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HP Prime Triangle solver
Message #1 Posted by BruceH on 26 Nov 2013, 7:41 p.m.

Not found by me, but...

Enter: a=1E490, b=1E490, C=90. Press SOLVE

Solution found: A=90, B=0, C=90

Hmm.

Please can we have an error message if the inputs are out of bounds?

      
Re: HP Prime Triangle solver
Message #2 Posted by Tim Wessman on 26 Nov 2013, 8:22 p.m.,
in response to message #1 by BruceH

Aparently in france it is not...I've been wanting to fix this for 2 years.

TW

            
Re: HP Prime Triangle solver
Message #3 Posted by Kiyoshi Akima on 26 Nov 2013, 9:39 p.m.,
in response to message #2 by Tim Wessman

Apparently they changed something since that's a different result than what the 39gII gives.

      
Re: HP Prime Triangle solver
Message #4 Posted by cyrille de Brébisson on 27 Nov 2013, 2:04 a.m.,
in response to message #1 by BruceH

Hello,

Strange thing mathematics... We all think that they are simple and that we know them and that they are universal (after all, it looks like all extraterestrial use them to comunicate with us, because they are the 'universal language')....

And then, small stuff like that falls in :-)

As stated above, the definition of a triangle difeer per country!!! In the US, a triangle is defined by 3 non aligned points (which also forbids cases where 2 of the points are the same).

The French definition has NO limitations on any of the points. 3 points in 1 single location is still a triangle for us! We even have names for these degenerated triangles!

Your case combines issues of definitions of triangles and limits of numerical accuracy! everything there to cause troubles :-)

Fun with math!

            
Re: HP Prime Triangle solver
Message #5 Posted by Erwin Ried on 27 Nov 2013, 2:29 a.m.,
in response to message #4 by cyrille de Brébisson

US may seem to have weird formats (1) and funny units (2), but I don't think 3 points in the same location is considered a triangle anywhere except inside La France (maybe it should check the calculator language settings?)

Edited: 27 Nov 2013, 2:30 a.m.

                  
Re: HP Prime Triangle solver
Message #6 Posted by Cristian Arezzini on 27 Nov 2013, 8:12 a.m.,
in response to message #5 by Erwin Ried

In Italy too!! We also have other examples of degenerated entities (I'm thinking of the "extended" plane which includes the improper point of a straight line)... :)

                        
Re: HP Prime Triangle solver
Message #7 Posted by Gerson W. Barbosa on 27 Nov 2013, 9:33 a.m.,
in response to message #6 by Cristian Arezzini

Quote:
In Italy too!!

Everywhere:

http://en.wikipedia.org/wiki/Degeneracy_(mathematics)#Triangle

                              
Re: HP Prime Triangle solver
Message #8 Posted by Han on 27 Nov 2013, 11:31 a.m.,
in response to message #7 by Gerson W. Barbosa

Quote:
Everywhere:

http://en.wikipedia.org/wiki/Degeneracy_(mathematics)#Triangle


The degenerate cases are generally not taught in high school geometry classes (in the USA). However, I do remember seeing them (I didn't go to a typical high school, though) and they are definitely taught at the college level.

                  
Re: HP Prime Triangle solver
Message #9 Posted by Massimo Gnerucci (Italy) on 27 Nov 2013, 9:04 a.m.,
in response to message #5 by Erwin Ried

:-)

Thank you Erwin, I finally understood US units!

            
Re: HP Prime Triangle solver
Message #10 Posted by BruceH on 27 Nov 2013, 6:38 a.m.,
in response to message #4 by cyrille de Brébisson

Quote:
The French definition has NO limitations on any of the points. 3 points in 1 single location is still a triangle for us! We even have names for these degenerated triangles!
Fascinating. In that case can we have a result message that says "Degenerate solution (??) found" where ?? is the French word for that particular degenerate triangle? That way we all get to learn something and you get to help spread the French language, albeit in a small way!!
      
Re: HP Prime Triangle solver
Message #11 Posted by From Hong Kong on 27 Nov 2013, 3:21 a.m.,
in response to message #1 by BruceH

In my understanding, a should be the side opposite to angle A, b should be the side opposite to angle B and so on. Therefore, your input values should yield:

A=90
B=90
C=0

Are you sure you got the values you posted?

Edited: 27 Nov 2013, 3:22 a.m.

            
Re: HP Prime Triangle solver
Message #12 Posted by Tony Duell on 27 Nov 2013, 3:54 a.m.,
in response to message #11 by From Hong Kong

I'm the one (I think) who found this :

Enter sides a and b as 1e490. Enter angle C as 90 (in degrees mode).

