Thanks a lot Boud. Indeed Wikipedia exists and there are also many other books that provide the mathematical proofs. But the emphasis here is not on mathematical rigour, its on visualization/intuition for someone who is not too invested in theory, but needs to properly understand the outputs of the program: an observer.
Atleast when I was studying these subjects, I couldn't find any proper place to help in the visualization, everywhere I could find would jump so directly deep into the mathematics that even though I followed the equations and appreciated their abstract beauty, I could never actually visualize what I am doing or what all these concepts were. So I came up with this explanation (many years before creating Gnuastro).
The thing about Gnuastro is that it is not just a reference for abstract teaching or just a blackbox software that throws out results. Gnuastro is actually the book+software: not just a book or not just a software.
I have fully described the philosophy/manifesto behind creating Gnuastro in the introduction (link below), I would really appreciate your thoughts on it (maybe as a separate task):
https://www.gnu.org/software/gnuastro/manual/html_node/Scienceanditstools.html
You see this in many other contexts throughout the book. For example here is a very long section on frequency domain convolution:
https://www.gnu.org/software/gnuastro/manual/html_node/FrequencydomainandFourieroperations.html
It starts with visualizing the complex plane and goes onto the fourier series and transform and sampling theory and etc. Observers (users of Gnuastro's convolve) need to understand these concepts (I have seen many who don't, they just know the equations, but have no intuition).
Another nice example in another context might be the introduction to libraries in the book:
https://www.gnu.org/software/gnuastro/manual/html_node/Reviewoflibraryfundamentals.html
Like the discussion above for curvature, all this information is available in other abstract teaching books (on digital signal processing and programming respectively), but I don't think that makes these sections redundant. Given the discussion in the "Science and its tools" section, does this convince you?
Ofcourse, we don't want the Gnuastro book to be a full encyclopedia, we can put links to references (books/wikipedia) for people interested in further reading to avoid going into too much detail in what ever context we are discussing.
