Oops! Try labelling your axis and you will discover that you left out zero. 72.208.56.148 00:57, 15 April 2007 (UTC)
- Concur, the axis should be labelled, however the series is 1, -1, 2, -2, 3, -3, …, which are the partial sums. Addhoc 18:23, 15 April 2007 (UTC)
- I didn't mean the axis should be labelled just for labelling's sake. I meant that if you labelled the axis, you would see that you didn't draw a line representing the value zero. There should be room at least, if not a line, for zero between -1 and 1. Get a piece of graph paper. Mark the Y axis from -10 to 10 by 1. Plot your series, 1, -1, 2, -2 etc. Notice that the distance between 1 and -1 is more than 1. Most mathematicians would probably say 2 in fact. 72.208.56.148 19:57, 15 April 2007 (UTC)
- Agreed. The lack of a zero makes for a more dramatic, but inaccurate, image.--Paulski.mcb 11:35, 17 April 2007 (UTC)
- The series begins at zero. It's the first dot. The next dot is at 1, and the next at -1. You can see this in the POV-Ray code if you look hard enough. It's also evident from the description, in that the camera is placed over 1/4. Short answer: don't worry, nothing is missing. Melchoir 19:10, 17 April 2007 (UTC)
- Do me a favor. Print out the picture. Write the number "0" next to the light gray line that intersects the first dot. Now write "-1" next to the light gray line that intersects the second dot. Continue identifying the gray lines: +1, -2, +2, -3, +3... THAT is not the sequence described in the article.
- Graph shows: 0, -1, +1, -2, +2, -3, +3...
- Should be: +1, -1, +2, -2, +3, -3...
- If you write THOSE numbers next to each dot in the order you encounter them, you will see that there is no gray line you could label "0". The zero line is missing. Or the sequence is not correctly illustrated.
- If there is any other way to interpret this graph, I can't see it, and apparently others cannot either. So you need to label the axis to make it clear, either to yourself or to your readers.
- Short answer: worry. Something is missing. Or more likely, flat out wrong. 72.208.56.148 01:44, 19 April 2007 (UTC)
- Why would I write -1 next to the light gray line that intersects the second dot? Melchoir 03:33, 19 April 2007 (UTC)
- Because, when you are graphing a function, each line corresponds with a number value, and -1 is the number adjacent to 0 in the negative direction. What number would you write there? And next to the other lines? 72.208.56.148 11:18, 19 April 2007 (UTC)
- 1. Melchoir 16:55, 19 April 2007 (UTC)
OK I think maybe I get it now. The graph is plotting x=f(y). I'm more used to seeing y=f(x). Maybe it's a cultural thing, or where I went to school. Still, labels would help, or would have helped. 72.208.56.148 03:09, 21 April 2007 (UTC)
I like this picture... imagine if it were a landscape.--h i s s p a c e r e s e a r c h 10:01, 15 April 2007 (UTC)
SVG edit
I'm an SVG-ophile, but I find the convert-to-svg tag on this image to be dubious. Any reasonably-renderable SVG of this image is going to fake the far distance with gradients or something, at which point you may as well just have a high-quality PNG like what we have now. --TotoBaggins 18:11, 15 April 2007 (UTC)
This image confuses me edit
Okay, I'm starting to realize how little i understand perspective. 1-2+3-4... is an infinite sequence. So why is it that at the horizon, the black zigzag infinitely wide? Would it be that wide with an image of infinite amount of depth? I can't imagine that that is the case since it seems like you can connect all of the positive or all of the negative points with a straight line.--Kento 19:08, 15 April 2007 (UTC)
- I think it's not infinitely wide due to some implied curvature of the Earth, or whatever strange planet this zigzag was drawn on. --TotoBaggins 17:20, 17 April 2007 (UTC)
- I had some trouble understanding the original questioner's grammar, but the thing is, it's *not* infinitely wide at the horizon. There's clearly white on either side, which I assumed was due to the plane being, er, non-planar. --TotoBaggins 01:24, 18 April 2007 (UTC)
- Oh, well the zigzag does take up a finite proportion of the horizon, or the circle at infinity as it's known in projective geometry, which is itself infinitely long in the usual sense. A convergent series would head toward a single point on the horizon. On the other extreme, a series like 1 − 2 + 4 − 8 + · · · would occupy an entire half of the horizon. The fact that 1 − 2 + 3 − 4 + · · · takes up more than a point but less than a half is peculiar; it's a consequence of the partial sums diverging at two different linear rates. Melchoir 16:43, 18 April 2007 (UTC)
