# Why are online log-log plots so inaccurate? **URL:** \ **Category:** Factual Questions\ **Created:** [February 23, 2014, 2:55pm UTC](https://boards.straightdope.com/t/why-are-online-log-log-plots-so-inaccurate/682019 "2014-02-23T14:55:25Z")\ **Posts on this page:** 16\ **Page:** 2
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [February 23, 2014, 10:04pm UTC](https://boards.straightdope.com/t/why-are-online-log-log-plots-so-inaccurate/682019/21 "2014-02-23T22:04:19Z")
> [@Stranger\_On\_A\_Train](#): > > Every explicit (e.g. graphically useful) description of an oval has the ends as circular (constant radius) section connected by curves which are tangent at the connections and symmetric about an axis going through the radial center of the ends, forming a smoothly continuous purely convex (or in the case of stright connecting lines, flat) parametric curve. Your description includes ellipses. The circular “caps” would be degenerate: infinite radius and zero arc length. The connecting curves–which you left unspecified–are of course half-ellipses and tangent to the degenerate caps. ---
**Author:** ![Stranger\_On\_A\_Train](https://avatars.discourse-cdn.com/v4/letter/s/13edae/32.png) [@Stranger\_On\_A\_Train](https://boards.straightdope.com/u/Stranger_On_A_Train)\ **Post date:** [February 23, 2014, 10:10pm UTC](https://boards.straightdope.com/t/why-are-online-log-log-plots-so-inaccurate/682019/22 "2014-02-23T22:10:25Z")
So of all of the citations you provide, the three dictionary definitions are recursively defined in casual language (e.g. an oval is “oval in shape”) or in the case of Webster’s, factually incorrect (describing the cross-section of an egg as “elliptical”), the Wikipedia page provides the typical sprawling and self-contradictory information afforded by whatever random person decided to edit the entry, and Eric Weisstein’s MathWorld page explicitly describes how an oval is not an ellipse, including formal definitions. Just because people use the terms “ellipse” and “oval” interchangeably in casual discourse does not mean that they are analogous or one the subset of another, any more than the broad usage of “fish” to describe all finned swimming creatures in the ocean is accurate in referring to a cetacean. An ellipse has a very specific form with a well defined metric, and does not incorporate any segments of a circle except in the degenerate (_e_=0) case, which nobody would consider to be oval. An oval is a more general description of a family of different shapes which are generally formed by the combination of segments of two circles with tangent curves and does not include ellipses (except, again, in the degenerate case that no one would call an ellipse). The two terms are not equivalent, one is not a subset of the other, and in any descriptive sense, i.e. with enough detail to reproduce the shape, are distinctly not interchangeable. > [@Dr.Strangelove](#): > > Your description includes ellipses. The circular “caps” would be degenerate: infinite radius and zero arc length. The connecting curves–which you left unspecified–are of course half-ellipses and tangent to the degenerate caps. By that logic, all shapes are a point. Stranger ---
**Author:** ![ThisUsernameIsForbidden](https://avatars.discourse-cdn.com/v4/letter/t/b4bc9f/32.png) [@ThisUsernameIsForbidden](https://boards.straightdope.com/u/ThisUsernameIsForbidden)\ **Post date:** [February 23, 2014, 10:58pm UTC](https://boards.straightdope.com/t/why-are-online-log-log-plots-so-inaccurate/682019/23 "2014-02-23T22:58:37Z")
> [@](#): > > It is like calling a dophin a fish because it swims in the ocean; while it is true dolphins and fish share certain superficial characteristics, no zoologist would ever conflate them, even in a general sense. > [@](#): > > And really, equating it to calling a dolphin a fish? That’s just ignorant. A dolphin is categorically not a fish. Dolphins are mammals. They have lungs. Fish have gills. Dolphins do not fit the definition of a fish. :smack: ---
**Author:** ![Reply](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/reply/32/15952_2.png) [@Reply](https://boards.straightdope.com/u/Reply)\ **Post date:** [February 24, 2014, 1:30am UTC](https://boards.straightdope.com/t/why-are-online-log-log-plots-so-inaccurate/682019/24 "2014-02-24T01:30:34Z")
> [@septimus](#): > > I noticed a different amazing ignorance a few days ago. Googling “image latitude” one finds many [sites like this one](http://www.worldmapsonline.com/LESSON-PLANS/6-latitude-globe-lesson-5.htm) which think latitude lines are equally spaced along the axis. :smack: (And that page is a “lesson.”) Are they not? ---
