The example shows about 10 sprint lines. They all have "\n". But nowhere else on the entire page is found the \ backslash character. It must mean some flag or directive, with the argument being "n" in many cases.
Why is there no definition of \ followed by a single character indicates this or that?
Why is there no statement such as "\ followed by an argument does (this or that). The argument can be (list of arguments, one of which would be "n").
The backslash ‘\’ denotes an escape sequence. This provides a way of being able to specify a character that would otherwise be non-printable such as tab, newline or carriage return. The above linked reference shows a table of these. The example you gave prints two newlines (sometimes called linefeeds as well) before the output data. The value held in the variable period is printed using the format specified by:
%.1f
which is shorthand for a float type with 1 character after the decimal point. The % just marks the start of the format specifier. The characters ‘rpm’ will be printed immediately after the value. The table you lined already shows a table with a list of specifiers.
This hobby will be a lot easier if you take the time to learn. There are plenty of C/C++ guidebooks (pick them up for next to nothing at thrift stores and used book shops) as well as on line tutorials on every aspect of the languages.
A good read and reference for you would be the Arduino Cookbook. It is readily available world wide. I have seen it free for the download on this forum a year or so back. Start by simply skimming the whole thing then as you find something interesting give it a try.
Have you ever wondered: if a literal string is a bunch of characters between double-quotes, how do you get a double-quote in a string? One way is the aforementioned escape sequence. When designing these, the character chosen to start the sequence was not used that much for anything else at the time: the backslash (aka reverse solidus, and a bunch of other aliases).
to indicate you want a double-quote in the string and not end the string: \"
what if you actually want a backslash though: \\
while we're at it, we could also have some commonly used control characters, especially whitespace, using meaningful letters
newline/line feed: \n
carriage return: \r
tab: \t
NUL (not to be confused with null): \0 (zero)
in fact, you can specify a character directly by its numeric value (its code point); unfortunately, it has to be in octal, base-8, which has fallen out of practice; up to three digits: e.g. ESC is \033
ok, you can use hex instead; ESC is also \x1B. Tricky part in this case, it "consumes" all contiguous characters that are valid hex digits. So you can have ESC followed by "G" -- \x1BG -- but not followed by "F" -- \x1BF means something else entirely.
Escape sequences can be used in all strings, not just with printf. The magic character for that is the format specifier: %