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Ikas90
13-12-06, 03:02
Hi everyone. I just thought I'd share this very interesting maths puzzle with you.

This is about finding the distance between two cities... So, let's say the difference between Sydney and Athens.

First of all, you have to find the co-ordinates of both cities...

The approximate co-ordinates of Sydney are:
3352' S, 15113' E

The approximate co-ordinates of Athens are:
3759' N, 2344' E

Now that we have those co-ordinates, we have to find the difference between them.

So, since Athens is in the Northern hemisphere, and Sydney is in the Southern hemisphere, we have to add the two co-ordinates together to find the difference.

Firstly, the difference in latitude: 3352' + 3759' = 7151

Now, since Athens and Sydney are both in the Eastern hemisphere, we subtract the co-ordinates.

So, longitude: 15113' - 2344' = 12729'

So, now that we have both differences in co-ordinates, it's time to turn them to distances.

Note that there is 360 degrees in a circle, and that the Earth's average radius is 6,367.25 km.

7151' / 360 x 2 x π x 6,367.25 = 7984.65 km

12729' / 360 x 2 x π x 6,367.25 = 14,167.16 km

Now that we got those 2 distances, time to find the hypotenuse.

c = a + b

7984.65 + 14,167.16 = 264,463,058

Now we need to find the square root of that answer...

√264,463,058 = 16,262

Therefore, the distance between Sydney and Athens is 16,262 km (10,105 miles)

Use this to find distances between any two cities, though, it wont be EXACTLY accurate, though, it may be MUCH more accurate than measuring on Google Earth.

Satu
13-12-06, 03:08
lol Saki, you lost me about half way down.

I was hopeless at maths but intresting to see how you worked out the distance.

CerebralAssassin
13-12-06, 03:22
Hi everyone. I just thought I'd share this very interesting maths puzzle with you.

This is about finding the distance between two cities... So, let's say the difference between Sydney and Athens.

First of all, you have to find the co-ordinates of both cities...

The approximate co-ordinates of Sydney are:
3352' S, 15113' E

The approximate co-ordinates of Athens are:
3759' N, 2344' E

Now that we have those co-ordinates, we have to find the difference between them.

So, since Athens is in the Northern hemisphere, and Sydney is in the Southern hemisphere, we have to add the two co-ordinates together to find the difference.

Firstly, the difference in latitude: 3352' + 3759' = 7151

Now, since Athens and Sydney are both in the Eastern hemisphere, we subtract the co-ordinates.

So, longitude: 15113' - 2344' = 12729'

So, now that we have both differences in co-ordinates, it's time to turn them to distances.

Note that there is 360 degrees in a circle, and that the Earth's average radius is 6,367.25 km.

7151' / 360 x 2 x π x 6,367.25 = 7984.65 km

12729' / 360 x 2 x π x 6,367.25 = 14,167.16 km

Now that we got those 2 distances, time to find the hypotenuse.

c = a + b

7984.65 + 14,167.16 = 264,463,058

Now we need to find the square root of that answer...

√264,463,058 = 16,262

Therefore, the distance between Sydney and Athens is 16,262 km (10,105 miles)

Use this to find distances between any two cities, though, it wont be EXACTLY accurate, though, it may be MUCH more accurate than measuring on Google Earth.

where did you get this?or did you figure it out by yourself?:p

Ikas90
13-12-06, 03:24
I figured it out by myself, actually :p I used spherical geometry, which I was taught recently, and I knew pythagoras' theorem, so I just combined the two of them together :D

Tomb of Legends
13-12-06, 03:33
MY GOD, you figured that out yourself. You have WAY to much spare time.

Ikas90
13-12-06, 03:35
Not really, lol :vlol: It only took me 5-10 minutes to figure it out. After all, I am in Year 12 :D

CerebralAssassin
13-12-06, 03:35
I figured it out by myself, actually :p I used spherical geometry, which I was taught recently, and I knew pythagoras' theorem, so I just combined the two of them together :D

I just calculated it. you're off by 6,000 km :p not good..I've got to admit though..good try!!

the calculation confirmed the flaw in your reasoning that I found..:p

Ikas90
13-12-06, 03:38
You probably miscalculated something... because I actually measured it on Google Earth to make sure I had the right answer, and I was only 300km off, but, don't forget that on Google Earth, the radius of the Earth is rounded off :D

