The "German" way of showing three — thumb, index, and middle finger — is the standard convention across most of continental Europe.
Countries that use it include:
France
Austria
Switzerland
Italy
Spain (though some Spanish speakers report using the index-first method
Poland
Slovakia
Netherlands (most Dutch people count from the thumb, though they often use index + middle for "two").
This "thumb-first" system (thumb = 1, index = 2, middle = 3, etc.) is contrasted with the "index-first" system used in the US, UK, Ireland, Australia, and parts of Russia, where three is shown with the index, middle, and ring fingers.
The difference is studied under the term dactylonomy (finger-counting), and it varies even within individual countries — some British people, for example, use the thumb-first method as well.
The movie "Inglourious Basterds" has a scene about this.