Touch Solve.

It will find angles A = 90, B = 0 and side c (hypotenuse) as something like 1.4142e250

It strikes me this is an overflow error, but surely it should warn about it rather than giving nonsensical results.

Now delete B (go to the angle B box and hit backarrow) and solve again. This time it will calculate B as 90 (!).

      
Re: HP Prime Triangle solver
Message #13 Posted by Walter B on 27 Nov 2013, 4:27 a.m.,
in response to message #1 by BruceH

Generally, the angles opposite of the triangle sides a, b, c are called [alpha], [beta], [gamma] AFAIK. Do we see on the Prime another example of adaption to illiterate people?

d:-(

            
Re: HP Prime Triangle solver
Message #14 Posted by Han on 27 Nov 2013, 9:12 a.m.,
in response to message #13 by Walter B

Quote:
Generally, the angles opposite of the triangle sides a, b, c are called [alpha], [beta], [gamma] AFAIK. Do we see on the Prime another example of adaption to illiterate people?

d:-(


Actually A B C are fairly standard in geometry. In fact most labels for angles and points have been capital letters. The only place where Greek letters are still common are in the original Greek geometry texts (as far as geometry is concerned).

                  
Re: HP Prime Triangle solver
Message #15 Posted by Walter B on 27 Nov 2013, 10:52 a.m.,
in response to message #14 by Han

Quote:
Actually A B C are fairly standard in geometry. In fact most labels for angles and points have been capital letters.
Agree for points but not for angles. A quick crosscheck in Wikipedia brought e.g. this. The first picture claims this is the standard notation - even in the English edition:

d:->

                        
Re: HP Prime Triangle solver
Message #16 Posted by Han on 27 Nov 2013, 11:41 a.m.,
in response to message #15 by Walter B

Quote:

Agree for points but not for angles. A quick crosscheck in Wikipedia brought e.g. this. The first picture claims this is the standard notation - even in the English edition:

d:->


While I personally don't take info from Wikipedia as absolute truth (although I do tend to think their info is factual), here's some info on angle notation:

Convention for Angles

1. By naming the vertex of the angle (only if there is only one angle formed at that vertex; the name must be non-ambiguous) <B

2. By naming a point on each side of the angle with the vertex in between. <ABC

3. By placing a small number on the interior of the angle near the vertex.

One may of course use any variable to label an angle. While some folks prefer Greek (and it is a convention -- though not necessarily a universal convention), others will use whatever they find most convenient. As far as textbooks go, though, use of capital letters is fairly standard. They also tend to lean heavily toward #1 and #2 (at least in the US).

Edited: 27 Nov 2013, 11:46 a.m.

                              
Re: HP Prime Triangle solver
Message #17 Posted by Walter B on 27 Nov 2013, 12:25 p.m.,
in response to message #16 by Han

Quote:
While I personally don't take info from Wikipedia as absolute truth (although I do tend to think their info is factual), here's some info on angle notation:

1. By naming the vertex of the angle (only if there is only one angle formed at that vertex; the name must be non-ambiguous) <B

2. By naming a point on each side of the angle with the vertex in between. <ABC

3. By placing a small number on the interior of the angle near the vertex.

One may of course use any variable to label an angle. While some folks prefer Greek (and it is a convention -- though not necessarily a universal convention), others will use whatever they find most convenient. As far as textbooks go, though, use of capital letters is fairly standard. They also tend to lean heavily toward #1 and #2 (at least in the US).


Also I don't take info from Wikipedia as absolute truth but sometimes as counter-evidence. The "Convention for Angles" you quote from Wiki... (!) isn't universal either though reasonable to some extent (though incomplete). Did you notice, however, that throughout above posts the angle symbol '<' is missing? Thus the point A and the angle next to it carry identical names - which is also in contradiction to the convention you quote. Thus my first post above. Please let me quote Albert Einstein: "Everything should be made as simple as possible but not simpler."

d:->

                                    
Re: HP Prime Triangle solver
Message #18 Posted by Michael de Estrada on 27 Nov 2013, 12:33 p.m.,
in response to message #17 by Walter B

And to quote a far wiser philosopher named Yogi Berra, "When you arrive at a fork in the road, take it."

                                          
Re: HP Prime Triangle solver
Message #19 Posted by Marcel Samek on 27 Nov 2013, 12:39 p.m.,
in response to message #18 by Michael de Estrada

I think it might be time to stick a fork in this discussion.

