Affine space and Coordinate System

This interactive demonstration that explains the difference between an affine space and a coordinate system. The demonstration uses two side-by-side canvases. The first canvas shows an abstract affine space with points p, q, and o plotted without any grid or axes, highlighting that a point's existence is independent of a coordinate system. The second canvas adds a coordinate system to the space, using point o as the origin. It then illustrates how the coordinates of p and q are found by projecting them onto the new x1 and x2 axes. Users can adjust the positions of p and q to see how their coordinates dynamically change, making the relationship between the two concepts clear.

$\complement\cdots$Counselor

</aside>