Sofia's constant

Sofi likes the number guessing game I taught her which is supposed to teach her the value of log n searches but she hasn't quite figured that out yet. "Is it 1?" "Higher" "Is it 2?"

Every now and then I pick pi just to mess with her.

Today it was my turn to guess:

Jamie: is it 13?

Sofia: lower

Jamie: is it 9?

Sofia: higher

Jamie: is it 11?

Sofia: higher

Jamie: is it 12?

Sofia: higher

Jamie: are you sure? more than 12 and less than 13? 12 and a half?

Sofia: it's pi!

Jamie: it can't be pi, pi is between 3 and 4

Sofia: it's cupcake!