**Author:** ![yabob](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/yabob/32/2821_2.png) [@yabob](https://boards.straightdope.com/u/yabob)\ **Post date:** [February 24, 2014, 2:21am UTC](https://boards.straightdope.com/t/why-are-online-log-log-plots-so-inaccurate/682019/25 "2014-02-24T02:21:02Z")
> [@Reply](#): > > Are they not? No, they are spaced at equal arc lengths along a meridian (considering the Earth to be spherical). The projection of a line of latitude onto the axis with 0 at the equator will be +/- R\*cos(L) where R is the radius of the Earth and L is the latitude. ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [February 24, 2014, 2:38am UTC](https://boards.straightdope.com/t/why-are-online-log-log-plots-so-inaccurate/682019/26 "2014-02-24T02:38:54Z")
> [@Stranger\_On\_A\_Train](#): > > So of all of the citations you provide, the three dictionary definitions are recursively defined in casual language (e.g. an oval is “oval in shape”) I included both the noun and adjective definitions. “an object of oval shape.” gives the definition for the noun. the word “oval” is the adjective form, which is defined earlier. It is not a recursive definition. > [@](#): > > or in the case of Webster’s, factually incorrect (describing the cross-section of an egg as “elliptical”), No, it does not describe the cross-section of an egg as elliptical. It gives two descriptions. > [@](#): > > the Wikipedia page provides the typical sprawling and self-contradictory information afforded by whatever random person decided to edit the entry, Still better than any cite you’ve given… > [@](#): > > and Eric Weisstein’s MathWorld page explicitly describes how an oval is not an ellipse, including formal definitions. Wrong again. It is saying that an oval does not have a precise mathematical definition, as opposed to an ellipse which _does_ have a precise mathematical definition. > [@](#): > > Just because people use the terms “ellipse” and “oval” interchangeably in casual discourse does not mean that they are analogous or one the subset of another, any more than the broad usage of “fish” to describe all finned swimming creatures in the ocean is accurate in referring to a cetacean. Back to equating it with calling dolphins fish, when dolphins are specifically excluded from the definition of fish. There is no analogy with ellipses being specifically excluded from the definition of oval. > [@](#): > > An oval is a more general description of a family of different shapes which are generally formed by the combination of segments of two circles with tangent curves and does not include ellipses (except, again, in the degenerate case that no one would call an ellipse). The two terms are not equivalent, one is not a subset of the other, and in any descriptive sense, i.e. with enough detail to reproduce the shape, are distinctly not interchangeable. Unsupported statements, worse than Wikipedia. You’re clearly wrong here. I have no idea why you have such a hard time admitting that, to the point that you seem to be intentionally misreading cites to make them be wrong. ---
**Author:** ![yabob](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/yabob/32/2821_2.png) [@yabob](https://boards.straightdope.com/u/yabob)\ **Post date:** [February 24, 2014, 2:47am UTC](https://boards.straightdope.com/t/why-are-online-log-log-plots-so-inaccurate/682019/27 "2014-02-24T02:47:55Z")
> [@yabob](#): > > No, they are spaced at equal arc lengths along a meridian (considering the Earth to be spherical). The projection of a line of latitude onto the axis with 0 at the equator will be +/- R\*cos(L) where R is the radius of the Earth and L is the latitude. To amplify, I should say the projection from a viewpoint at an infinite distance, centered on the equator, which is what is strongly implied by that style of drawing. That should look like this - note the spacing of latitude lines: > **[File:Orthographic projection SW.jpg](https://en.wikipedia.org/wiki/File:Orthographic_projection_SW.jpg)** > > Original file (2,058 × 2,058 pixels, file size: 1 MB, MIME type: image/jpeg) > > If you think this file should be featured on Wikimedia Commons as well, feel free to nominate it. > If you have an image of similar quality that can be published under a suitable copyright license, be sure to upload it, tag it, and nominate it. > Click on a date/time to view the file as it appeared at that time. Having spun off elliptically into this discussion, I now return you to the main track, oval or otherwise. ---
