Article citationsMore >>

H. S. M. Coxeter, Non-Euclidean Geometry (Univ. Toronto Press 1942, reissued 1998 by Mathematical Assoc. of America).

has been cited by the following article:


Carl Sagan’s Conjecture of a Message in π

1B&E Scientific Ltd, Seaford BN25 4PA, United Kingdom

International Journal of Physics. 2014, Vol. 2 No. 6, 264-266
DOI: 10.12691/ijp-2-6-9
Copyright © 2014 Science and Education Publishing

Cite this paper:
Arne Bergstrom. Carl Sagan’s Conjecture of a Message in π. International Journal of Physics. 2014; 2(6):264-266. doi: 10.12691/ijp-2-6-9.

Correspondence to: Arne  Bergstrom, B&E Scientific Ltd, Seaford BN25 4PA, United Kingdom. Email:


In his novel Contact, the astrophysicist Carl Sagan hypothesized an alien message to be buried somewhere deep inside the numerical representation of the transcendental number π. The present article looks for markers that might possibly support such a hypothesis, and surprisingly finds a sequence of seven successive zeros (actually seven successive nines rounded off) at a depth of 3256 digits into the representation of 2π in the special case of base ten. Finding such a sequence of zeros within the first 1000 digits has a probability of 1 in 10000. No such occurrences happen even remotely for 2π at any base other than ten, nor even remotely in corresponding representations of other common transcendental numbers, such as e, which appear in physical applications. In π, this occurrence thus also remarkably appears at a depth that is a multiple of the same power of two as bits in a computer byte, which thus makes it even more enigmatic. Still, these effects are most probably just numerical coincidences without physical relevance.