Origin of Clapping for Applause

I’m curious:
How long have people been clapping as applause in the current style? Did the Romans do it? Did Asian cultures do it? When did it start? etc.

I know that in Greek theatre, applause was used to “boo” poor performers off the stage, but I don’t know when it became transformed into something appreciative.

Wikipaedia’s article has some interesting tidbits, but no comment on the origins…

Grim

Film-maker Rob Reiner said the first joke he ever wrote that was performed on-air was an answer to this question. Rob’s dad Carl Reiner and Mel Brooks were writing jokes for their “2000 year old man” bit, and Rob suggested one about the origin of clapping as approval. (This is not an exact quote.)

Originally, when people saw something good on stage, they’d smack their hands to their cheeks and say, “Oh, boy, that was good!” Eventually, somebody was jostled while doing that, and his hands clapped together, missing the face. It hurt less that way, so everybody started applauding that way.*

*the “Home Alone” pose.