Wikipedia:Featured picture candidates/pi

From Wikipedia, the free encyclopedia

[edit] Pi

Factual and interesting representation of how pi helps figure out the circumcfrence of a circle.

• Nominate and Support -- Viva La Vie Boheme! 01:04, 15 August 2006 (UTC)

• Oppose. Informative, but badly needs antialiasing and a better choice of colors. Redquark 01:31, 15 August 2006 (UTC)

what's wrong with the colors?Nnfolz 03:17, 15 August 2006 (UTC)

• Support I wish i had this animation back when I was learning this. it would have helped me understand the whole concept (and relations between them) so much better. very valuable contribution, nice addittion to wikipedia.Nnfolz 03:17, 15 August 2006 (UTC)
• Weak support. It does need some antialiasing, but it is so useful for those trying to grasp the concept that I think that overrides the ultimately-unimportant aesthetic factor. — BRIAN0918 • 2006-08-15 03:35
• Oppose per Redquark. --Hetar 03:53, 15 August 2006 (UTC)
• Neutral. It's a useful teaching tool, but its pedagogical value would be greater if the circle had only a single, thin spoke -- which would make the fact that it's turning exactly once more obvious. (I realize the bold red line achieves the same purpose, but the viewer has to realize that the red line is what's important, and pay attention to it rather than the spokes.) Also, I don't like that the arrowhead is shaped like a heart (and red, too) - a stylistic choice that adds nothing to the pedagogical value, but might make one wonder "Why a heart?" -- Moondigger 03:59, 15 August 2006 (UTC)
• Oppose for several reasons, the main being that this gives an impression that pi somehow represents the red-shaded area. Other reasons: Aliasing, strange-looking arrow point, red circumference too close in color to red-brown wheel, animation is a little too fast. --Janke | Talk 04:24, 15 August 2006 (UTC)
  • It actualy is the area as well. --Dschwen 06:38, 15 August 2006 (UTC)
    • Nope - the area of that rectangle is much larger than the area of the wheel - or there's something far more wrong with my eyes than just myopia... It's πr² vs. π, and since r is 0.5, the rectangle has four times the area of the wheel! --Janke | Talk 08:12, 15 August 2006 (UTC)
      • Correct, π is four times the area of that wheel... I'm not sure where your problem is? Note that this image is concerned primarily with the circumference of the wheel, not its area. I guess your confusion arises from the illustration of π as an area in the first place; for consistency, it might be better to represent it as a one-dimensional length. Redquark 13:27, 15 August 2006 (UTC)
        • Exactly. Just a red line, length π. --Janke | Talk 18:08, 15 August 2006 (UTC)
      • Dschwen never said the area of the rectangle was less than that of the wheel. Reread the comments. The length of the rectangle is pi, and the area of it is also pi, because the height is 1. That's all Dschwen was saying. — BRIAN0918 • 2006-08-17 15:10
      • And the rectangle has sides with length π and length 1. That makes the area 1*π (which is π last time I checked ;-) )--Dschwen 16:16, 15 August 2006 (UTC)
        • Well still not quite right ;-). The diagram above shows a circle/wheel with a diameter of 1 unit (it could be centimeters, feet, light years, etc.). Each mark of 1, 2, 3 and 4 represent 1, 2, 3 and 4 units, respectively. We'll call this unknown unit "u". Now, if you "roll" out the circumference of this wheel, you get π units. You just said that 1*π = π, but you're forgetting your units. It's really 1 unit * π units, which equals π units squared (1 u * π u = π u²). As an example, you could replace units (u) with centimeters (cm). That would give you 1 cm * π cm = π cm². ...So if anyone wants my opinion, I think the way the diagram displays the shaded region as π could be misleading to someone who didn't understand what π exactly was. I should just be left as a red line to clarify that π was a length, not an area. --Tewy 19:23, 15 August 2006 (UTC)
          • Yes, it's π cm², not π² cm. The diagram is accurate in its depiction of area. I do agree that it would be simpler to ignore the area question completely for the purposes of this demonstration. -- Moondigger 20:54, 15 August 2006 (UTC)
          • still not quite right? Sorry, but this is getting ridiculous. π is unitless and neither a length nor an area. Nowhere is a unit u mentionend in the diagram. So whether you are looking at the line or the area it is π in any case. Full stop. --Dschwen 23:23, 16 August 2006 (UTC)
