Talk:Prism (geometry)

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Polyhedra

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Untitled section[edit]

What consists of the base on a prism? Length times width?--STANG281 05:50, 7 November 2005 (UTC)[reply]

This passage, which i have rewrit, must reflect a failure of visual imagination by someone reconstructing what they had learned:

The rectangular prism, or cuboid, and square prism are among the types of right prism, with a rectangular and square base, respectively.

I say so for the following reasons:

It is unmathematical to waste those prism terms on the cuboid and the square cuboid.
A std. dictionary, in case of the analogous right circular cylinder, does not waste the name "circular cylinder" on it: if you make the proper parallel oblique cuts off the ends of a right elliptical cylinder, you get an oblique circular cylinder; the oblique and right circular cylinders together constitue the circular cylinders.

To imagine an oblique rectangular prism, picture two identical rigid rectangles, with eyes at the vertices; tie the eyes together in pairs with 4 equal-length inelastic strings. Hold one horizontal; the other will hang below it, also horizontal; that's your right rectangular prism. Have someone you trust nail down the bottom one, and keep all the strings taut. If you displace the top in any direction not parallel to a side, while keeping the strings taut, you have an oblique rectangular prism. Or, if you have trouble seeing that, move the top so that two edges stay in the same vertical plane they previously occupied, then (try to) move it perpendicular to that plane (it won't move a finite distance perpendicularly). In either case, the only right angles are on the top and bottom, and you have what must be called an oblique rectangular prism. The rectangular prisms must be the oblique rectangular prisms and the right rectangular prisms.
If i'm wrong, come up with a reliable reference that verifies the other supposed meaning. (If you do, the old article still needs work to clarify the illogical terminology.)
--Jerzy (t) 19:07, 2005 Apr 15 (UTC)

I suggest one more good formula[edit]

current article (quote):"Take a polygon with n vertices, n edges. Its prism has 2n vertices, 3n edges, and 2 + n faces. Take a polyhedron with v vertices, e edges, and f faces. Its prism has 2v vertices, 2e + v edges, 2f + e faces, and 2 + f cells. Take a polychoron with v vertices, e edges, f faces and c cells. Its prism has 2v vertices, 2e + v edges, 2f + e faces, and 2c + f cells, and 2 + c hypercells."

I suggest "Take a polygon, polyhedron, or polychoron and sum the number of vertices w/ number edges, and number of faces,and,..,number of polychorons(=1). If one takes the prism of the original object, the corresponding sum is 3 times larger." I don't have a citation for this theorem, but it's easy to prove from the above formulae, and there aren't citations for those formulae either.-Rich Peterson75.45.106.99 (talk) 22:51, 6 June 2009 (UTC)[reply]

I should have said that this along with the formulas, not formulae, already there would provide nice setting for the Pascal's triangle method of counting vertices edges etc on an n-cube:Just go to the nth row of triangle for 1+2x.(I know this method used to be on Wikipedia but I can't find it now.)Best wishes, Rich Peterson75.45.106.99 (talk) 23:04, 6 June 2009 (UTC)[reply]

Do prism really have to have polygonal faces?[edit]

If you slice a cylinder lengthways along its axis you get two shapes that have many of the properties of a prism, but are not prisms by the current definition. The solid has one flat face and one that is curved. It's volume is the area of the end face times it's length and its surface area can be found in the same way as a prism. But its not a prism and its not a cylinder. What is to stop this being considered a prism? (Aside from the obvious fact that the current definition exludes it by requiring polygonal faces).

Perhaps a prism could be "A solid with two congruent parallel faces, and where any cross section parallel to those faces is congruent to them." Thoughts?

The shape you are describing is a right semicircular cylinder, half of a right circular cylinder.

In the same way that "A cone with a polygonal base is called a pyramid.", a cylinder with two polygonal bases is called a prism. --DavidCary (talk) 17:50, 10 October 2020 (UTC)[reply]

Why the edit to the lead paragraph?[edit]

The previous text had been:

In geometry, an n-sided prism is a polyhedron made of an n-sided polygonal base, a translated copy, and n faces joining corresponding sides.

People reading that had found it confusing, largely because of the ambiguous use of "side": n-sided prism uses "side" to refer to (lateral) faces, while "n-sided polygon" uses "side" to refer to edges. The sense of "side" as "face" got the readers to ask "shouldn't a prism with an n-sided base have n + 2 sides (faces)?" I took the original intent of "an n-sided prism" to be an attempt to explain the nomenclature so, after clarifying the initial definition, I added the sentence about naming at the end.

The entry under faces in the table, too, was confusing because something like "p + 2" was expected, corresponding to the 2p and 3p in the vertices and edges entries, but that may just have been the result of the confusion set up by the initial paragraph, so I left it alone. An alternative --- p + 2 (two p-gons as bases and p parallelograms as lateral faces) --- would be clearer, but longer. PGoldenberg (talk) 13:49, 30 September 2010 (UTC)[reply]

One also can't count on a casual reader to understand translated. —Tamfang (talk) 01:31, 1 October 2010 (UTC)[reply]

Claim that Azrieli Towers are prism is incorrect.[edit]

The claim made in this article that the Azrieli Towers are prism (sic) is incorrect. A cylinder is not a prism, and those buildings include a cylinder, therefore the statement is incorrect. The fact that cylinders can be approximated by prims is irrelevant to this fact. Aparently the claim was made by a non-existent user, Ace-af [1]

Moreover, the inclusion in this article of an image of these buildings is misleading and confusing given that only two of them are prisms, and one is not. One of my students was in fact confused by this image.

I hope the usual maintainer of this page can fix these issues. I am not proficient in using wikipedia hypertags. Thanks! — Preceding unsigned comment added by c-67-175-215-221.hsd1.il.comcast.net (talk) 07:37, 23 August 2013 (UTC)[reply]

Euclid's inconsistency[edit]

Where is the inconsistency in Euclid's definition of a prism? How is a triangular-based prism in conflict with it? — Preceding unsigned comment added by 92.0.106.148 (talk) 18:37, 16 October 2020 (UTC)[reply]

There is no inconsistency. Whoever wrote that paragraph was synthesizing from the comments of two older works, both of which mention that they hold minority opinions. I would not consider those older works to be reliable sources, but I'll rewrite that paragraph to mention the opposing views.--Bill Cherowitzo (talk) 20:43, 16 October 2020 (UTC)[reply]