# What is the correct geometrical name for this figure? **URL:** \ **Category:** Factual Questions\ **Created:** [January 3, 2012, 7:00pm UTC](https://boards.straightdope.com/t/what-is-the-correct-geometrical-name-for-this-figure/608277 "2012-01-03T19:00:19Z")\ **Posts on this page:** 8\ **Page:** 2
**Author:** ![engineer\_comp\_geek](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/engineer_comp_geek/32/504_2.png) [@engineer\_comp\_geek](https://boards.straightdope.com/u/engineer_comp_geek)\ **Post date:** [January 3, 2012, 11:30pm UTC](https://boards.straightdope.com/t/what-is-the-correct-geometrical-name-for-this-figure/608277/21 "2012-01-03T23:30:26Z")
You can make an oblique cone that is circular with respect to its axis. This would end up being an oblique elliptical cone (but still an oblique cone) since its base would not be circular. You are describing an oblique circular cone (also still an oblique cone), since it has a circular base. This would necessitate an elliptical cross section perpendicular to its axis. ---
**Author:** ![murrmac](https://avatars.discourse-cdn.com/v4/letter/m/50afbb/32.png) [@murrmac](https://boards.straightdope.com/u/murrmac)\ **Post date:** [January 3, 2012, 11:48pm UTC](https://boards.straightdope.com/t/what-is-the-correct-geometrical-name-for-this-figure/608277/22 "2012-01-03T23:48:56Z")
> [@engineer\_comp\_geek](#): > > You can make an oblique cone that is circular with respect to its axis. This would end up being an oblique elliptical cone (but still an oblique cone) since its base would not be circular. > > You are describing an oblique circular cone (also still an oblique cone), since it has a circular base. This would necessitate an elliptical cross section perpendicular to its axis. I think we are getting there, but I would venture to suggest that you have gotten the definitions reversed, and that what I described in the OP is in fact an elliptical oblique cone, or we could even dispense with the "oblique " and simply call it an "elliptical "cone, since any section of the cone perpendicular to the axis will yield an ellipse, whereas any section of a right cone perpendicular to the axis will yield a circular section, whether it is oblique or not. Problem solved, I thank you all , I love this forum. ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [January 4, 2012, 12:39am UTC](https://boards.straightdope.com/t/what-is-the-correct-geometrical-name-for-this-figure/608277/23 "2012-01-04T00:39:18Z")
> [@murrmac](#): > > I think what you guys are missing is that there is a substantive, qualitative difference between the construct which I am describing (and which, incidentally, _ **can** _ be turned very easily on a lathe) and a normal cone. > > […] > > The “cone” I am describing _ **does** _ have a elliptical cross section perpendicular to the axis, […] On a lathe, the item will rotate about the axis. How are you making an elliptical cross-section perpendicular to the axis? I would expect you would always get a cross-section that is circular perpendicular to the axis. ETA: if you then cut the base perpendicular to the axis, you get a right circular cone. If you cut it at an angle, you can call it an oblique elliptical cone. > [@](#): > > […] but **as I understand it so far** , that is not the case in a “oblique cone”, which will always have a circular cross section perpendicular to the axis. I don’t believe this is true. Ignoring the base, the same cone can be described as elliptical or circular. A right circular cone can be called an oblique elliptical cone. For any elliptical cone, you can find an angle to cut it so that the cross-section is circular, so any cone can be called a (possibly oblique) circular cone. ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [January 4, 2012, 12:45am UTC](https://boards.straightdope.com/t/what-is-the-correct-geometrical-name-for-this-figure/608277/24 "2012-01-04T00:45:59Z")
Just to be clear, looking at [this picture](http://www.icoachmath.com/image_md/Cone2.gif) **engineer\_comp\_geek** linked to, the dashed line is not the axis. The axis would be a line connecting the vertex and the center point of the base. ---
**Author:** ![BigT](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bigt/32/12044_2.png) [@BigT](https://boards.straightdope.com/u/BigT)\ **Post date:** [January 4, 2012, 3:36am UTC](https://boards.straightdope.com/t/what-is-the-correct-geometrical-name-for-this-figure/608277/25 "2012-01-04T03:36:40Z")
> [@Indistinguishable](#): > > Perhaps the easiest thing to say is “A circular cone whose apex is directly above the rim of its base”. See, I’d say it was a “cone with one side straight up and down, but not flat.” Not only because I don’t think a lot of people know the word apex, but also because I don’t know too many people who conceptualize cones as starting from the apex. The start from the circle/ellipse, and meet at a point. ---
