Talk:Straight Line and its construction
From Math Images
Smaurer1 17:48, 16 June 2010 (UTC) Well, we did have a talk, and among other things I suggested lots of revisions to the linkage history section, where engineering terms like "beam", "tension" have to be explained. When Xingda does a revision and says he wants me to look at it again, I will. I wouldn't call it 90% done.
More explanation needed
- In the second paragraph of what is a straight line?-a question rarely asked, add an explanation for cartesian coordinates
- In the second paragraph of what is a straight line?-a question rarely asked, last sentence, what if two points were on the sphere but very close to each other? Explain how the distance is a part of the great circle
- First sentence of The quest to draw a straight line - the practical need, you did not define what a straight line is. Either define it in the previous paragraph, or define it in the beginning of this paragraph
- what is mechanical linkage in The quest to draw a straight line - the practical need,? add balloon
- In your explanation of Image 3, add a sentence to this paragraph why or how the steam engine is related to straight line construction
- In your explanation of how the steam engine works (the hidden part after explanation of image 3), explain why the vertical movement of the piston is ideal
- In james watt's breakthrough section, I thought the piston had to move in a vertical direction(as you explained in previous paragraphs). Why did James Watt try to convert linear motion into circular motion?? This seems contradictory & problem seems a bad word choice
- the motion of point p section, explain why the very first paragraph is important to this page about constructing straight lines. It seems irrelevant without any explanation
- In the motion of point p - algebraic description derivation, the last part seems unfinished. If it is complicated, can you at least show the result? Or the relationship between x, y coordinates of P? It's not clear what you were trying to derive
- Is the second paragraph of the first planar straight line linkage section really relevant?
- In the inversive geometry in peaucellier section, what is inversive pairs, inversive center? add a balloon for each
- In Hart's linkage section, where did you get OP/BD=m, OQ/AC=1-m? If you are assigning OP/BD=m, say so, and show why OQ/AC=1-m
- In the same section, at the end, explain that OP*OQ is constant and explain how this is related to straight line
- in Other straight line mechanism how did you get ??
Coordination between picture and text
- 2nd paragraph of what is a straight line?, refer to image 1 & image 2
- In your explanation of Image 3, explain in more detail where the cylinder with piston is
- In your explanation of Image 5, the sentence the piston rod is confined between.... in the up-and-down motion is hard to find in the picture. Explain better?.
- In motion of point p-parametric description derivation, the vector AD can be written as (c,d) only if point A is assigned (0,0). Add this
- In the same section, in your explanation for Image 12, I can't find . Draw it in image 12
Word choice problems
- In The motion of point P - Algebraic description you use the word between the coordinates of P. Maybe you meant between the 'x- and y- coordinates of P'??
- in the same section, what does closed form mean?
- in the [[show/hide]], write show derivation of ____. what are you trying to derive?? This also works for the hide/show of parametric description
- There were some grammar mistakes and typos, but I won't write them down here
Break up long paragraphs
- Break up introduction paragraph at "These are questions that seem..."
- Break up What is a straight line paragraph at "So what is a straightness anyway?"
- Break up the paragraph above Image 4 and 5 at what used to be "Now considering that the..."
- Break up the planar linkage in action paragraph at "Mr. Prim's blowing engin..."
- Remove the content in the parenthesis in the paragraph that explains how the engine works. It is fine and less confusing without it.
- Give the imitation paragraph a heading and explain more explicitly what Watt left out in the patent.
- Switch the order of the first wo paragraphs from the the Peaucellier-lipkin section.
- Rephrase the conclusion so it sounds less preachy.
Major strengths of the page
- Great job framing the nature of the problem, its solution, and its importance
- Good sequencing of material
- Inclusion of lots of images, especially representing the same image in several different ways
- Good integration of mathematical content and non-strictly mathematical applications
- The layout is hugely improved (Anna 7/14)
- Abram, 6/4
- Anna, there are a lot layout issues hidden below that you brought up that seem satisfactorily fixed, but they are here in case you want to review them.
- Why are the images for the algebraic and parametric description of P not hidden by default? It seems like the only reason one would ever look at these images would be if one wanted to read the hidden derivation. (Abram, 7/14)
- reason 1. even if i put it under hide, it will show because it is on the first line. reason 2. they are there to remind the reader that there are stuff hidden and don't over look that. (Xingda 7/15)
- reason 1. It seems worth it to find some way around this technical glitch, so that people don't have to see the image if they aren't reading the proof. reason 2. It seems that between the all the introductory text and the new handy-dandy hide template, readers will get it. (Abram, 7/16)
- This would be less of a big deal if the images were much smaller. Basically, each image that you use for a proof fills up literally half the vertical viewing space on my 13" laptop. The images could be much smaller and still be readable. (Abram, 7/14)
- Some of the images seem smaller. Images 14, 15, and 18, and kind of Image 16, are still huge. (Abram, 7/16)
- i cannot do it. it just does not hide and it won't hide the math as more. I mean the pictures there do not bother anyone it is actually good for the smarter of the readers because once they look at the picture, they know what is coming and they don't even need to see the detailed math. it is like an experienced researcher knows what is in the a paper by simply looking at the abstract (Xingda 7/19)
- I thought Iris had some way around this? Anyway, images 14, 15, 16, and 18 could still be smaller. (Abram, 7/21)
- i shrank the images. but i tried iris's way and it won't do. i think it is because it is in a table (Xingda 7/22)
- Images 14 and 15 could still be 25% smaller or so. (Abram, 7/23)
- Some of the images seem smaller. Images 14, 15, and 18, and kind of Image 16, are still huge. (Abram, 7/16)
Amount of material
We may come back to this issue, but for now, it's good.
