Is it possible to type a π on the keyboard of WP(8.1)? I know you can copy and paste it, but that takes a lot of time.
How to do this? Are there also some other mathematics symbols (like Alpha, Beta...)?
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For symbols that are simply upper- or lowercase Greek letters (e.g. pi, sigma, delta) you can install the Greek keyboard layout:
Note that it's a ~16 MB download, and you may have to install a language support update that requires a phone restart. At least that was the case when I tested it.
A few other common symbols (e.g. plus-minus sign, not equal sign, square root symbol) are available in the second panel of the symbols layout. Tap the &123 button and then the → button to access it. As shown below, most of the less common symbols aren't immediately visible and require a long press on some other symbol's button:
You already have an excellent answer that will help you wherever you may be typing, but I’d like to add an app-based option that might be easier if you are writing a lot of mathematical formulae.
As you can tell from the name, the primary purpose of the app is to input formulae into Wolfram|Alpha, but it also has the option to copy everything to the clipboard:
Even though many of these symbols and letters can be approximated with the regular keyboard, I’ve found that the layout of this app’s keyboard makes it very easy to write something quickly and copy it.
Hopefully being able to write a whole formula quickly will make up for the copying and pasting that you wanted to avoid.