The discussion focuses on determining the number of distinct combinations of the point (x, y, z) in three-dimensional space, where each variable can be either positive or negative. It is established that there are eight octants in 3D space, corresponding to the combinations of signs for x, y, and z. The mathematical principle behind this is that in n dimensions, the number of subsets is given by 2^n. Thus, for three dimensions, the total combinations are 2^3, resulting in eight unique configurations.
PREREQUISITESMathematicians, students studying geometry, educators teaching coordinate systems, and anyone interested in combinatorial analysis in multi-dimensional spaces.
In 3D coordinates, how many "quadrants" are there?Rosebud said:How do I find all the different combinations of the point (x,y,z) when x,y, and z can be either positive and negative? For example, what I'm trying to solve is (+,+,+), (+,+,-), (+,-,-), etc. How do I find out how many different points there are and the sign of each variable for each distinct point?
Right. So how many ways could you have the point positioned, from the point of view of differing signs?Rosebud said:There are eight octants. I'm not sure about quadrants.
Yeah, that's why I put "quadrants" in quotes, to mean just "sections", which you more appropriately identified as octants.Rosebud said:There are eight octants. I'm not sure about quadrants.