Civility and Angles - Hewlett Packard

This is a discussion on Civility and Angles - Hewlett Packard ; 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 ...

1. Civility and Angles

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

2. Re: Civility and Angles

[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, Beauzeau wrote:
> 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

3. Re: Civility and Angles

On Apr 19, 9:04 pm, Irl wrote:
> [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, Beauzeau wrote:
>
>
>
> > 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- Hide quoted text -

>
> - Show quoted text -

my master thesis was in quantum mechanics, when the equations in
quantum mechanics for wave functions were presented, they were
presented in spherical cordinantes, which were rho, theta and phi. I
hope this is not a dumb question, but can the same angles not be
'enclosed' by spheres of diferent radii ?? Either way, the problem in
the manual relates to plane Eucledian triangles, and I believe there
are a infinite number of solutions for plane geometry in the case
sited in my note. It would seem that there is not a unique solution
either for the spherical if rho is not fixed ?? by the way , any
recommended book, which I can obtain from Amazon.com, on spherical
geometry with three spherical angles as opposed to rho , theta and
phi? As always , thanks for taking the time.

4. Re: Civility and Angles

On Thu, 19 Apr 2007 21:46:01 -0500:

> my master thesis was in quantum mechanics, when the equations in
> quantum mechanics for wave functions were presented, they were
> presented in spherical cordinates, which were rho, theta and phi.

HP48G/49G/50G calculators all have this "spherical coordinate" mode
(SPHERE) for representing individual *points* in 3-D space
in this format, relative to an origin and axes,
but solving for the angles and arcs of spherical triangles
isn't about individual points, nor relative to any particular
coordinate system, just as the solving of plane triangles
for the related angles and lengths of sides
isn't about expressing any single-point coordinates.

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