On the Ratio of Circumference to Diameter for the Largest Observable Circles: An Empirical Approach

TL;DR

This paper empirically measures the ratio of circumference to diameter for the largest observable circles, examining historical and theoretical implications, and ruling out some common approximations with high confidence.

Contribution

It provides an empirical assessment of pi for the largest observable circles and discusses its implications for cosmology and fundamental physics.

Findings

The value 16/5 remains viable for the largest observable circles.

The value 3 is statistically ruled out at over 5 sigma.

Connections are discussed between circle ratios and theories like string theory and neutrinos.

Abstract

I present here a measurement of pi as determined for the largest observable circles. Intriguingly, the value of 16/5 asserted by the House of Representatives of the State of Indiana in 1897 is still viable, although strongly disfavored relative to 22/7, another popular value. The oft-used `small-circle' value of 3 is ruled out at greater than 5\sigma. We discuss connections with string theory, sterile neutrinos, and possibilities for (very large) lower limits to the size of the Universe.