Philosophical discussion about straightness is a bit confusing
The basic description of the page is really interesting. It just throws me off-balance makes it seem like the page will be devoted in equal parts to a philosophical discussion about a) what defines straightness and b) how to make straight things. In fact, 90% page is devoted to the question of how to create a linkage that will force a point to move in a straight line. For a similar reason, it seems a little bit strange to right, "Hopefully, you will start questioning the flatness of a plane, roundness of a circle and the nature of a point. This was how real science and amazing discoveries were made and this is how you should learn and appreciate them." (This sentence is also really preachy).
Moreover, I'm not sure that the section on "What is a straight line - a question rarely asked" is actually that helpful. In the space of one small paragraph, you introduce two or three different ideas, none of which are actually all that relevant to the main purpose of the page. The problem may just be bringing up great circles. It seems weird to bring up this *caveat* to the definition of a sraight line as the shortest distance between two points, when the definition of straightness is not the main point of the page. It's not that having tangential information is bad, and I also like the idea of starting with this question of straightness. That is all fine. And again, it's all interesting. It's just that it's hard for me as a reader to know what you're getting at.
Later, you mention that creasing a paper is an easy way to create a straight line. This is *great* material, and should be moved to the same area where you are discussing the definition of straightness. This example is a great way of giving the reader a sense that, "Oh, making a straight line is really easy, but making a linkage that forces points to move in a straight line is really hard", especially if you point this out explicitly. (Abram, 7/14)
1. the purpose of the page is restated as "This page explores the answer to the question "how do you construct something straight without a straight edge?" " so we don't get hung up on "what is straight line" business.
This looks good, except that the page is really about creating a linkage that forces a line to move in a straight point, not about the general topic of constructing something straight without a straightedge. (Abram, 7/16)
- now it reads "This page explores the answer to the question "how do you construct a straight line without a straight edge?"" i think we dont have to talk about linkage that early. (Xingda 7/19)
- Now that you mention linkages in the Question Rarely Asked section, I agree. The only problem is that *that* sentence about linkages (in the Question Rarely Asked section) is confusing. The sentence is "However, to achieve our ultimate goal, the linkage that produces a straight line motion..." but it seems to come out of left field. You haven't been talking about linkages at all, and now suddenly it's our ultimate goal. Why? What if you put a sentence before it introducing the reader to the challenge (and purpose) of creating such a linkage. (Abram, 7/21)
- done (Xingda 7/22)
- This sentence is still kinda confusing. If our goal is simply to create a straight line without a straightedge, why do we "need" a linkage? Didn't we just say folding a piece of paper would work. You probably need a full sentence to explain why we are interested in linkages, or you can drop this sentence entirely, and replace it with something like, "This page, however, focuses specifically on the history of making machine parts move in a straight line in engineering contexts" or something like that. (Abram, 7/23)
2. "What is straight.....rarely asked" section points out the fact that the concept of being straight is not easy to articulate we cannot take it for granted. but that is not the whole point of the page. The last sentence of the section know reads "The rest of the page revolves around the discussion of straight line linkage's history and its mathematical explanation." (Xingda 7/15)
Yeah, I get the point, and I think it's a really good one. The problem is just that there are so many ideas: a Cartesian definition of straightness, an "intuitive" definition of straightness (shortest distance), a *caveat* on the "intuitive" definition of straightness, a discussion of how the motion of a beam of light *isn't* straight, and the idea of creasing a paper. (Abram, 7/16)
Some inconsistencies in scope
There are a few places where you either give some information about a topic but not enough for it to actually be useful, or where there is inconsistency in scope: the amount of detail you go into about idea X isn't commensurate with the amount of detail you go into about idea Y. An extreme example of this kind of problem would be if I were to say to you, "Tell me about London. I've never been there", and you responded, "In order to get to the main post office, you have to take the green line of the Tube. The fare is 2 pounds."
- The section on Mr. Prim's reciprocating airpump is confusing. What is a reciprocating airpump? Why do you mention "The slate-lined air cylinders had rubber-flap inlet and exhaust valves and a piston whose periphery was formed by two rows of brush bristles. Prim's machine was driven by a steam engine?" I assume this meant to help explain Image 17, but that is not nearly enough to explain it.
