When to use “on” and “in” prepositions in math:
Point on/in the plane
Point on/in the cartesian coordinate system
Answer
ON
We can describe features on surfaces or boundaries. Those surfaces can be of any dimension. (A point ON a line, a point ON a circle, a point ON “the plane,” a point ON the surface of a cylinder, a point ON the surface of a klein bottle.)
INSIDE
For closed surfaces, we can refer to points that are on one side of the surface or the other (within boundaries). (A point INSIDE a circle, a point INSIDE a cylinder. A point WITHIN/INSIDE the boundaries of a region)
IN
When we refers to systems or spaces we use in. (A point IN 3-space. A point IN a coordinate system. A vector IN Hilbert Space)
Attribution
Source : Link , Question Author : Yaroslav Holod , Answer Author : Adam
