Wikipedia:Reference desk/Archives/Mathematics/2016 April 24

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April 24

Card models ( making a Bridge Arch)...

Posting in maths , but it's essentialy a geometric construction problem.

I have the elevation of a bridge. ( for example File:Bridges_27.png)

I'd like to use 2 elevations and a centre piece modelled in card.

How do I construct the flattened centre piece from the eleveation? Sfan00 IMG (talk) 11:19, 24 April 2016 (UTC)

I.E How do I construct a line that is equal in distance to the length of an arc? ShakespeareFan00 (talk) 08:52, 25 April 2016 (UTC)

If it's not piecewise straight or circular, you'll need to do some integrating. Have you a mathematical description of the arc? —Tamfang (talk) 09:00, 25 April 2016 (UTC)

I'm not an expert on bridge construction, but my observations of bridge arches lead me to the conclusion that quite a wide range of curves are possible and used in practice. Perhaps an engineer can advise on the strongest. The oldest bridges seem to be closer to a circular arc. Dbfirs 11:24, 25 April 2016 (UTC)

I don't have a mathematical description, but I do have the elevation (like in the example image given..)ShakespeareFan00 (talk) 12:20, 25 April 2016 (UTC)

See Catenary arch. Bo Jacoby (talk) 16:37, 25 April 2016 (UTC).

At first I thought you were building a bridge out of playing cards, but now I think you meant something else by "card". Care to elaborate ? StuRat (talk) 17:11, 25 April 2016 (UTC)

paper model ShakespeareFan00 (talk) 18:53, 25 April 2016 (UTC)

I see, card stock versus playing cards. StuRat (talk) 19:03, 25 April 2016 (UTC)

I suggest a "practical method". In this case, place a string over your illustration, following the arc, measure it's length, and apply the scale difference between the illustration and your model. StuRat (talk) 19:07, 25 April 2016 (UTC)

Thanks, that will work but I was sure there was a geometrical method I could use in Inkscape. Bridge arches are just the start of what I'm trying to do. Sfan00 IMG (talk) 19:14, 25 April 2016 (UTC)

This is the elevation I have - File:Model bridge.svg, There should be a geometric approach that let's me find how long to make the piece of card for the arch (lablled.) ShakespeareFan00 (talk) 12:18, 28 April 2016 (UTC)

• It should be able to be reasonably approximated by a conic section, and I believe those can be defined by 5 points. So, if you can find the coords of the 2 endpoints and 3 interior points you should be able to find a formula for the arc length.

• Another method is just to break it down into many tiny line segments, and add the lengths. If you can find each point on the curve accurately, this should work well, and has the advantage of working for any curve (or flat), although you would need to be careful in how you find the points, in the case of horizontal or vertical curves, or those which bend back on themselves. StuRat (talk) 12:41, 28 April 2016 (UTC)

Arc length for an ellipse is nontrivial; I don't think it has a closed expression. —Tamfang (talk) 07:09, 29 April 2016 (UTC)

It does not. See elliptic integral.--Jasper Deng (talk) 15:33, 29 April 2016 (UTC)

OK, then my second option sounds like the best choice. StuRat (talk) 16:04, 29 April 2016 (UTC)

My data does not make sense.

I have an Excel spreadsheet. The data is located here: User:Joseph A. Spadaro/Sandbox/Page79. (That is one column of data from my Excel spreadsheet. I just did a copy-and-paste.) Excel tells me that I have 66 data points. The sum of all of the data points is negative 100.12. And the average of all of the data points is negative 0.23. This does not seem to make any sense to me. Can this possibly be accurate? If not, what's the problem in Excel that I am not seeing? Thanks. Joseph A. Spadaro (talk) 18:46, 24 April 2016 (UTC)

If there is a blank cell in the column, does Excel treat that cell as a value of zero? But, even if that were the case (which I do not think that it is), the average still does not seem correct. What could be going on? Joseph A. Spadaro (talk) 18:53, 24 April 2016 (UTC)

