## A Conversation for Longitude

### Er, shouldn't that be "Cartesian"?

Joolsee Started conversation May 22, 2000

It's from the geometrical work of René Descartes.

### Er, shouldn't that be "Cartesian"?

Joolsee Posted May 22, 2000

Searching on Google, I see 53,500 hits for "cartesian", versus 123 hits for "carthesian". Spelling error or allowable variant? Perhaps someone can post the answer here.

### Er, shouldn't that be "Cartesian"?

Paul Prefect (It's been 2 years now... wow... 8-)) Posted May 27, 2000

Hm... Thanks for pointing that out, Joolsee...

Now that you mention it, I think "cartesian" is more wide-spread... but I'm sure I've seen "carthesian" in scientific works, so I suppose both versions are acceptable... I may be wrong, though...

I would change it to "cartesian" now, only I don't seem to be able to edit the entry any more...

I mean, yes, I wrote it, but since Keeza appears as the Editor, I suppose only he can update the entry... I hope he sees this forum some time soon...

### Er, shouldn't that be "Cartesian"?

Paul Prefect (It's been 2 years now... wow... 8-)) Posted May 28, 2000

Hm... Thanks...

Took me quite some time to write... But it was fun... Especially the "wounded dog method"... Not that I like dogs being injured...

I changed it to "cartesian" in the non-approved entry, but that's about as much as I can do...

### Er, shouldn't that be "Cartesian"?

Joolsee Posted May 28, 2000

Now I come to think of it, it might be worth checking if you really mean Euclidian. If I remember correctly, Euclidian geometry is geometry on a flat, two-dimentional surface. Cartesian geometry includes the third dimention, as it includes x, y and z planes, so the surface of a sphere can be described in Cartesian terms. Euclidian geometry, as they say in the lager adverts, cannot do this.

On the subject of Longitude, the the most photographed lightning conductor in the world must be the one beside the entrance to the main museum building (Flamsteed House?) at Greenwich Observatory. People pose against is, thinking it marks the meridian. Strange, really, as the line is clearly marked where it crosses the courtyard about twenty feet to the right. Bless them.

### Er, shouldn't that be "Cartesian"?

Paul Prefect (It's been 2 years now... wow... 8-)) Posted May 29, 2000

Hm... Nope, I'm pretty sure I'm right this time...

You're right... Euclidian geometry is on a flat, two-dimensional surface, a plane, to be exact...

Carthesian geometry means adding two (or three) axises to the plane (space) so you can refer to points in it by their coordinates...

OK, I agree you can describe the surface of a sphere in a 3-dimensional Cartesian coordinate system...

But you can describe if in terms of offsets from its origin, which would logically (but not necessarily) be the middle of the earth... What I meant (and what the sailors needed) was a way to give coordinates in a two-dimensional space, which just happens to be a sphere's surface in our case... They don't really care how to get from point (1302/482/1753) to point (2302/1482/1853), but how to get from 18° EL 29°NL to 57° WL 5° NL, if you get my point... A three-dimensional system would have been way too complicated...

As for this lightning conductor you mentioned (The one besides Flamsteed House, yes, it is the main museum building), I admit that I didn't even notice it when I was in Greenwich last year... Oh well... I'll have to pay better attention next time... But the people were certainly photographing the meridian in the yard...

### Er, shouldn't that be "Cartesian"?

Joolsee Posted May 29, 2000

Another way of putting it is that for pretty much all purposes, geographical locations are most simply expressed in a polar co-ordinates, which is what latitude and longitude are. (We all tend to ignore the length of the vector, quite reasonably, as it is almost constant.)

Euclidian goemetry is no good for analysis the surface of a sphere, and Cartesian geometry makes this possible but very complicated, so polar it is then!

### Er, shouldn't that be "Cartesian"?

Paul Prefect (It's been 2 years now... wow... 8-)) Posted May 31, 2000

Yep... I should suppose so...

In fact, I never really realised we were ignoring the length of the vector all the time... Hm...

Then again, you can't call it exactly polar... Only the longitude part of it is polar... Sort of... Lattitude is given in... er...

Is that certesian?

Hm... I don't know...

But it's not polar, as it's not really an angle that's given...

### Er, shouldn't that be "Cartesian"?

Joolsee Posted Jun 2, 2000

Well, my atlas says that Sevenoaks (where I live) has the following co-ordinates:

51° 16' N 0° 12' E

The latitude is measured in degrees N or S of the Equator, i.e. the angle between the line joining Sevenoaks to the centre of the Earth and the "Equatorial disk" as it passes through the centre.

The Longitude is in degrees from the Greenwich meridian, as you know, so it's the same kind of measurement, but made where the vector crosses the "Meridian disk" at the centre of the Earth instead.

We use two lines around the globe (where the line of Longitude is a "Great Circle", passing through both Poles) to define the location, just like using two lines on a flat grid, except we have to exclude the other point in the Northern hemisphere where the lines cross (and the other two symetrical points in the Southern hemisphere), which is why we need to specify the "N" and "E" bits.

It's a 3 dimensional grid on the surface of a spheroid. Good, huh?

### Er, shouldn't that be "Cartesian"?

Paul Prefect (It's been 2 years now... wow... 8-)) Posted Jun 3, 2000

*dazzled* Yep... Good it is...

Yes... Now that you mention it, I realise that both longitude & lattitude can be regarded as angles between a vector from the middle of the Earth to a point and a plane - the equatorial or the prime meridian "disk"...

Polar coordinates after all?

Nope...

It's a 3 dimensional grid on the surface of a spheroid is the best way to put it...

Key: Complain about this post

### Er, shouldn't that be "Cartesian"?

- 1: Joolsee (May 22, 2000)
- 2: Joolsee (May 22, 2000)
- 3: Paul Prefect (It's been 2 years now... wow... 8-)) (May 27, 2000)
- 4: Joolsee (May 27, 2000)
- 5: Paul Prefect (It's been 2 years now... wow... 8-)) (May 28, 2000)
- 6: Joolsee (May 28, 2000)
- 7: Paul Prefect (It's been 2 years now... wow... 8-)) (May 29, 2000)
- 8: Joolsee (May 29, 2000)
- 9: Paul Prefect (It's been 2 years now... wow... 8-)) (May 31, 2000)
- 10: Joolsee (Jun 2, 2000)
- 11: Paul Prefect (It's been 2 years now... wow... 8-)) (Jun 3, 2000)

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