**Author:** ![Stranger\_On\_A\_Train](https://avatars.discourse-cdn.com/v4/letter/s/13edae/32.png) [@Stranger\_On\_A\_Train](https://boards.straightdope.com/u/Stranger_On_A_Train)\ **Post date:** [February 24, 2014, 5:43am UTC](https://boards.straightdope.com/t/why-are-online-log-log-plots-so-inaccurate/682019/28 "2014-02-24T05:43:26Z")
> [@ZenBeam](#): > > You’re clearly wrong here. I have no idea why you have such a hard time admitting that, to the point that you seem to be intentionally misreading cites to make them be wrong. _In your opinion_, which, given a clear understanding of even the citations you provided means just about diddly squat. You chastized the o.p. based upon your believe that an ellipse is an oval, and then have persistently refused to understand the distiction. Go back and look at the Mathworld page, which clearly makes the distinction between an ellipse–which has a very precise analytical definition–and an oval, which is one of many different forms, but none of them in the form of a single conic section. Stranger ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [February 24, 2014, 12:43pm UTC](https://boards.straightdope.com/t/why-are-online-log-log-plots-so-inaccurate/682019/29 "2014-02-24T12:43:50Z")
“chastized”? Seriously? What a ridiculous statement. Did you even notice that the OP _himself_ looked up the definition of oval, and found his understanding was wrong? Perhaps _you_ should look at the Mathworld site again, and note where it says “The **particular variant** illustrated above”. Again, you conveniently ignore anything that doesn’t fit into your preconceived belief. You’re looking more foolish with every post you make here. You really should just move along. ---
**Author:** ![Napier](https://avatars.discourse-cdn.com/v4/letter/n/ce73a5/32.png) [@Napier](https://boards.straightdope.com/u/Napier)\ **Post date:** [February 24, 2014, 1:13pm UTC](https://boards.straightdope.com/t/why-are-online-log-log-plots-so-inaccurate/682019/30 "2014-02-24T13:13:27Z")
Heavens! Look, it’s indisputable that definitions of “oval” vary considerably, and many of the definitions would include ellipses. I am sure I was wrong to say that DrawOval() (IIRC) was some kind of mistake because it generated ellipses. It was merely a function that should have been named more specifically DrawEllipse() given that it could be. I think shapes with straight sides and semicircle ends deserve a name all their own, but I was wrong in thinking that name was “oval”. Perhaps Stranger and I were both working off the same apparently incorrect reference? ---
**Author:** ![Napier](https://avatars.discourse-cdn.com/v4/letter/n/ce73a5/32.png) [@Napier](https://boards.straightdope.com/u/Napier)\ **Post date:** [February 24, 2014, 3:25pm UTC](https://boards.straightdope.com/t/why-are-online-log-log-plots-so-inaccurate/682019/31 "2014-02-24T15:25:17Z")
> [@DataX](#): > > I couldn’t replicate the problem. I see them all the time, but didn’t see one from a manufacture - found one from a math website - and the lines line up (they were a pixel or two off - I’m guessing due to rounding. > > How large are these graphs? If you are talking 100 pixels wide - maybe it is rounding issues. > > Anyway you can post - or PM an example? OK, here’s an example: [http://www.chromalox.com/resource-center/design-guide-pages/dg-cartridge.aspx](http://www.chromalox.com/resource-center/design-guide-pages/dg-cartridge.aspx) Notice how the 0.010 on the horizontal axis is way left of the center of the 0.001 to 0.1 log axis, though it should be centered. I think 0.0125 is about where the center appears. ---
