Hiiii
What’s your favorite math
hmmm.... i'm a pascal's triangle enjoyer. lots of fun identities, and i dont come across binomial expansions that often but i always use pascal's triangle for that. if you highlight all the odd numbers, you get sierpinski's triangle. the diagonals give you the triangular numbers, the tetrahedral numbers, and so on. the rows sum to powers of 2. the hockeystick lemma. probably some other stuff that i dont know.
this is a hard question because the word "favorite" makes me think about picking the absolute best one and having a passionate explanation for why i like it so much. pascal's triangle is not groundbreakingly cool or advanced, but it's kind of fun.
other math party tricks that i like:
the dropping sticks approximation of pi (buffon's needle)
the Long Line
the well ordering theorem
axiom of choice proofs
godel's incompleteness theorems reduces down to the halting problem