concept circle in category deep learning

This is an excerpt from Manning's book Math and Architectures of Deep Learning. Login to get full access to this book.

Figure 2.14: Rotation in plane about Origin. By definition rotation does not change the distance from the center of rotation, that is what the circle indicates.

Figure 2.14 shows a point (x, y) rotated about the origin by an angle q. The original point’s position vector made an angle a with the X axis. Post rotation, the point’s new coordinates are (x′, y′). Note that by definition rotation does not change the distance from the center of rotation, that is what the circle indicates. Some well known rotation matrices:

Figure 2.14: Rotation in plane about Origin. By definition rotation does not change the distance from the center of rotation, that is what the circle indicates.

[26] This has nothing to do with the natural number π denoting the ratio of circumference to diameter of a circle, we are just re-using the symbol π following a popular convention.

[27] once again, this has nothing to do with the natural number π denoting the ratio of circumference to diameter of a circle - we are simply reusing that symbol.