Comments on: Spherical trigonometry

By: Mel Hagen

Mel Hagen — Sat, 05 Sep 2009 04:44:13 +0000

I am revisiting Spherical Trig after 30 years by going back over some of my books that I have collected over the years. Here are two that you may want to find.

1) on Amazon.com: Schaum’s Outline Series – Theory and Problems of Plane and Spherical Trigonometry by Frank Ayres, Jr. [1954 McGraw-Hill]

2)very old text book: Trigonometry For Home Study by William L. Schaaf
[1945 The New Home Library The Blakiston Company - Philadelphia]

I also have copies of sheets with 40+ problems and exercises I can share with anyone who is interested.

By: John

John — Thu, 30 Apr 2009 21:52:30 +0000

Thanks for the link to krysstal.com. Looks good.

By: L. D. Rafey

L. D. Rafey — Thu, 30 Apr 2009 21:41:23 +0000

http://www.krysstal.com/sphertrig.html

This is a great website for spherical trig with exercises, etc.

By: John

John — Wed, 22 Apr 2009 16:51:26 +0000

Evelyn, I’d look at the book by Donnay referenced in the post. It has been reprinted by Dover. Amazon lists several spherical trig books, all reprints of old books.

By: Evelyn Ames

Evelyn Ames — Wed, 22 Apr 2009 16:42:00 +0000

My math academic team is studying shperical trig. Is there someplace that I can find some practice questions? We only need problems that use the Law of Cos, Law of Sines , Napiers Circle and the area equation.

By: Bunbury

Bunbury — Sun, 08 Mar 2009 19:36:46 +0000

There is also hyperbolic trigonometry with its own sine and cosine laws. This link is the best I can find on the web but it does little to emphasise the logical similarity to Euclidean trigonometry.

By: Jan Theodore Galkowski

Jan Theodore Galkowski — Fri, 06 Mar 2009 22:43:38 +0000

Spherical trigonometry and the vector algebra of the unit sphere are both useful in applications involving directions, especially directions in 3D. There’s even a statistical subfield, typified by N.I.Fisher, T.Lewis, B.J.J.Embleton, STATISTICAL ANALYSIS OF SPHERICAL DATA, 1987.

As Bill the Lizard mentioned, the math mechanics of directions and such do get big billing in robotics work, too.

By: John Venier

John Venier — Fri, 06 Mar 2009 19:34:36 +0000

Interesting … I always heard that before surveyors could demonstrate the curvature of the Earth by finding that the interior angles of a triangle on the surface added to more than 180 degrees, the vertices had to be on Himalayan mouintains, and even then it was dubious.

Here’s a guess — with WWII over and radar becoming more widely used, many fewer people needed to know old fashioned navigation. In the first place, there were a lot fewer night bomber sorties and covert reconnaisance flights. Those who did travel far could use radar as a much simpler and more accurate alternative, as it still is.

But I seriously doubt surveyors ever worried about the curvature of the Earth. First off, most surveying is done locally, and secondly local surface variation probably dwarfs any curvature effects.

As for astronomers, I don’t know, but it is not obvious to me why they would need it, unless it is simply beacuse they use spherical coordinates to locate things. And there aren’t that many of them, proportionally speaking.

Geographers and some map makers need to account for it, and the results at least need to be used for planning long range travel, but that still requires relatively few people to know how to do the calculations.

An interesting thing not many people know (present company excepted of course) is that the Earth was known to be a sphere at least since the ancient greeks, who even calculated the curvature using shadows of sticks. The old saw about Columbus having to convince Queen Isabella that the Earth was round instead of flat is a recent fiction. The controversy was over the distances involved in getting to East Asia by going West; Columbus had a radically optimistic opinion, which is why he assumed he had hit Asia when he hit the Americas.

By: Bill the Lizard

Bill the Lizard — Fri, 06 Mar 2009 15:54:32 +0000

I’ve been learning spherical triginometry in bits and pieces over the past year without knowing that that’s what it’s called. I took a job a year ago with a robotics company that makes UAVs. It’s amazing how large the error in your navigation calculations can grow when you try to ignore the curvature of the Earth.