In the CMYK color model, which like the RGB color model is formed by a cube, the edges of the cube form vectors of length "1". These unit vectors are the colorscyan, magenta and yellow (Yellow), hence the name CMY. The "K" stands for key and is deliberately intended to be different from the designation black, since in printing terms it is only used to increase contrast.
The additional black is necessary because, in practice, no real black is produced from the three primary colors CMY, even if all three primary colors are printed at 100%, since pure inks are not available in practice. The print results therefore appear less saturated and low in contrast.
The two color models RGB and CMYK have no mathematical connection, there are only approximations in the conversion from one model to the other. One of these conversion models is the UCR process, Under Color Removal (UCR).