CerebralAssassin
13-12-06, 03:44
You probably miscalculated something... because I actually measured it on Google Earth to make sure I had the right answer, and I was only 300km off, but, don't forget that on Google Earth, the radius of the Earth is rounded off :D

I'm getting ten thousand something...what is google earth..show it to me!:p

Ikas90
13-12-06, 03:56
I'm not allowed to advertise, so I'll just post a screenshot:

http://i111.photobucket.com/albums/n131/Ikas90/GoogleEarth.jpg

CerebralAssassin
13-12-06, 04:01
I'm not allowed to advertise, so I'll just post a screenshot:

http://i111.photobucket.com/albums/n131/Ikas90/GoogleEarth.jpg

well...you're still off for about 800 km...:D

Joseph
13-12-06, 04:04
what is google earth..show it to me!:p
Well, here: http://earth.google.com/

Ikas90
13-12-06, 04:05
Yeah, well, on Google Earth, the radius is rounded off and not the "true" diameter, I just used the average diameter of both through the poles, and the equator.

CerebralAssassin
13-12-06, 04:08
Yeah, well, on Google Earth, the radius is rounded off and not the "true" diameter, I just used the average diameter of both through the poles, and the equator.

well,google earth may be right...I don't know..I used this...:D

http://www.wcrl.ars.usda.gov/cec/java/lat-long.htm

but the algorithm you used is wrong :D

Ikas90
13-12-06, 04:12
Yes, yes, but that is the distance if you go through the ground of the Earth and out the other side... I was talking about the arc length of Sydney to Athens.

SpongeBob Lover
13-12-06, 04:15
ahhh math!! *ducks for cover* man that looks like another language or something :p

CerebralAssassin
13-12-06, 04:16
Yes, yes, but that is the distance if you go through the ground of the Earth and out the other side... I was talking about the arc length of Sydney to Athens.

is says surface distance doesn't it? :confused: don't make me go bananas!!:D

Ikas90
13-12-06, 04:21
Yeah, the bottom one is the true surface distance, not the top one. It says 15,315 km, so I'm 800km off, not 6,000 :D That is also referring to the radius being rounded off again.

You're making me go bananas, lol :D

CerebralAssassin
13-12-06, 04:25
Yeah, the bottom one is the true surface distance, not the top one. It says 15,315 km, so I'm 800km off, not 6,000 :D That is also referring to the radius being rounded off again.

You're making me go bananas, lol :D

ok you're right I shouldv'e used the bottom one lol...BUT YOUR DERIVATION IS WRONG DAMN IT!!:p

Ikas90
13-12-06, 04:28
I must of had a co-ordinate wrong. I don't understand, I got the right answer before... something seems wrong, it shouldn't be 800km off :confused: The average radius of the Earth is 6,367.25 km. The equatorial radius is 6,378 and the rounded off radius is 6,400. Try putting 6,400 in, might get a different answer.

EDIT: I got a merit award in school for this, DAMN IT!!!

CerebralAssassin
13-12-06, 04:32
I must of had a co-ordinate wrong. I don't understand, I got the right answer before... something seems wrong, it shouldn't be 800km off :confused: The average radius of the Earth is 6,367.25 km. The equatorial radius is 6,378 and the rounded off radius is 6,400. Try putting 6,400 in, might get a different answer.

EDIT: I got a merit award in school for this, DAMN IT!!!

will you calm down and listen?don't be stubborn...accept the $ 0.02 that a veteran of math is offering you.sheesh..:rolleyes:

Ikas90
13-12-06, 04:45
LOL :vlol: Teach me some Engineering, lol :vlol:

CerebralAssassin
13-12-06, 04:46
LOL :vlol: Teach me some Engineering, lol :vlol:

what are you laughing at? I ain't no engineer..I'm a math major! :rolleyes:

JACOBryanBURNS
13-12-06, 04:56
Consider my brain like a car engine....

It overheated and stopped working at about the second question. :p

Andromeda66
13-12-06, 07:39
I figured it out by myself, actually :p I used spherical geometry, which I was taught recently, and I knew pythagoras' theorem, so I just combined the two of them together :D

Brilliant! :D

kryptonite23
26-01-07, 12:34
I think my head will explode to this puzzle!!!