            • Ha ha, ok, you're right, I made the mistake of calling the rolled-out length π, when it was really the circumference of length π. I meant to say that if you were looking at the diagram and seeing the rolled-out length (the circumference), you would have to deal with units...but yes, π is unitless, and I agree this is getting out of hand, so I'll stop. I think I can safely conclude that this diagram is confusing though, as it only shows that a circle of diameter 1 has a circumference of π, and not that π is the ratio of the circumference to the diameter. --Tewy 23:56, 16 August 2006 (UTC)
• Weak support. Per all above (Both positive and negative comments). It explains the concept well, but not well enough, and could use some simplification in colors, spokes, etc. --Tewy 05:06, 15 August 2006 (UTC)
  • Weak oppose. After reading and participating in these vast discussions on what π is and how the diagram represents it, it is extremely clear that this diagram is highly confusing to voters, let alone new learners of the subject. The idea is a good one, but was executed in the wrong way, i.e., the rectangle, only showing that a circle with a diameter of 1 has a circumference of π (but how would new learners apply that to a circle of diameter 2?), and the minor details of the spokes, colors, etc. that I mentioned above. I will support this diagram if it is recreated to address all the comments that have been added to this page. --Tewy 18:26, 18 August 2006 (UTC)
• Oppose - poor resolution, hard to understand for average viewer, poor graphics, not that eye-catching. --GoOdCoNtEnT 07:36, 15 August 2006 (UTC)
• Oppose this version, but would support a rehashing to address the concerns above. --Yummifruitbat 12:10, 15 August 2006 (UTC)
• Oppose I would support this if it was antialiased, larger, and perhaps less bright primary colors. HighInBC 12:53, 15 August 2006 (UTC)
• Oppose. per Janke and others. say1988 21:56, 15 August 2006 (UTC)
• Support personally, i think it's very interesting and encyclopedic, and that these qualities overrides the color and the heart-shaped arrow issue. --Vircabutar 23:14, 15 August 2006 (UTC)
• Oppose. Good idea, but a FP should look slick and professional. This doesn't. —Keenan Pepper 01:53, 16 August 2006 (UTC)
• Oppose Good idea but flawed execution per above. Perhaps the original artist will try to improve it, taking these comments into account -- if not, it's still a good addition to the article, but not quite up to FP standards.--Eloquence* 10:57, 16 August 2006 (UTC)
• Oppose until Pi ceases to be shown as an area - Adrian Pingstone 14:23, 16 August 2006 (UTC)
  • That would be trickly so long as we use pixels. --Billpg 14:42, 16 August 2006 (UTC)
    • Obviously I meant that the box should be removed and the unrolling red line left there - Adrian Pingstone 17:30, 16 August 2006 (UTC)
• Oppose per Yummifruitbat. --Billpg 14:42, 16 August 2006 (UTC)
• Neutral. The heart and color scheme say 'Pi is for Girls!', which is rather amusing. But it isn't clear that the red line is more important then the spokes on the wheel, and the line turning into a big rectangle could be misunderstood. —Preceding unsigned comment added by Algr (talk • contribs)
• Oppose. The notion of an area in this diagram is apperently confusing and misleading. Nice idea though. --Dschwen 23:36, 16 August 2006 (UTC)
• Strong support First off, the area *is* Pi, we should strike all votes claiming otherwise because they are factually inaccurate. Secondly, the complaints about the point being heart shaped are unreasonable: Plumb-bob's often have heart shaped cross sections and are often illustrated as such in patent drawings, for example. Thirdly, because this is an animated GIF the resolution can't be greater because our scaling for animated gifs is almost totally broken... And finally, because of the limited colors in GIF the possibilities of anti-aliasing without introducing additional artifacts are pretty limited. --Gmaxwell 04:54, 17 August 2006 (UTC)
• Oppose. Just because the area is numerically equivalent to the value of Pi, does not mean the area is Pi; as some were getting at above, Pi is a constant with no units and no dimensions. To represent it as an area is clearly misleading. I'm not even convinced the author intended this, but it has caused enough confusion here to lead me to oppose. --jjron 12:30, 17 August 2006 (UTC)

Comment: jjron, the area you describe is Pi (units²). That's like saying 2 isn't a number because it doesn't have units or dimensions. 1+1=2. 1x2=2. Or, we can specify units. 1 unit + 1 unit = 2 units. A rectangle with a long side of 2 units and a short side of 1 unit has an area of 2 units². A rectangle with a long side equivalent in length to the circumference of a circle and a short side equivalent in length to the same circle's diameter has an area of Pi units².