Excel treats blank entries as if they're not there. I pasted the data into my own Excel spreadsheet and it tells me that average is -1.517 which I assume is correct. But there may be some setting somewhere that tells Excel to treat blanks as 0, which might explain what you're getting. Another likely explanation is that the range of cells you're averaging over doesn't include all the data; this can easily happen if you're adding/removing the numbers from month to month. --RDBury (talk) 19:20, 24 April 2016 (UTC)

Thanks. What is have is a bunch of rows. Let's say 75. And I fill them up one-by-one (each month). So, apparently, I got down to Row 66. In this column, there are 9 blank rows under the data. I take the sum -- and also the average -- of the entire column (from Row 1 all the way down to Row 75). This way, the sum and average will change month-by-month as each Row value is added. That should work correctly. Also, even if Excel puts "zero" in each blank cell, that average does not come out right. Is there a way to attach/include the actual spreadsheet somehow? Joseph A. Spadaro (talk) 19:43, 24 April 2016 (UTC)

@Joseph A. Spadaro: You could upload it to google drive (or another cloud platform) and link it from there —  crh ₂₃  (Talk) 19:45, 24 April 2016 (UTC)

Thanks. How do I do all that? I have no idea what that even means. Joseph A. Spadaro (talk) 20:20, 24 April 2016 (UTC)

Just go to the Google Drive website and either log in (if you already have a Google account such as Gmail), or create a new account. My Excel agrees with RDBury's average of negative 1.517. What formulas appear in your total and average cells? We might be able to diagnose the problem from those. Dbfirs 11:36, 25 April 2016 (UTC)

These are the three formulas ... =COUNT(H3:H82) ... =SUM(H3:H82) ... and, lastly, ... =AVERAGE(H43:H82) ... Thanks. Joseph A. Spadaro (talk) 13:10, 25 April 2016 (UTC)

Unless H43 is a typo for H3, that could be where your problem is. Gandalf61 (talk) 13:44, 25 April 2016 (UTC)

That may be it! I will double check! Thanks. Joseph A. Spadaro (talk) 19:17, 25 April 2016 (UTC)

O.M.G. --JBL (talk) 14:46, 25 April 2016 (UTC)

One potential problem is if the range of cells which is averaged is finite, and you keep adding items, then you eventually exceed that range. From your description above it sounds like you have 80 cells in the range, and currently have 66 entries, so you won't hit this limit for another 14 months. If there's a way to define the cell range to be infinite, or at least large enough that you will never hit the end, like 1000, then that will fix the problem. StuRat (talk) 15:52, 25 April 2016 (UTC)

That's a good point. And I always consider that. When I have to add in a new row, I always add it into the middle of the range somewhere. I never add it right at the end (i.e., the last row). This helps to preclude the common error of having to modify the formula (when you extend the range by adding new rows) yet forgetting to do so. So I can just keep the old formula. And the old formula simply adjusts itself when new rows are added in to the middle of the range. Joseph A. Spadaro (talk) 19:15, 25 April 2016 (UTC)

Follow up question

Referring to the above problem, it seems that the error came about as a typo in a cell formula. The formula was =AVERAGE(H43:H82), which contained a typo. It should have been =AVERAGE(H3:H82). My question is: does Excel have any type of way to "catch" an error like this? Thanks. Joseph A. Spadaro (talk) 03:44, 26 April 2016 (UTC)

Excel sometimes puts a little green triangle at the top left corner to indicate a problem of some kind, such as a formula that isn't consistent with those around it. When the cell is selected you get an icon you can hover over to see a detailed message: with a similar situation to yours I got "The formula in this cell differs from the formulas in this area of the spreadsheet". AndrewWTaylor (talk) 07:47, 26 April 2016 (UTC)

