Talk:Pyramid (geometry)

Volume and surface area formulæ

We need to stop edit warring on the volume and surface area sections. Here are issues that need to be addressed:

• We need to find a reliable citations for these formula.
• Proofs and derivations are not really necessary unless they are concise and to-the-point. These should be replaced with a citation instead of cluttering the page.
• We should not post formulæ derived from our own calculations, based on parameters that are not general for all pyramids, or worse yet, based on assumptions that aren't always true.

—Tetracube (talk) 22:38, 26 March 2009 (UTC)

==

Another poorly written article from Wikipedia. So there is someone, apparently more than one person, who believes a pyramid has a radius. I am certainly no expert, but I believe this to be false. If it is true it, it is certainly NOT something that is known broadly enough to be used without explanation. Perhaps the authors meant the circle on which the vertices of the base lie? If so, this would only be true for those with a regular base, right? The article needs to clearly explicitly state when it referring to general prisms and when it is about square pyramids. This should happen in every section. Why is this not self-evident?71.31.149.105 (talk) 23:23, 30 March 2012 (UTC)

Since when was a tetrahedron a pyramid?

Just wondering why a tetrahedron, and shapes with more than four sides on their base, are being classed as pyramids.--78.146.175.222 (talk) 12:45, 9 February 2013 (UTC)

Mathematically, any shape with a polygonal base and plane faces sloping to a vertex is called a pyramid, but culturally nearly all pyramids have square bases (there might be rare exceptions somewhere?). The article covers both usages. Should this be clarified? Dbfirs 21:35, 9 February 2013 (UTC)

[1] a. A solid figure with a polygonal base and triangular faces that meet at a common point. Tom Ruen (talk) 22:42, 9 February 2013 (UTC)

Simplices, complices, duplices?

I notice that the English plural simplexes has been changed to the "false Latin" simplices. I'm not going to revert this because it is probably the case that some mathematicians use this etymologically dubious plural (simplex is not a Latin noun), and this is a mathematical article, but I question the claim in the edit summary that a false Latin plural is "more correct". Dbfirs 07:32, 21 March 2013 (UTC)

Removed section on symmetry

A grumpy editor removed this section. Tom Ruen (talk) 07:44, 11 June 2015 (UTC)

Symmetry In general, any planar polygon can represent the base of a pyramid. The symmetry of a right pyramid will be the same as the base polygon. A right pyramid with a regular polygon base with 2D dihedral symmetry Dihn, order 2n has Cnv in Schoenflies_notation. A base polygon with 2D cyclic symmetry Cn, order n is called also Cn in 3-dimensions. An oblique pyramid in general, whether acute, right-angled, or obtuse, has no symmetry, but it can have mirror symmetry if the apex is directly above a mirror line of the base polygon. A triangular based pyramid may also have higher symmetries from other apex-base orientations as well. For example, on a square pyramid, with the apex colored blue, and vertical height drawn in red, and with blue symmetry lines drawn on the base:

Because it's original research, and (as is likely with original research) partly incorrect. In particular I have twice pointed out that it is not true that the symmetry of a right pyramid is not always the same as the base. The regular tetrahedron is an exception, with more symmetry than its base. —David Eppstein (talk) 14:38, 11 June 2015 (UTC)

You're just being grumpy, expressing a special case as if its a flaw. With the base distinct from the sides, the symmetry is correct. So instead of improving the wording to fit your mental perfection, you remove the whole section. Why not just say you don't want this information up? That would be more honest. Should we also say a general nonsquare rhombus has Dih₂ symmetry to make sure people don't get confused that a square rhombus also only has order-4 symmetry? Tom Ruen (talk) 15:20, 11 June 2015 (UTC)

It makes me grumpy when people think they are doing mathematics, get it wrong, present their mistakes to the world on Wikipedia as if they were truths, and then try to defend the mistakes. —David Eppstein (talk) 16:19, 11 June 2015 (UTC)

Yes, indeed, and I just looked up what Coxeter said on the symmetry of pyramids, and imagine that, he also fails to give the regular tetrahedron as a special case as higher symmetry than a general regular right pyramid. He must have been a poor thinker and writer too, just like me. Tom Ruen (talk) 16:24, 11 June 2015 (UTC)

BTW, that is not the only exception. It is also possible for a right pyramid over an iscosceles triangle to have more symmetry than its base. —David Eppstein (talk) 20:12, 12 June 2015 (UTC)

How do you suggest you express these exceptions? Currently it says A triangular based pyramid may also have higher symmetries from other apex-base orientations as well. Tom Ruen (talk) 16:30, 13 June 2015 (UTC)

I would suggest we find a reliable source that gets it right and follow what they do. That is the correct way of avoiding original research. —David Eppstein (talk) 17:12, 13 June 2015 (UTC)

That's the whole problem. You can quote sources without understanding the limitations of those source, or which can also ignore special cases, and you're back where you started. So the only answer is to assume the general case is what we're interested in, not special cases.

And as I already contrasted, do we need to say a Rhombus has Dih₂ symmetry, unless its a square, in which case it has Dih₄ symmetry. And both are true statements, but what if no sources say that, what if that is synthesis? What if there's a different special case of a rhombus with higher symmetry, like a skew rhombus of course which can have 3D D_2d symmetry. What if no sources say that? Maybe we have to add a qualifier planar rhombi. Would that be enough? What if we can't dare say a general rhombus has Dih₂ symmetry because an imaginary case we can't see, or which all sources ever written don't say, then we can't say it. And if we say "well, let's just exclude the square and assume no other cases exist.", but no source explicitly says that. It's hopeless by unless you brow beat some "reliable" author to explicitly prove all cases, and states them and fails to make any mistakes and fails to ignore specific cases. Maybe someone should write a PhD thesis on the symmetry of a general rhombus?! Tom Ruen (talk) 17:47, 13 June 2015 (UTC)

References

typo in first section

Where it says "A triangle-based is more often called a tetrahedron." should it not say "A triangle-based pyramid is more often called a tetrahedron." David.daileyatsrudotedu (talk) 17:30, 12 October 2016 (UTC)

Sure, I added the word. Tom Ruen (talk) 06:21, 15 October 2016 (UTC)