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I've only started studying $3D$ geometry and hence came about octants.

I tried combining sources online, but there seems to be a lot of ambiguity.

  1. My maths book labels the coord axes; and numbers and names the octants in a certain order, the rules for which are not specified.
  2. WolframAlpha does not label octants at all.

The ambiguity further deepens because Wikipedia says that "Octant ( + + + ) is sometimes referred to as the first octant, although similar ordinal name descriptors are not defined for the other seven octants" - which is in alignment with what WolframAlpha says - yet Wikipedia goes on to list names and numbers for all the octants (like my maths book did), without referencing a valid source as to where did it get that from.
There's even a mention of this ambiguity on the Talk page.

So, I basically want to know what exactly is the correct, authoritative numbering of octants?

Are all octants numbered and named OR is only the (+, +, +) called the first octant and are the rest ignored?

If your answer is the first part above, then please also state the correct numbering for the octants.

I know this is too trivial a problem but let's just fix it for once and for all!

Gaurang Tandon
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    I don't think I've ever heard someone refer explicit to the $n$th octant for any $n > 1$. Given the ambivalence of your sources, I'd say there is no "correct, authoritative numbering" and that efforts to "fix it once and for all" are futile and, given the rarity of the usage, not very helpful anyway. – Travis Willse Mar 31 '17 at 11:52
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    As far as I know, there is no numbering convention for the octants. This is because there is no natural order around the origin, unlike in 2D. The notation with $\pm\pm\pm$ is good enough. –  Mar 31 '17 at 11:52

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