This study illustrated a very easy method to approximate pi. With it's help to derive the stochastic functions of Doppler effect of observation. It explained why redshift detection is dominating in cosmic observation. It also showed the delivery of information and other globular effects from point-dimension to infinity sphere of space, and an thought experiment to understand the illusive space we live in. pi is a natural constant, however, an irrational number to us. I believe the approximation of pi shows the fact that mathematical models can never perfectly represent nature. It is not coincident that nature fits the mathematics. Instead, it is the logically constructed mathematical models can describe the nature sufficiently. We can say universe is musical, artistic, mathematical, and on. Nevertheless, our observation and measurement of the universe can only be approximate. Isn't it galactic elephant for visually-impaired to feel?