Three dimensional space in the context of Mathematical space

In vector calculus and physics, a vector field is an assignment of a vector to each point in a space, most commonly Euclidean space ${\displaystyle \mathbb {R} ^{n}}$. A vector field on a plane can be visualized as a collection of arrows with given magnitudes and directions, each attached to a point on the plane. Vector fields are often used to model, for example, the speed and direction of a moving fluid throughout three dimensional space, such as the wind, or the strength and direction of some force, such as the magnetic or gravitational force, as it changes from one point to another point.

The elements of differential and integral calculus extend naturally to vector fields. When a vector field represents force, the line integral of a vector field represents the work done by a force moving along a path, and under this interpretation conservation of energy is exhibited as a special case of the fundamental theorem of calculus. Vector fields can usefully be thought of as representing the velocity of a moving flow in space, and this physical intuition leads to notions such as the divergence (which represents the rate of change of volume of a flow) and curl (which represents the rotation of a flow).

In chemistry, a space-filling model, also known as a calotte model, is a type of three-dimensional (3D) molecular model where the atoms are represented by spheres whose radii are proportional to the radii of the atoms and whose center-to-center distances are proportional to the distances between the atomic nuclei, all in the same scale. Atoms of different chemical elements are usually represented by spheres of different colors.

Space-filling calotte models are also referred to as CPK models after the chemists Robert Corey, Linus Pauling, and Walter Koltun, who over a span of time developed the modeling concept into a useful form. They are distinguished from other 3D representations, such as the ball-and-stick and skeletal models, by the use of the "full size" space-filling spheres for the atoms. The models are tactile and manually rotatable. They are useful for visualizing the effective shape and relative dimensions of a molecule, and (because of the rotatability) the shapes of the surface of the various conformers. On the other hand, these models mask the chemical bonds between the atoms, and make it difficult to see the structure of the molecule that is obscured by the atoms nearest to the viewer in a particular pose. For this reason, such models are of greater utility if they can be used dynamically, especially when used with complex molecules (e.g., see the greater understanding of the molecules shape given when the THC model is clicked on to rotate).