Hatted off-topic discussion

I must have missed the part of this discussion where you made a general apology for wasting people's time. --JBL (talk) 13:12, 26 April 2016 (UTC) To - Joel B. Lewis (JBL). Give me an honest answer to this question. Do you think that this was an honest and sincere mistake? Or do you think this was some big elaborate scheme that I concocted for the devious and nefarious plot to waste people's time? What's your honest answer to that question? Joseph A. Spadaro (talk) 04:48, 28 April 2016 (UTC) That's rather unnecessarily harsh. I see it as an example of tunnel vision, where he couldn't see that the formula was wrong even when he cut and pasted it here, because he wasn't looking at the lower limit as a possible problem. StuRat (talk) 16:16, 27 April 2016 (UTC) I agree that this is an easy mistake to make and that we shouldn't be harsh, and I had half a mind to make a comment to that effect myself - however, JBL didn't ask the OP to perform Harakiri for the shame of committing unforgivable sins. He merely asked for an apology. Given that the OP's silly, non-mathematical mistake did bring about a wasting of time, an apology isn't too much to expect. -- Meni Rosenfeld (talk) 21:26, 27 April 2016 (UTC) Tell me what, pray tell, I should be apologizing for? Please be specific. And if this whole thing is such a waste of your precious time, why are you expending any time here replying? Joseph A. Spadaro (talk) 04:42, 28 April 2016 (UTC) Please note that I didn't ask you for an apology, JBL did. I was merely replying to StuRat and explaining JBL's reasoning. You don't need to be defensive and hostile about everything. It's not my time that was wasted - I didn't participate in the discussion. I am speaking with 0% skin in the game. As for expending time replying - I believe discussing the finer points of this forum's etiquette is a productive use of my time. (Well, probably not, but that's my own problem). As for what you should be apologizing for - You made a typing/visual error in your spreadsheet. This has caused you to ask a question in this forum, which is meant for helping people with mathematical problems, including also dealing with mathematical mistakes that they make. This has led several people on a wild goose chase, trying to find a mathematical error that is not there. As it turns out, people have been wasting their time debugging a non-mathematical error, which is not what they signed up for when they volunteered to reply here. To summarize - discomfort to others has been brought about by your actions. By definition, when this happens one should apologize - it doesn't matter that this was all a result of an honest mistake, and an easy one to make at that (see also reply to StuRat below). It's not like giving an apology is such a big deal - it can be as easy as adding "Sorry about that!" to the followup question. Anyway, I apologize for upsetting you with my comment. (That was a sincere apology, though not particularly heartfelt; and also a demonstration of how easy that is.) -- Meni Rosenfeld (talk) 08:41, 28 April 2016 (UTC) If he had intentionally wasted our time I might agree, but an accidental oversight doesn't require an apology, IMHO. StuRat (talk) 23:18, 27 April 2016 (UTC) We seem to have different definitions of apology. Intention to do harm is definitely not a prerequisite. Apologies can be about regret for bad actions or poor choices but they don't have to be, they are about empathy more than anything else. When one realizes discomfort/harm was caused to others as a result of his actions, he should apologize - even if he couldn't have done anything better! (In our case, I believe the OP's mistake is excusable but he wasn't 100% in the right either, he could have triple-checked for typos before coming here). -- Meni Rosenfeld (talk) 08:41, 28 April 2016 (UTC) I am the OP. I assure you that no apology will be forthcoming. Please bank on that. I do, however, say "thanks" to those who helped answer my query. Most of you, that is. Not all. Thanks. Joseph A. Spadaro (talk) 04:35, 28 April 2016 (UTC) This fact, however, cracks me up. An individual editor considers this question a "waste of his time". Yet, he goes out of his way to take the time to read, respond, and so forth. Not once, but multiple times. Indicating that he "followed" the conversation. It's a waste of his time. Yet, he finds time to invest in it. You can't make this shit up! Joseph A. Spadaro (talk) 04:39, 28 April 2016 (UTC) Instead of laughing, consider trying to understand other people's motivations. Like me, JBL has found it appropriate to spend time refining this forum's etiquette. This has nothing to do with the effectiveness of spending time on the original question. And also, it doesn't take much time at all to scan the thread looking for an apology - much less time than it took to try answering the original question, as some people did. If you'll excuse my armchair psychology, I'd say that both your reluctance to apologize, and the lack of interest in understanding people's motivations, might indicate a problem with empathizing. You might