                                    
Re: HP Prime Triangle solver
Message #20 Posted by Han on 27 Nov 2013, 1:05 p.m.,
in response to message #17 by Walter B

Quote:

Also I don't take info from Wikipedia as absolute truth but sometimes as counter-evidence. The "Convention for Angles" you quote from Wiki... (!) isn't universal either though reasonable to some extent (though incomplete). Did you notice, however, that throughout above posts the angle symbol '<' is missing? Thus the point A and the angle next to it carry identical names - which is also in contradiction to the convention you quote. Thus my first post above. Please let me quote Albert Einstein: "Everything should be made as simple as possible but not simpler."

d:->


Your first post was a comment about the Prime trying to accommodate illiteracy by suggesting that alpha, beta, and gamma were the standard angle names based on a wikipedia entry and that any other labels for these angles suggests (mathematical?) illiteracy. My response to that was that the choice of A, B, and C as the labels for the angles was fairly common, if not more so than the Greek notation. This most recent response is merely a technicality about whether to include the angle symbol "<" (a best approximation due to not having that symbol readily on my keyboard). This is also a likely explanation for the lack of the angle symbol within prior posts, but I think we are both speculating, no?

As for the "contradiction" -- there is no contradiction. At best, the wiki reference I mentioned is incomplete. The first bullet, if I may clarify, distinguishes cases such as a point X, being the intersection of two lines, being used as a label for an angle because there are four angles whose vertex is X. On the other hand, if X is the vertex of exactly one, unambiguous angle, then X may be used to refer to both the angle and the vertex. And when necessary, the angle symbol is used to differentiate between an angle and a vertex. The reason for the angle symbol is because of possible ambiguity (e.g. a path through points A, B, and C given by ABC vs. the angle formed by those same points: <ABC. When there is ambiguity between an angle and a point having the same labels, then the angle symbol would add clarity where it may be lacking.

Just as we do not normally use any special symbol for any measurement (length, volume, etc), we generally do not use the angle symbol when there is no possibility for confusion. This is why one rarely ever sees "sin(<x)" in any textbook. Notice that the Greek letters in the wiki entry for Solution of a Triangle do not explicitly include the angle symbol in the calculations (in fact, it is not used at all).

As for Einstein's quote -- would it not be simpler to stick with regular letters (and differentiate via upper/lower case) as opposed to having two different alphabets?

                                          
Re: HP Prime Triangle solver
Message #21 Posted by Walter B on 27 Nov 2013, 2:55 p.m.,
in response to message #20 by Han

Quote:
As for Einstein's quote -- would it not be simpler to stick with regular letters (and differentiate via upper/lower case) as opposed to having two different alphabets?
It is simple: lower and upper case Latin letters are already employed: the first for sides and the second for vertexes (vertices). Now we need something *different* for angles to avoid ambiguity: e.g. either two characters (like <A) or one letter of another alphabet. That's all. But sin(A) is plain wrong.

d:-/

                                                
Re: HP Prime Triangle solver
Message #22 Posted by Han on 27 Nov 2013, 3:47 p.m.,
in response to message #21 by Walter B

Quote:

It is simple: lower and upper case Latin letters are already employed: the first for sides and the second for vertexes (vertices). Now we need something *different* for angles to avoid ambiguity: e.g. either two characters (like <A) or one letter of another alphabet. That's all. But sin(A) is plain wrong.

d:-/


We are solving a triangle. Where is there any confusion between a point and an angle? Even without the use of the angle symbol, at what stage does the user of a triangle solver become confused with the vertex A vs. the angle A? Perhaps you have a different notion of solving a triangle -- one in which a "point" can be solved for (and hence causing confusion with solving for the corresponding angle of the same name)? Having read the other posts you've written and deduced that you do not own an HP Prime (because you stated so yourself), I must ask: are you aware that there is a corresponding picture shown in the solver on the HP Prime? In that accompanying picture, each angle is labeled at a single vertex, where there can be no confusion even if a point and an angle were labeled with the same symbol -- whether roman letter or otherwise. That said, labeling the vertices would actually cause the diagram to be more complicated than necessary (as the names of vertices are irrelevant with respect to solving triangles) -- to keep with the simplicity quote of Einstein. And though I digress, in all the diagrams listed in Wikipedia's page for solutions to a triangle, the only time the name of the vertices were ever used or referenced was in the section on solving spherical triangles. And curious still, they use the vertex label for their angles.

Your insistence that sin(A) is "plain wrong" does not make it so, and seems more like you are trying to force an issue of ambiguity where there is none. Google the law of sines or cosines and you would be further disappointed given your insistence on Greek letters for angles.