**Author:** ![Stranger\_On\_A\_Train](https://avatars.discourse-cdn.com/v4/letter/s/13edae/32.png) [@Stranger\_On\_A\_Train](https://boards.straightdope.com/u/Stranger_On_A_Train)\ **Post date:** [February 24, 2014, 5:44pm UTC](https://boards.straightdope.com/t/why-are-online-log-log-plots-so-inaccurate/682019/32 "2014-02-24T17:44:46Z")
> [@ZenBeam](#): > > Perhaps _you_ should look at the Mathworld site again, and note where it says “The **particular variant** illustrated above”. Again, you conveniently ignore anything that doesn’t fit into your preconceived belief. The forms that an oval can take is not “preconceived belief”; it is one of many forms created from two circular segments and connecting lines. An ellipse has a very specific form which contains _no_ circular segments except in the degenerate case. > [@ZenBeam](#): > > You’re looking more foolish with every post you make here. You really should just move along. You really need to take your a_d homenin_ someplace else. I have made every effort to avoid making any kind of personal attack and would respectfully request the same from you. Stranger ---
**Author:** ![Colibri](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/colibri/32/1841_2.png) [@Colibri](https://boards.straightdope.com/u/Colibri)\ **Post date:** [February 24, 2014, 5:48pm UTC](https://boards.straightdope.com/t/why-are-online-log-log-plots-so-inaccurate/682019/33 "2014-02-24T17:48:51Z")
> [@ZenBeam](#): > > You’re looking more foolish with every post you make here. You really should just move along. **Moderator Note** **ZenBeam** , as you should know, insults are not permitted in General Questions. I’m making this a note rather than an official warning, but dial it way back. Colibri General Questions Moderator **Moderator Instructions** Let’s all dial it back. It seems to me that this heated debate about the distinction between ellipse and oval is getting the thread wildly off track. Let’s get back to the specific question in the OP. If you wish to debate the semantic or mathematical differences between the two shapes, please open a new thread in Great Debates or the Pit. ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [February 24, 2014, 6:06pm UTC](https://boards.straightdope.com/t/why-are-online-log-log-plots-so-inaccurate/682019/34 "2014-02-24T18:06:43Z")
> [@Stranger\_On\_A\_Train](#): > > The forms that an oval can take is not “preconceived belief”; it is one of many forms created from two circular segments and connecting lines. An ellipse has a very specific form which contains _no_ circular segments except in the degenerate case. You keep saying that, but haven’t given any sort of cite that ovals _must_ have circular segments. ---
**Author:** ![Reply](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/reply/32/15952_2.png) [@Reply](https://boards.straightdope.com/u/Reply)\ **Post date:** [February 24, 2014, 6:47pm UTC](https://boards.straightdope.com/t/why-are-online-log-log-plots-so-inaccurate/682019/35 "2014-02-24T18:47:10Z")
> [@yabob](#): > > To amplify, I should say the projection from a viewpoint at an infinite distance, centered on the equator, which is what is strongly implied by that style of drawing. That should look like this - note the spacing of latitude lines: > > [File:Orthographic projection SW.jpg - Wikipedia](http://en.wikipedia.org/wiki/File:Orthographic_projection_SW.jpg) > > Having spun off elliptically into this discussion, I now return you to the main track, oval or otherwise. I’m still confused by this, but I don’t wan’t to hijack this discussion any further. Would you be willing to take a minute to explain more in the [new thread](http://boards.straightdope.com/sdmb/showthread.php?t=716645)? Thanks! ---
**Author:** ![Colibri](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/colibri/32/1841_2.png) [@Colibri](https://boards.straightdope.com/u/Colibri)\ **Post date:** [February 24, 2014, 8:37pm UTC](https://boards.straightdope.com/t/why-are-online-log-log-plots-so-inaccurate/682019/36 "2014-02-24T20:37:18Z")
> [@ZenBeam](#): > > You keep saying that, but haven’t given any sort of cite that ovals _must_ have circular segments. [Moderator Instruction] As I said, the discussion of ovals vs. ellipses has become a hijack and is interfering with answering the actual question in the OP. Let’s drop this side issue here. Start another thread if you really want to pursue this. Colibri General Questions Moderator [Previous page](https://boards.straightdope.com/t/why-are-online-log-log-plots-so-inaccurate/682019.md?page=1)