want to work on that. -- Meni Rosenfeld (talk) 08:41, 28 April 2016 (UTC) @StuRat:, @Joseph A. Spadaro:, this is what happened the last time I wasted someone's time on the refdesk by my own sloppiness. Joseph A. Spadaro, you would be well-served to read and reflect on Meni Rosenfeld's excellent, thoughtful comments. --JBL (talk) 12:39, 28 April 2016 (UTC) I also recommend watching Vsauce - The Science of Awkwardness. While not directly about what the whole apologies issue, it is very relevant. Vsauce, by the way, is an excellent channel that also discusses mathematical topics. -- Meni Rosenfeld (talk) 14:55, 28 April 2016 (UTC) Hey User:Joel B. Lewis- this is indeed very funny. Since you're pinging other users, I assume you are soliciting further comment. I warn you, you might feel that reading this a waste of your time so proceed at your own risk! I wonder: would you yell at a student in your office hours for wasting your time, and demand an apology because they had made a typo and not some deeper error? I sincerely hope not. At least you presumably have been paid to teach, so wasting of time is at least potentially possible in that scenario. But here, you are not paid, and you can't blame anyone else for the time you choose to volunteer here. Well you can, and you did, but it reflects poorly on you. If you aren't happy with the time spent, don't do it. Learn your lesson and move on. OP Joseph asks tons of questions here, but mostly on other desks. He is not a scientist, not a mathematician, and not an expert computer user. Like many, he comes here for help, because he doesn't know what the answer is or how to find it. Sometimes I can help Joseph, sometimes I do help, sometimes I walk away because it looks like it might be a waste of my time. OP's question and follow up are both fine, and I completely understand him feeling ill-used by your demand for apology. Blaming the asker is rude and childish, and you should know better. SemanticMantis (talk) 15:39, 28 April 2016 (UTC) What does this long rant have to do with anything I or anyone else has said? For example, can you please point out exactly where I did something that could be construed as "yelling" or "blaming" anyone for anything? I refer you to Meni Rosenfeld's comments above in case you care to learn what the actual issues are here. (I would also be perfectly happy just to have you retract your comment and this one without further comment.) --JBL (talk) 16:11, 28 April 2016 (UTC) "I must have missed the part of this discussion where you made a general apology for wasting people's time." - bolded for clarity, said by you, not long ago, for no good reason that I can see. That's what it has to do with this thread. True, it was not "yelling", but it was out of line, and then rather than walking away, you doubled down. That is why I wrote those words. I wrote to stand up for Joseph and many other users who are sometimes mistreated here. You are not the only one who is rude and dismissive to askers, but you're the one who I saw doing it today. I am not singling you out. If you pay attention and look around, you'll see me telling other users to play nice too. It's just a matter of WP:AGF and WP:CIVIL. With some more practice and attention, I think you can get better at those, and learn that they are good policies that make WP better for all of us. SemanticMantis (talk) 17:01, 28 April 2016 (UTC) By "doubled down" you appear to mean "pointed out to users who questioned whether I believe the view I put forward that I practice what I preach." This is an unconventional usage, to say the least. Perhaps, while you're quoting policies about civility at me, you could go retract all the personal content in your comments? --JBL (talk) 17:29, 28 April 2016 (UTC) Meta-meta comment: I agree that this sub-thread should be collapsed, so as not to distract from the primary questions being asked. I don't agree that "probably nobody should [read it]". Obviously there are differing views about the respective responsibilities of question askers and answerers. Discussing these matters is important if we want to improve as a community. -- Meni Rosenfeld (talk) 20:11, 30 April 2016 (UTC)

Rings surjecting to localizations

Let R be a commutative ring. When is it true that the natural map from R to S^-1R is surjective for every multiplicative subset S of R? Is this equivalent to every prime ideal of R being maximal? GeoffreyT2000 (talk) 21:38, 24 April 2016 (UTC)

Do you mean Epimorphism, not Surjection?John Z (talk) 22:21, 24 April 2016 (UTC)

1. If R→S^-1R is surjective then S contains only units. Since if s is in S, there must be r in R so r→r/1=1/s, which implies rs=1.
2. If P is a prime ideal then S=R-P is multiplicative. If R→S^-1R is onto then R-P must contain only units, in other words P is maximal.

I believe that proves one direction, but Z is a counterexample for the other direction. Z-pZ is multiplicative but certainly contains non-units. Actually I'm having a hard time coming up with an example where the first condition holds other than a field. Maybe a local ring?--RDBury (talk) 08:27, 27 April 2016 (UTC)