- see response to point 1
- Two things. First, see my response to your response to point 1. Second, this is a totally separate issue. Point 1 is about a sentence that doesn't make any sense unless the reader clicks on the hidden text. Point 2 is about some confusing stuff that isn't explained *anywhere* on the page. Here the approach seems to be, "Confuse the hell out of them! Then they'll click on external links!" (Abram, 7/16)
Small, easy fixes
- Put the definition of a great circle either in a mouse over or in it's own sentence. You've got too many clauses there. (Anna 6/25)
- I don't quite get what you mean. (Xingda 6/28)
- Read the sentence out loud, and you might be able to tell that it's kind of awkward. If you put the definition of a great circle in a mouse-over, it may feel much less so. (Abram, 7/16)
- You've got a couple of places where you say "We intend to..." but you don't explicitly state WHY. Make sure your reader understands the motivation behind what's going on.
- There are only two instances that I used "we intend to" and now the issue is addressed (Xingda 6/28)
- Looks good to me now. (Abram, 7/16)
- Drop all references to "I", "My", etc. (Abram, mid-July sometime)
The purpose of the parameterization section is not clear and/or this section is overkill
You've done a huge amount of work on the algebraic and parametric descriptions of the path traced by P, and congratulations on wading through all that algebra! Well-done. Here are some concerns about this section, however:
- If the point of this section is to show that P does not move in a straight line, there is a much easier way to achieve this. We discussed an outline of this reasoning at the chalkboard a few weeks ago. I can fill in the details if you would like.
- In a similar vein, how does the final parametric equation show that P does not move in a vertical line? There's currently no proof included that the nasty equation you end up with can't be simplified to something much nicer, especially given that the equation involves alpha, which is defined in terms of l, which is itself changing. And similarly for the equations for x' and y'.
- I think we don't even have to prove that it does not move in straight line. The animation already does that. I think the point of parametrization is to know the position of . Also, the final parametrization does not involve at all. It is in terms of and which are known quantities. (Xingda, 7/7)
- If the point of the section is something other than demonstrating that P does not move in a straight line, then this section is straying pretty far from the purpose of the page (see also "Amount of Material" discussion below). If you want to include it, it should at least be hidden.
- Abram, 6/30
- I change the beginning sentence to "We intend to described the path of so that we could show it does not move in a straight line (which is obvious) and more importantly to pinpoint the position of using certain parameter we know such as the angle of rotation or one coordinate of point . This is awfully important in engineering as engineers would like to know that there are no two parts of the machine will collide with each other throughout the motion. " Also, I added some mini introductions to both Algebraic and Parametric section so the train of thought is not broken and the math is not so abrupt. Does that work? (Xingda, 7/7)
- Abram, 6/30
This looks great, except for a layout issue that is described in the "layout issues" section. (Abram, 7/14)
- Number images and animations. Replace every reference to an image that currently says something like "image to the right" with a reference to the image number. Right now I sometimes truly have no idea what you are referring to. Some of these images may end up getting removed, though (see "Amount of material" discussion below).(Abram, 6/30)
- Issue addressed (Xingda, 7/7)
- Looks good. (Abram, 7/14)
Small, easy fixes
- Drop the triple dots meaning "therefore" and "because". The "therefore" dots aren't used very often, and the "because" dots are just about never used, at least in American sources that I've seen (Abram, 6/4).: Issue addressed (Xingda 6/28)
- I definitely agree with dropping the dots. (Anna 6/25)
- Issue addressed (Xingda 6/28)
- Looks good. (Abram, 7/14)
Define engineering terms
The terms "linkage", "member", and "flywheel" are all used, and many readers won't know what they mean. (Abram, 6/30)
- Issue addressed. I either used balloon or external link to give definition. (Xingda, 7/7)
- Great. The only problem is the mouse-over definition of linkage. As we (very briefly) discussed one meeting, if we only have a sentence or two of text preceding the table of contents, that text is often overlooked, so many readers will never see your mouse-over definition. (Abram, 7/14)
- Issue addressed. (Xingda 7/15)
- Sorry, how was this addressed? (Abram, 7/16)
- I repeated the mouseover definition of linkage again. Is that not good enough? (Xingda, 7/19)
- Yeah, that's fine. For some reason it didn't appear as a mouse-over when I was viewing it. The only thing is, now that you've mentioned linkages in "A Question Rarely Asked", the repeat mouse-over should go there instead of at its current location. (Abram, 7/21)
- done (Xingda, 7/22)
- Looks good. (Abram, 7/23)
Problems with the "imitations" section
- "How would we find the parametric equation for point F then?" currently only hides "It is easy enough. Refer to Image 12." (Abram, 7/14)
- cannot help it. that is the template
- Can't you hide as much or as little as you want? (Abram, 7/16)
- No, it shows previews of a few lines only and hides the rest but since in this case there are only a few lines and all of them are math, they show up in preview (Xingda 7/19)
- I thought Iris had a way around this problem? (Abram, 7/21)
- taken care of long time ago (Xingda 7/22)
- Great. (Abram, 7/23)