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:

33°52' S, 151°13' E

The approximate co-ordinates of Athens are:

37°59' N, 23°44' 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: 33°52' + 37°59' = 71°51

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

So, longitude: 151°13' - 23°44' = 127°29'

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.

71°51' / 360 x 2 x π x 6,367.25 = 7984.65 km

127°29' / 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.

c² = a² + b²

7984.65² + 14,167.16² = 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.

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:

33°52' S, 151°13' E

The approximate co-ordinates of Athens are:

37°59' N, 23°44' 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: 33°52' + 37°59' = 71°51

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

So, longitude: 151°13' - 23°44' = 127°29'

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.

71°51' / 360 x 2 x π x 6,367.25 = 7984.65 km

127°29' / 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.

c² = a² + b²

7984.65² + 14,167.16² = 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.