Edit: in case anyone has the wrong idea, you would be completely correct in insisting a distinction between vertex and angle in a general discussion about various components of a triangle -- i.e. in a situation where there is a need to actually distinguish a point from the vertex. But as far as solving triangles go, only the lengths of the sides and the measure of the interior angles are relevant.

Edited: 27 Nov 2013, 3:52 p.m.

                                                      
Re: HP Prime Triangle solver
Message #23 Posted by Walter B on 27 Nov 2013, 4:06 p.m.,
in response to message #22 by Han

Quote:
you would be completely correct in insisting a distinction between vertex and angle in a general discussion about various components of a triangle -- i.e. in a situation where there is a need to actually distinguish a point from the vertex. But as far as solving triangles go, only the lengths of the sides and the measure of the interior angles are relevant.
I agree on your first sentence. And in addition I don't think it's good to change notation whenever you slightly modify the problem -- I prefer to keep notation constant for such geometric figures (for sake of clarity). So we presumably agree to disagree on the second sentence.

d:-I

                        
Re: HP Prime Triangle solver
Message #24 Posted by Michael de Estrada on 27 Nov 2013, 11:41 a.m.,
in response to message #15 by Walter B

It's all Greek to me.

                              
Re: HP Prime Triangle solver
Message #25 Posted by Walter B on 27 Nov 2013, 12:10 p.m.,
in response to message #24 by Michael de Estrada

:-) Know that, been there.

            
Re: HP Prime Triangle solver
Message #26 Posted by Dale Reed on 27 Nov 2013, 1:53 p.m.,
in response to message #13 by Walter B

Okay, I'm going to stick my neck out here and go with Heath's translation to English of Euclid's Elements. Points and magnitudes are given single capital letters. Line segments (and so the sides of triangles) are always given by the two capital letters of the endpoints -- thus: "Let AB be the given finite straight line." Triangles are given by the three capital letters of the vertices: "Therefore the triangle ABC is equilateral;..."

Italics above are Heath's, not mine, by the way.

I flipped quickly through all 13 books of propositions, and not a single Greek letter or lowercase letter to be found in any diagram. ALL points are given as italicized caps, all triangles with three letters, all angles as three letters with the vertex in the middle.

Reference: Heath, Thomas L., translation, and Dana Densmore, editor: Euclid's Elements: all thirteen books complete in one volume, Green Lion Press, Santa Fe, NM, 2003. Printed and bound by Sheridan Books, Inc., Ann Arbor, MI -- ISBN 1-888009-19-5.

Just sayin'....

                  
Re: HP Prime Triangle solver
Message #27 Posted by Walter B on 27 Nov 2013, 4:15 p.m.,
in response to message #26 by Dale Reed

Quote:
I flipped quickly through all 13 books of propositions, and not a single Greek letter or lowercase letter to be found in any diagram. ALL points are given as italicized caps, all triangles with three letters, all angles as three letters with the vertex in the middle.
So Euklides, living around 300 B.C. in Alexandria (sic!), did write his books in Latin? No, I don't have any further questions, Sir.

d#-(

                        
Re: HP Prime Triangle solver
Message #28 Posted by Kiyoshi Akima on 27 Nov 2013, 5:35 p.m.,
in response to message #27 by Walter B

By that same logic the Old Testament prophets wrote in Shakespearean English, since the last Bible I leafed through was the King James version.

Dale did state that he flipped through a "translation to English" (his words).

                              
Re: HP Prime Triangle solver
Message #29 Posted by Dale Reed on 27 Nov 2013, 10:51 p.m.,
in response to message #28 by Kiyoshi Akima

Well, with a name like Thomas Heath, I assume it's nothing but the Queen's finest!

                        
Re: HP Prime Triangle solver
Message #30 Posted by Dale Reed on 28 Nov 2013, 12:03 a.m.,
in response to message #27 by Walter B

Walter -- Understood. Thanks for the reminder. Yes, I'm not a scholar of Greek or Latin, nor of the origins of mathematics / geometry, nor of higher mathematics in general. Just a lowly chemical engineer by degree (although, come to think of it, I majored in ham radio if you look at time spent!).

BTW, a capital 'alpha' sure looks like an 'A' and a capital 'beta' sure looks like a 'B' in the texts I've seen that use modern Greek letters. Numerous editions of the CRC Handbook of Chemistry and Physics come to mind.

Not having seen the original Evklides text personally, I'm afraid I'm at the mercy of respected translators like Mr. Heath to do a good job of it. The abbreviation of using the single letter of the vertex to represent an angle would seem, if Mr. Heath stayed true to Eudlid's notation, a more modern shortcut...

Enough on this tangent!


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