1500 Km distance between 2 places on the same meridian, and a 13-degree angular deviance, then 1500/13 = kilometers per degree of separation, and that x 360 = circumference of Nearth.

41,538.46 kilometers.

This is probably too simple to be correct, been years since I did maths...

R.

Good, that's pretty much the same approach and answer as I posted yesterday evening. So it must be correct if the two of us agree.

Oh, I didn't see that, sorry... Of course, just because a couple bozos like us are in agreement doesn't make us *right*, but...

:-) R.

ETA: Just checked your earlier work and yup, we both are saying the exact same thing. I slept on this overnight, thinking to myself "If Erastothenes could get it right thousands of years ago without the higher math functions, there has to be a more straightforward way to calculate this...", and my brain kind of blinked and said "Oh, *YEAH*!"

Message edited by author 2009-10-18 15:46:45.

ErikV

Nikon D7000

10/18/2009 03:42:53 PM · #11

Originally posted by Bear_Music:

It seems to me that if there's a 1500 Km distance between 2 places on the same meridian, and a 13-degree angular deviance, then 1500/13 = kilometers per degree of separation, and that x 360 = circumference of Nearth.

41,538.46 kilometers.

This is probably too simple to be correct, been years since I did maths...

R.

Good, that's pretty much the same approach and answer as I posted yesterday evening. So it must be correct if the two of us agree.

Canon EF 70-200mm f/4.0L USM

10/18/2009 12:21:26 PM · #12

cujee

Canon EOS-30D

10/18/2009 12:02:05 PM · #13

Yeah this problem is suppose to be based on Eratosthenes Theory of figuring out the circumference of the earth. This is actually an astronomy class, and I didn't think we would be doing geometry, which I haven't done in like 3 years.

Sony FE 200-600mm f/5.6-6.3 G OSS

10/18/2009 11:29:42 AM · #14

Originally posted by zxaar:

Originally posted by Spazmo99:

Originally posted by zxaar:

Originally posted by Spazmo99:
Ok, first take the formula for arc length

Arc length= 2 pi*r*(c/360)

where r is the radius and c is the angle the arc covers in degrees.

Re-arrange to solve for r

Plug in what you know: Arc length = 1500km and c = 13 degrees (90-77)

That will give you the radius in km

From there use Circumference = 2*pi*r

everything sounds alright, except
c = 13 = 90 -77.

the c in your formula is angle to observer from earth center, not angle of sun for observer.

is the way you calculated c correct??

yes

nope,

in your solution

c = 90 - angle of altitude.
distance between cities = c * r = l
that is distance between cities = function of c = function of angle of altitude.

it means that by changing angle of altidude distance between cities changes.
which is completely wrong as distance between two cities is independent of position of sun.
So the way c is calculated in your formulation is wrong.

c should be independent of where sun is positioned.

wrong.

please see Eratosthenes

vawendy

Sony Alpha 1

10/18/2009 11:00:09 AM · #15

Originally posted by Bear_Music:

Originally posted by vawendy:
I realize that! :P that's what makes it so interesting -- there's not enough data.

Oh, I thought you'd gone blonde on us...

R.

Well, I am a blond.... (yeah, yeah, yeah)

10/18/2009 02:37:08 AM · #16

Originally posted by GeneralE:

Seems to me that Eratosthenes solved essentially the same problem around 200 BC ... :-)

thanks for this, it seems he also has to make assumption (which is very much valid assumption):

" The calculation is based on the assumption that the Earth is spherical and that the Sun is so far away that its rays can be taken as parallel."

anyway still i could not think how he did. very busy to seriously think.

here is a link about how he did.

//www.windows.ucar.edu/tour/link=/citizen_science/myw/w2u_eratosthenes_calc_earth_size.html

Message edited by author 2009-10-18 02:47:05.

10/18/2009 02:17:46 AM · #17

Originally posted by Spazmo99:

Originally posted by zxaar:

Originally posted by Spazmo99:
Ok, first take the formula for arc length

Arc length= 2 pi*r*(c/360)

where r is the radius and c is the angle the arc covers in degrees.

Re-arrange to solve for r

Plug in what you know: Arc length = 1500km and c = 13 degrees (90-77)

That will give you the radius in km

From there use Circumference = 2*pi*r

everything sounds alright, except
c = 13 = 90 -77.

the c in your formula is angle to observer from earth center, not angle of sun for observer.

is the way you calculated c correct??

yes

nope,

in your solution

c = 90 - angle of altitude.
distance between cities = c * r = l
that is distance between cities = function of c = function of angle of altitude.

it means that by changing angle of altidude distance between cities changes.
which is completely wrong as distance between two cities is independent of position of sun.
So the way c is calculated in your formulation is wrong.

c should be independent of where sun is positioned.

