In a math book, is it OK to have a diagram wider than text width (so overriding the margins)?
Also, how do I center a wide figure so that it occupies both the left margin and the right margin (not only the right margin) using LaTeX software?
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It depends on the book design. Generally speaking, the width of a text column is kept within certain bounds in order to make the text scannable. A column of text will become much more difficult to read if the text gets wider than the reader can comfortably scan. But many books choose a wider page width so that they can accommodate wider elements such as diagrams, illustrations, and equations. Art books often have text that is less than half the width of the page (or in two columns) so that there is room to show the art at a reasonable size.
In other words, the printable limits of the page are often wider than the width of the text column precisely to accommodate cases like yours. In this case, the equation is not overriding the margin of the page. Rather, it is the text column that is deliberately less wide than the margins of the page.
You can extend visual media as far as you want on the printed page; so long as there is an adequate benefit to the reader (bigger will be more clear, diagram is complex, want subscripts and other symbols more readable...) The only limit is (of course) the page itself and the left-hand gutter.
Recommend asking the technical q re: LaTex separately or diff forum. I just wanted to address that since I'm ostensibly "a-ing the q" -thx.