**Author:** ![engineer\_comp\_geek](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/engineer_comp_geek/32/504_2.png) [@engineer\_comp\_geek](https://boards.straightdope.com/u/engineer_comp_geek)\ **Post date:** [January 4, 2012, 5:32am UTC](https://boards.straightdope.com/t/what-is-the-correct-geometrical-name-for-this-figure/608277/26 "2012-01-04T05:32:33Z")
> [@murrmac](#): > > I think we are getting there, but I would venture to suggest that you have gotten the definitions reversed, and that what I described in the OP is in fact an elliptical oblique cone, or we could even dispense with the "oblique " and simply call it an "elliptical "cone, since any section of the cone perpendicular to the axis will yield an ellipse, whereas any section of a right cone perpendicular to the axis will yield a circular section, whether it is oblique or not. Whether it is circular or elliptical depends on the shape of the base, not the shape of a slice perpendicular across its axis. Since your cone has a circular base, it’s a circular cone. You could call it a cone, you could call it a circular cone (though some might assume it’s a right cone if you called it that without specifying), you could call it an oblique cone, or you could call it an oblique circular cone. Reminds me of the old “you can call me Ray” comedy routine from the 70s… ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [January 4, 2012, 6:34am UTC](https://boards.straightdope.com/t/what-is-the-correct-geometrical-name-for-this-figure/608277/27 "2012-01-04T06:34:47Z")
> [@BigT](#): > > See, I’d say it was a “cone with one side straight up and down, but not flat.” Not only because I don’t think a lot of people know the word apex, but also because I don’t know too many people who conceptualize cones as starting from the apex. The start from the circle/ellipse, and meet at a point. Who said anything about whether it “starts” vs. “ends” at the apex? But, fair enough on the first point; replace the word “apex” with “tip” or “point” or such things as you like. ---
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [January 4, 2012, 7:58am UTC](https://boards.straightdope.com/t/what-is-the-correct-geometrical-name-for-this-figure/608277/28 "2012-01-04T07:58:03Z")
> [@murrmac](#): > > OK, just clarify one thing for me. > > **If you take a standard right cone, tilt it over so that one side becomes perpendicular to the base, then slice it through so that it sits on the base with one side perpendicular to the base** , does it then become an “oblique cone”? > > It’s times like this you really miss not having the [IMG] code … Okay, here’s the picture I’m getting from this description, and why I think at least some other people are getting confused. From your description, if your original (right circular) cone is a solid block of rigid kryptonite, and you “tilt” it as you describe, it is _still a right circular cone!_ You can move (translate) or tilt (rotate) it any why you want, and it is still the same shape, and that is still a right circular cone. Now, if you slice it as you describe, you are just passing a plane through the cone, parallel to the plane of the original base, but not parallel to the base of the cone in its new position. So yes, this will create a new “base” (let’s call it a pseudo-base) perpendicular to whatever you just said it’s perpendicular to. But that is by no means a true base of anything. It’s just a plane passed through the (now tilted) cone, creating an elliptical section. You might be able to set the cone on this face and not have it tip over. So the new “shape” you have is nothing more than the original right circular cone you originally had, tilted, with a piece of it sliced away. I doubt there’s a more specific name for it than that. NOW: As to what almost everyone else seems to be thinking (maybe): Picture a deck of playing cards. Skew it so that each card sits just a little to the left of the card below it. I think in analytic geometry this is called “shear” or maybe “skew”. [Here’s the best picture I can quickly find](http://www.sanandreasfault.org/Deck_of_Cards.jpg). Now do this process with your cone. This creates the “oblique cone” that most everyone else seems to be thinking of, and I think you could make one line of the surface of the cone be perpendicular to the base. This base would still be the same circular base as the original. But it sounds like this isn’t what you are describing. NOW: Upon re-reading your OP, it becomes less clear which of these figures you are trying to describe. Your OP seems to be describing the sheared cone that I just described. But the post that I quoted above (post #9 I think) is clearly just the tilted sliced-off block of kryptonite. These are two distinctly different shapes. Now I see why we are _all_ confuzled. [Previous page](https://boards.straightdope.com/t/what-is-the-correct-geometrical-name-for-this-figure/608277.md?page=1)