The plastic constant ,
sometimes also called le nombre radiant, the minimal Pisot number, plastic number,
plastic ratio, platin number, Siegel's number, or silver number, is the limiting
ratio of the successive terms of the Padovan sequence
or Perrin sequence. It is given by

The plastic constant
was originally studied in 1924 by Gérard Cordonnier when he was 17. In his
later correspondence with Dom Hans van der Laan, he described applications to architecture,
using the name "radiant number." In 1958, Cordonnier gave a lecture tour
that illustrated the use of the constant in many existing buildings and monuments
(C. Mannu, pers comm., Mar. 11, 2006).

satisfies the algebraic identities

(6)

and

(7)

and is therefore is one of the numbers for which there exist natural
numbers
and
such that
and .
It was proven by Aarts et al. (2001) that and the golden ratio are in fact the only such numbers.

The identity
leads to the beautiful nested radical identity

(8)

The plastic constant is also connected with the ring of integers of the number field since it the real root of the Weber
function for the smallest negative discriminant with class
number 3, namely .
In particular,