# Equivalent of the word "quadrant"

What would be the equivalent of the word quadrant when referring to 1/2 and 1/8 of an area? I'm looking for a more specific term than simply a half.

To give more detail, I'm looking for a term which can refer to a node of a binary tree data structure. In a quad tree data structure, you can refer to each node as a quadrant. I'm looking for the equivalent reference in a binary tree. It would be incorrect to refer to a node in a quad tree as a quarter or a quarter-plane, likewise for a binary tree it would be incorrect to refer to a node as a half or half-plane.

• One half is perfectly technical, and I am not sure to what end I'd be looking for an obscure term where a universally understood one will do. Feb 6, 2014 at 11:52
• @RegDwigнt I'm actually looking for a term which specifically means a sub-node of a binary tree, in terms of area. For example, in a quad-tree you refer to each sub-node as a quadrant. It wouldn't be correct to refer to a node as a quarter or a quarter-plane, likewise in a binary tree it would be incorrect to refer to each sub-node as a half or a half-plane. Feb 6, 2014 at 12:03
• Well. That makes sense. Though of course you'll agree we can't quite read people's minds to that extent. So providing such information up-front is always a good idea. Feb 6, 2014 at 12:09
• It’s not specific to binary, quaternary, or octonary relations, but in a tree structure in general, I would normally call any individual node a branch. In a binary tree, the singular ‘branch’ will itself be equal to ‘half’, but somehow sounds more specific. Feb 6, 2014 at 13:39
• Nodes in binary trees are often called the "left" and "right" nodes of their parent. Feb 6, 2014 at 17:35

1/2 = semi-circle or half

1/8 = octant

In general, they are all orthants.

• Is there a more technical term for 1/2 than simply one half? Feb 6, 2014 at 11:42
• @Someone not that I could find or know of. Feb 6, 2014 at 11:57
• "The upper half-plane" is a technical term used in mathematics; if there were a better word, I suspect mathematicians would be using it. Feb 6, 2014 at 13:36

Octant for an eighth.

For a half, there's the general half, and some more specific terms; of a circle, semi-circle, of an n-dimensional space, half-space, of a 2-dimensional space, half-plane. Of a line, ray.

For "half", depending on the context, you might also use "bifurcate". The disadvantage for the "use case" is that this generally describes the splitting into two, rather than the resultant (two) areas.