Pi is more than just the ratio of the circumference of a circle to its diameter -- though that is the most famous definition and the one first taught. But just as "2" is more than just 1+1 (it's also the square root of 4; 18 divided by 9; etc), Pi can also be described other ways. For example, it is the ratio of the area of a circle to the area outside the same circle but within a square with sides of one circle diameter length. (This would be easier to imagine with a picture -- draw a square on a piece of paper, and then draw a circle within it that touches all four sides. The ratio of the area within the circle to the area outside the circle but within the square is Pi.)

Area in circle: пr^2. Area in square: 4r^2. Area outside circle but in square: 4r^2 - пr^2. How do you get п from any ratio?? — BRIAN0918 • 2006-08-17 19:03

Hazy and apparently incorrect recollection of a programming project I did in college 17 years ago. Whoops. It's the ratio of a circle's area to the area of a square with sides the same length as the circle's radius. My first example was bad, but the point stands... Pi can be defined by methods other than the ratio of the circumference of a circle to its diameter. -- Moondigger 19:52, 17 August 2006 (UTC)

Back to the animation we've been discussing. If the point is to demonstrate the ratio of a circle's circumference to its diameter, specifying the area of the rectangle laid out in the animation is superfluous and potentially confusing. That it lacks the units² designation is potentially even more confusing, though it's no more 'incorrect' than if somebody made an animation showing a rectangle twice as long on one side as the other, and calling the area "2." (The units² is understood.) In any case, I agree this animation shouldn't even bother specifying the area. -- Moondigger 13:33, 17 August 2006 (UTC)

Eh, I didn't think it did specify the area.. though I suppose we'd have to ask the author. But the area is as much Pi as it could be 3 if the box ended a bit earlier. --Gmaxwell 19:34, 17 August 2006 (UTC)

But if the box 'ended earlier,' it wouldn't have a side that's equivalent to the circumference of the circle, with the circle's diameter as its height. -- Moondigger 19:55, 17 August 2006 (UTC)

That comment of mine was to address the complaint that unitlessness was a problem, I wasn't suggesting a change. I wouldn't change anything about the image. --Gmaxwell 19:59, 17 August 2006 (UTC)

Ah, I understand now -- I agree that unitlessness is not a problem from a technical perspective, since the "units²" is generally understood. But I do think demonstrating the area in the 'growing pink rectangle' is ill-advised from a pedagogical perspective. -- Moondigger 20:31, 17 August 2006 (UTC)

Sigh. Firstly, Moondigger, that stuff you were saying about 2 was the strangest thing I've ever read from you - if it made any sense it could only be that you totally misinterpreted my comment.

Now, an analogy for those who think π and π units² are the same thing. I ask you to do a job and say I'll pay you $100 for it. After you've done the job I give you a scrap of paper with the number 100 written on it. Now are you going to be happy with my payment? Unlikely. But when you argue that π and π units² are the same thing, you are making the same mistake. π is not the same as π units² (just as the $100 is different from the number 100). You see, the units do make a difference. The number is the same, but the thing is not.

When you also say that "the units² is generally understood", that is also not valid. Let's be realistic; is this graphic aimed at people that understand the concept of Pi intimately, or those learning the concept? It might be fine for you and me, who can conceptualise it, but what about the 13yo kid this is presumably aimed at as a learning aid? If you don't think it will be a problem for 99.9% of them then I'd say you've obviously never tried to teach this sort of thing. And if you're happy to teach the concept of area without reference to units, then please don't ever try teaching it as that would be an unfortunate experience for any hypothetical students.

