According to [constructivism](http://en.wikipedia.org/wiki/Constructivism_(mathematics\)), "it is necessary to find (or "construct") a mathematical object to prove that it exists". There are several formulas to calculate pi, such as:

formula for pi http://mathworld.wolfram.com/images/equations/PiFormulas/NumberedEquation3.gif

so I take it pi exists according to constructivism.

According to finitism, which is a form of constructivism, "a mathematical object does not exist unless it can be constructed from natural numbers in a finite number of steps."

Where does that leave irrational numbers, such as pi? Do they simply not exist according to finitism? How does one reason about the ratio between a circle's circumference and its diameter, if one is working within a finitistic/ultrafinitistic framework?