My belief, which could be wrong, if we change π and distance metric i.e. definition of unit distance between 1 and 2, 4 and 5, 10 and 11 to be their unit distan

My belief, which could be wrong, if we change π and distance metric i.e. definition of unit distance between 1 and 2, 4 and 5, 10 and 11 to be their unit distance, all the equations involving numbers and pi would come out to be same. e.g. basel problem etc.