If this is so confusing for people who presumably already understand π, then it would surely be even moreso for students who would henceforth associate π with an area. In fact what I'm getting from a number of the comments is that there are several voters that don't understand this fully, and probably don't understand one or more of that (i) π is a constant and not an area, (ii) the area of the rectangle shown is not same as the area of the circle shown, and therefore (iii) that the area of a circle is not π (or π units²), i.e., to simplify, using this many students could interpret that π is the area of a circle (and most likely any circle). And if you knocked that out of them, then they'd still think π was some sort of area, so then you'd have to unteach that, and so on - doesn't seem very effective.

I'm not totally convinced the author even intended to equate π with the area, and I'm sure they didn't intend this confusion. And all because of that darn rectangle. --jjron 08:10, 18 August 2006 (UTC)

First, I think it's clear based on the way the pink box "grows" that the author did intend to show that the area of a rectangle with length equivalent to the circumference of a circle and height equivalent to the diameter of the circle is Pi, and that the units² is understood but unstated. Nevertheless, I agree that it is potentially confusing and shouldn't be a part of this animation, and have agreed on that point from the start.

As for the rest of it, I'm not sure why you didn't follow what I was saying. The basic gist of it is that like 2, Pi is a number. 2 can be defined many ways - 1+1, 18/9, etc. Ditto for Pi. One definition is "the ratio of the circumference of a circle to its diameter." That's the classic definition. Another is "the ratio of the area of a circle to the area of a square with sides the same length as the circle's radius." There are other definitions as well.

I don't think your analogy about being paid $100 for a job was directed at me, but I will say this. Dollars, like units², are often unstated but understood. To wit:

"How much are you paying for this job?" asked Harold.

"A hundred," replied Jim.

Now if Harold does the job and Jim attempts to hand him a piece of paper with the number "100" written on it for payment, Jim risks getting a punch in the nose. The units, dollars, were understood from the start even though they were not stated. I believe that's the same thing going on in this animation.

When children are taught the formulae for finding area, at least at the school I attended and the one my children are now attending, the units are seldom mentioned, because they are understood even if they're not stated. For example, they are taught that the area of a rectangle is length x width. The area of a circle is Pi times r². Nobody says the area of a rectangle is length units times height units, or that the area of a circle is Pi units times radius units squared. Yet you can't get units² in the answer unless the units were understood from the start to be attached to the length, width, radius, or Pi. They are present but unstated. This is all a side issue anyway, since it relates to the pink rectangle and we both agree that it shouldn't be in the animation in the first place. Given that we agree it should be eliminated, I see little point in discussing units² further.-- Moondigger 12:23, 18 August 2006 (UTC)

• Oppose due to the rectangle. The graphic attempts to communicate too much, and the rectangle is the culprit. If the rectangle is removed, leaving the line of length pi, count me in Support because it'll be a superlative animation. The same graphic can be repackaged to make a second animation demonstrating area (using the rectangle instead of the line), although since it's aimed at beginners, it would be much easier to make the radius 1 for the area demonstration. Fg2 00:57, 18 August 2006 (UTC) P.S. That is to say, this could become two featured pictures. 00:59, 18 August 2006 (UTC)
• Support It clearly demonstrates in pictures the idea that circumference is just a bit greater than 3 diameters, a quantity we call Pi. Very nice. Jeeb 03:31, 18 August 2006 (UTC)

Comment There is another, somewhat similar animation on the Pi article, shown here:

But the article is screwed up. The text description next to this animation is the correct description for what happens in the wagon-wheel demonstration nominated above. Somebody must have moved the images around without updating the text. In any case, neither animation is a worthy FP, IMO. The wagon-wheel suffers from trying to depict too much; this one doesn't show enough (like a horizontal scale). -- Moondigger 18:34, 18 August 2006 (UTC)

• Comment To reiterate, this animation might become two featured pictures if they separately illustrated circumference and area. Kudos to User:John Reid for excellent illustration. Fg2 02:01, 24 August 2006 (UTC)

Not promoted But it's clear from the comments that a similar animation addressing the concerns raised above would likely pass FP muster. -- Moondigger 01:02, 25 August 2006 (UTC)