3D angles- can they exist?

fromage

i would like to know if the 'angle' between lets say the walls of a room (ie. the intersection of 3 planes all perpendicular to each other) can be represented in mathematical terms, but as a kind of 3D angle- that is to say not as a combination of 2D angles but as an altogether new form of representing the gap between intersecting planes.
Is there any way to do this and if not why can't these 'angles' be represented in 3D?

Simon Bridge

Welcome to PF;
Look up "solid angle".

dkotschessaa

Cool, Simon.

I'm in Linear Algebra right now, so correct me if I'm wrong... But isn't this also what we are talking about with certain linear transformations, which can be rotations in any number of dimensions?

-Dave K

HallsofIvy

No, a "solid angle" is NOT a rotation in three dimensions, any more than a regular angle is a rotation in two dimensions. You can use an angle, in two dimensions to define a rotation but you will also need to specify a point to rotate about. You can use a solid angle to define a rotation but in three dimensions, you will need to specify a point to rotate about and an axis of rotation.

Simon Bridge

"angle" is one of those concepts you use, almost unconsciously, without really thinking about what it is. Looking at the "similar threads" section (below the "quick reply" box) there is a lot of discussion. You should look up the terms and then read some of the other threads.

Like HallsofIvy points out, it can be important to distinguish the thing from it's uses.
When you want to extend an idea that works in 2 or 3 dimensions, into 4 or more, then you really need to be clear about what the idea embodies.