Talk:Paraboloid

message: so in nature the ONLY place where a hyperbolic paraboloid is found is a shrimp? I have trouble with this.....  —Preceding unsigned comment added by 75.46.90.105 (talk) 20:56, 7 May 2010 (UTC)
replies: text: there have to be other examples of objects with paraboloid than the mantis shrimp mentioned in "in nature" — Preceding unsigned comment added by 75.46.90.105 (talk) 20:59, 7 May 2010 (UTC)
thread_title:  shrimp are tasty 

message: I came to this page because it was linked to from the Pringles page. The shape of those crisps was described as being a hyperbolic paraboloid. I wondered what this means, so I clicked on the link and... Uh... That's where the comprehensible part of my story finishes. This page has absolutely no meaning whatsoever to someone who doesn't have advanced knowledge of Mathmatics. At least, I think that the knowledge is Maths based - it seems that I don't even know what I'd need to know to understand the info on this page. Basically, not very useful to anyone wondering what shape a Pringle is...86.166.154.225 (talk) 01:21, 9 October 2011 (UTC)
replies: text: Well, what kind of understanding of the shape did you hope to get without the math? —Tamfang (talk) 02:50, 31 August 2013 (UTC)

text: It might be worth removing the Pringles reference, since it's a commercial product, and this is a page about math. Keeping it could even give Pringles a bad name, since companies in the past (e.g. "The North Face") have used replaced wikipedia images as part of their advertising campaign. —Whole Oats (talk) 06:40, 28 June 2022 (UTC)
thread_title:  None of this makes sense to a non-Maths person 

message: One of two "applications" mentioned in the article is this:
"The manufacturers of a widely-sold fried snack food, Pringles ersatz potato chips, utilize a hyperbolic paraboloid shape in order to produce a stackable snack."
But being a hyperbolic paraboloid has virtually nothing to do with stackability.  Any surface for the form z = f(x,y), i.e., that is the graph of a function, is stackable.  That is, its vertical translates z = f(x,y) + c where c ranges over an interval [a,b] are disjoint surfaces
that fill the solid region between z = f(x,y) + a and z = f(x,y) +b.Daqu (talk) 22:55, 16 November 2011 (UTC)
thread_title:  Criteria for stackability 

message: For a general paraboloid of the form z = ax^2+bxy+cx^2+dx+ey+f, am I right in guessing that it's hyperbolic if b^2 > 4ac, elliptic if b^2 < 4ac, and a cylinder (ruled parallel to the xy plane) if they're equal? —Tamfang (talk) 05:28, 31 August 2013 (UTC)
thread_title:  discrimination 

message: Under the section: Dimensions of a paraboloidal dish
"A more complex calculation is needed to find the diameter of the dish measured along its surface." The equation shown is unnecessarily complex. You can define the paraboloid with two variables. Here they use three. Is there a reason for this? The final form isn't any cleaner, so that's not a reason. I would suggest getting rid of the Ps and Qs.
Derivation: To get the arc length along the inside of the paraboloid or "linear diameter", measure the length along the curve of the parabola.
Using the arc length formula,
 Diameter = s = Integrate[Sqrt[1+(dy/dx)^2],{x,a,b}]. 
Choosing a and b to be defined in terms of R, the rim radius of the top of the paraboloid, and knowing y=x^2/(4F) is the general formula for a parabola, where F is the focus, we get:
 s = Integrate[Sqrt[1+x^2/(4F^2)],{x,-R,R}],
which is:
 s = diameter = (1/2)R*Sqrt[4+R^2/F^2]+2F*ArcSinh[R/(2F)]
You can also substitute ArcSinh[x] for the natural log form if desired:
 s = (1/2)R*Sqrt[4+R^2/F^2]+2F*Log[R/(2F)+Sqrt[(R/(2F))^2+1]]
This only uses two variables.
Note:I was plugging this straight into mathematica which is why I wrote the equations this way.
EvanN90 (talk) 01:45, 15 June 2018 (UTC)
thread_title:  Use Simpler Linear Diameter equation 

message: I don't know where in Wikipedia to post this.
Your z looks like your x.
Please use a fond for your Maths that is easy to read.
Mathematics on Wikipedia is brilliant.
Where do I post glowing praise from a lonely autodidact?  — Preceding unsigned comment added by Norm Tered (talk • contribs) 23:34, 30 October 2020 (UTC)
replies: text: They do, indeed, look similar: x, z. This is an artifact of the font.  I suggest zooming to a higher magnification on the device you are using to read the articles.—Anita5192 (talk) 00:04, 31 October 2020 (UTC)
thread_title:  z=x 

message: The section Hyperbolic paraboloid contains this paragraph:
"These properties characterize hyperbolic paraboloids and are used in one of the oldest definitions of hyperbolic paraboloids: a hyperbolic paraboloid is a surface that may be generated by a moving line that is parallel to a fixed plane and crosses two fixed skew lines."
The problem is that this is not a definition, because many other surfaces also fit this description.
I hope that someone knowledgeable about this subject can fix this problem. 2601:200:C000:1A0:EC4E:3D24:A106:AEAE (talk) 18:31, 16 July 2021 (UTC)
replies: text: "Many other surfaces also fit this description": No, this characterizes hyperbolic paraboloids. If you disagree, provide an example and a source. D.Lazard (talk) 20:31, 16 July 2021 (UTC)
thread_title:  "Definition" is not a definition