[this entire pos is in degrees, not radians]

In spherical triangles, given three angles there is _not_ an infinity

of solutions For example, a triangle with angles of 60,60,60 will be

vanishingly small. A trinangle with angles of 90,90,90 will be

precisely an octant of the sphere. This is the great distinction

between plane and spherical geometry. In fact, there is a nice formula

which the margin of this note is too small to contain which relates

the area of a spherical triangle to the "defect", i.e. (sum of angles)

- 180.

Also: please note that angles greater than 180 are quite distinct. A

triangle with angles of 299,299,299 is almost the triangle obtained by

replacing the lines at the corners of a 60-60-60 triangle with the

portions of the great circles which lie outside the original small

triangle. It is hard to visualize but very real.

--Irl

On Apr 19, 2:06 pm, Beauzeauwrote:

> Civility and Angles

>

> To John Meyers and Dave Boyd,

>

> I just want to thank each of you for answering my simple question and

> educating me on USENET. Both of you have treated me with respect and

> carried yourselves with dignity and civility. Again, I thank you.

> ================================================== ===================

>

> Question Concerning triangles: I hope to read the manual twice to

> obtain maximum benefit from it. In my first reading , on page 7-13 of

> the manual, there is a note: "If you get a value of larger than 180,

> try the following...." which is re-initializing the angle to a value

> of 10 degrees. Then solve for alpha again. I assume that a solution in

> the eyes of the HP 50 is 360 - the 'correct' angle. At first, I

> wondered why the gentleman who wrote these pages for HP did not

> include a conditional statement:' If alpha > 180, then alpha

> 10 store ' to re-initialize alpha. The reason, I assume, is that

> MES is a pre programmed routine, hard coded in the memory (a PROM?).

> And the program is a generic program to be used for types of systems

> of multiple equations. For situations such as these, it would be

> beneficial to add 'GO TO' program at the end of MES, to insure the

> solved angle is less than 180 degrees, such as the conditional

> mentioned above, of course in SysRPN. One could then apply the

> concept to other programs where conditional statements are needed to

> avoid pre-determined possible erroneous solutions. Question: is that

> possible? Was it possible for the person at HP to add a condtional

> statement to the MES program , obviously outside of the 'hard coded'

> MES program. ????

>

> Thanks , as always.

>

> Footnote: I suspect that there is an error on 7-10 : the three sides

> and the three angles are listed as variables in a hypothetical

> triangle. It is stated that if you know any of the three variables,

> the other three may be solved. However, if one knows three of the

> angles, there are an infinite number of solutions for the sides ,

> since all the triangles are similar with equal angles . Therefore,

> one side must be know to obtain a unique solution