Talk:Perfect magic cube

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Added a bit to alternate definition (Nasik) and references --Harvey Heinz 00:36, 8 September 2007 (UTC)[reply]

Minor changes to Alternative definition, and see 2 also links --Harvey Heinz 15:39, 13 September 2007 (UTC)[reply]

Changed i.e. nasik... sentence to bold --Harvey Heinz (talk) 20:10, 4 November 2009 (UTC)[reply]

Can someone please replace the phrase "cross section diagonal" with a comprehensible phrase?

The first sentence reads as follows:

"In mathematics, a perfect magic cube is a magic cube in which not only the columns, rows, pillars and main space diagonals, but also the cross section diagonals sum up to the cube's magic constant."

This is an encyclopedia article, not a guessing game. So can someone knowledgeable please replace "cross section diagonal" with a clear unambiguous explanation of exactly which diagonals are being referred to? Many thanks.75.25.141.89 (talk) 03:13, 28 January 2013 (UTC)[reply]

My conjectures for perfect magic n-dimension hypercube and pandiagonal magic n-dimension hypercube

Conjecture: for integers n, k > 1, a perfect magic n-dimension hypercube with order k exists if and only if k > 2^n-1.

A pandiagonal magic n-dimension hypercube with order k exists if and only if k is a multiple of 2ⁿ, or k is odd and k ≥ 2ⁿ.

For example:

For magic squares: Order 2 does not exist, but all order ≥ 3 exist.

For pandiagonal magic squares: Order 3 and 4k+2 do not exist, but all other order exist.

For perfect magic cubes: Order 2, 3, and 4 do not exist, but all order ≥ 5 exist.

For pantriagonal magic cubes: Order 3, 5, 7, 8k+2, 8k+4, and 8k+6 do not exist, but all other order exist.

Is it true?

Am I missing something here...

I'm not a mathematician, and the first thing I met in this article was "Perfect magic cubes of order one are trivial; cubes of orders two to four can be proven not to exist" WTF is order? I thought - but I worked it out, because a bit lower down there's an example "Order 4 cube by Thomas Krijgsman, 1982; magic constant 130."

Hang on though, "cubes of orders two to four can be proven not to exist" and yet here is an example.

I agree that using the word order without first defining it as the length of a side is not helpful to anyone unfamiliar with the specific terminology, which may even include most mathematicians. With regards to the discrepancy that has been pointed out, simple calculation shows that the example "Order 4 cube by Thomas Krijgsman, 1982; magic constant 130." is not a perfect cube by the definition given in the article, since the main space diagonals do not sum to 130 — for instance, 32 + 64 + 16 + 48 = 160. The citation for this example is also a 404 link, and so I believe this example should be removed. 90.244.184.188 (talk) 18:05, 4 September 2021 (UTC)[reply]