Canon 12x IS USM (S3 IS built-in Lens) -- 36-432mm (35mm EQ)

10/18/2009 12:51:37 AM · #18

Originally posted by vawendy:

I realize that! :P that's what makes it so interesting -- there's not enough data.

Oh, I thought you'd gone blonde on us...

R.

GeneralE

Canon PowerShot S3 IS

10/17/2009 11:57:07 PM · #19

Seems to me that Eratosthenes solved essentially the same problem around 200 BC ... :-)

vawendy

Sony Alpha 1

Sony FE 200-600mm f/5.6-6.3 G OSS

10/17/2009 11:36:05 PM · #20

Originally posted by Bear_Music:

Originally posted by vawendy:

Originally posted by cujee:
Here is the question for people who enjoy science and understand geometry as well:

You are an astronomer on planet Nearth, which orbits a distant star. It has recently been accepted that Nearth is spherical in shape, though no one knows its size. One day, while studying in the library of Alectown, you learn that on the equinox your sun is directly overhead in the city of Nyene, located 1500 kilometers due north of you. On the equinox, you go outside in Alectown and observe that the altitude of your sun is 77 degrees

What is the circumference

you guys completely misunderstood the question. He's not looking for the circumference of the nearth, he's looking for the circumference of the sun. He says ..."the altitude of your sun is 77 degrees. What is the circumference?"

Back to the drawing board people! :P

Nawp....

You are an astronomer on planet Nearth, which orbits a distant star. It has recently been accepted that Nearth is spherical in shape, though no one knows its size. One day, while studying in the library of Alectown, you learn that on the equinox your sun is directly overhead in the city of Nyene, located 1500 kilometers due north of you. On the equinox, you go outside in Alectown and observe that the altitude of your sun is 77 degrees

What is the circumference

He wants the circumference of Nearth. Impossible to calculate circumference of sun from these data anyway.

R.

I realize that! :P that's what makes it so interesting -- there's not enough data.

Sony FE 200-600mm f/5.6-6.3 G OSS

10/17/2009 11:33:34 PM · #21

Originally posted by vawendy:

Originally posted by cujee:
Here is the question for people who enjoy science and understand geometry as well:

You are an astronomer on planet Nearth, which orbits a distant star. It has recently been accepted that Nearth is spherical in shape, though no one knows its size. One day, while studying in the library of Alectown, you learn that on the equinox your sun is directly overhead in the city of Nyene, located 1500 kilometers due north of you. On the equinox, you go outside in Alectown and observe that the altitude of your sun is 77 degrees

What is the circumference

you guys completely misunderstood the question. He's not looking for the circumference of the nearth, he's looking for the circumference of the sun. He says ..."the altitude of your sun is 77 degrees. What is the circumference?"

Back to the drawing board people! :P

Nawp....

You are an astronomer on planet Nearth, which orbits a distant star. It has recently been accepted that Nearth is spherical in shape, though no one knows its size. One day, while studying in the library of Alectown, you learn that on the equinox your sun is directly overhead in the city of Nyene, located 1500 kilometers due north of you. On the equinox, you go outside in Alectown and observe that the altitude of your sun is 77 degrees

What is the circumference

He wants the circumference of Nearth. Impossible to calculate circumference of sun from these data anyway.

R.

vawendy

Sony Alpha 1

10/17/2009 11:23:40 PM · #22

Originally posted by cujee:

Here is the question for people who enjoy science and understand geometry as well:

You are an astronomer on planet Nearth, which orbits a distant star. It has recently been accepted that Nearth is spherical in shape, though no one knows its size. One day, while studying in the library of Alectown, you learn that on the equinox your sun is directly overhead in the city of Nyene, located 1500 kilometers due north of you. On the equinox, you go outside in Alectown and observe that the altitude of your sun is 77 degrees

What is the circumference

you guys completely misunderstood the question. He's not looking for the circumference of the nearth, he's looking for the circumference of the sun. He says ..."the altitude of your sun is 77 degrees. What is the circumference?"

Back to the drawing board people! :P

kleski

Canon EOS-7D

Canon EF 28-135mm F/3.5-5.6 IS USM

10/17/2009 11:09:12 PM · #23

"It was my understanding that there would be no math."

Chevy Chase as Gerald Ford, SNL