[DrRocket]

Santalum, on 11 February 2012 - 01:56 AM, said:

Yes apparently I don't. I am struggling to comprehend what you mean.

But now you have me absolutely intrigued even though I have never had any particular interest in maths.

I don't suppose there is a website as good as your book that I could read? Anyone?

No. But Singer and Thorpe's book is excellent.

However, if you have never taken any mathematics beyond, say, high school algebra, you may not find it readable. But then again, you might. While geometry and topology are usually taught to advanced undergraduates or beginniing graduate students (Singer and Thoroe is aimed at undergraduates) there is really no pre-requuisite beyond "mathematical maturity".

Unfortunately there is not much that can be done if find the book too imposing at this stage except go back farther and start learning more mathematics. Differential geometry simply requires some background.

There is all sorts of stuff on the internet. Some is OK and some is just trash. But you can't go wrong with a book by someone who actually knows what he is talking about. Mathematicians don't come much better than I.M. Singer.

This post has been edited by DrRocket: 11 February 2012 - 02:20 AM

[Santalum]

DrRocket, on 11 February 2012 - 02:18 AM, said:

No. But Singer and Thorpe's book is excellent.

However, if you have never taken any mathematics beyond, say, high school algebra, you may not find it readable. But then again, you might. While geometry and topology are usually taught to advanced undergraduates or beginniing graduate students (Singer and Thoroe is aimed at undergraduates) there is really no pre-requuisite beyond "mathematical maturity".

Unfortunately there is not much that can be done if find the book too imposing at this stage except go back farther and start learning more mathematics. Differential geometry simply requires some background.

There is all sorts of stuff on the internet. Some is OK and some is just trash. But you can't go wrong with a book by someone who actually knows what he is talking about. Mathematicians don't come much better than I.M. Singer.

http://www.gmat.unsw...fs/navpaths.pdf

Found this website explaining rhumb lines, geodesics and gnomic projections etc.

What I have been describing is a rhumb line or an small circle arc formed by the intersection of plane and the earth's surface, that does not include the centre of the earth.

I can see from their diagram that it is clearly not going to be the shortest distance between two points on the earth's surface.

Where as if you tilt that plane until it includes the earth's centre then you have shortened the distance, albeit slightly, between the two points.

The penny is starting to drop DrRocket.

In fact what I have been assuming is an arc of the circumference of the earth is in fact an arc of the circumference of what would be a smaller earth..........the distance on the earth's surface between two points at a given latitude. This amounts to a tighter curve and when you project that onto the surface of the earth it ends up being a slightly longer distance.

Am I correct DrRocket?

Also has a perfect decription of the difference between geodesics (ellipsoids and ellipses) and arc (circles and spheres)

The 19th century term 'the antipodes' suddenly becomes meaningful to me.

This post has been edited by Santalum: 11 February 2012 - 10:48 AM