Definition:Tribonacci Constant

Definition

The Tribonacci constant $\eta$ is the one real root of the cubic:

$x^3 - x^2 - x - 1 = 0$

Its decimal expansion starts:

$\eta = 1 \cdotp 83928 \, 67552 \, 1416 \ldots$

This sequence is A058265 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Also known as

Some sources leave its first letter in lowercase: tribonacci constant.

Linguistic Note

The word Tribonacci, in the context of Tribonacci constant and Tribonacci sequence, is a portmanteau word formed from tri, from the Greek word for three, and the name of the mathematician Fibonacci.

Hence it is pronounced trib-bo-nat-chi, or trib-bo-nar-chi, according to taste.

The word arises as a direct analogy with the Fibonacci numbers.

Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1 \cdotp 83928 \, 67552 \, 1416 \ldots$

• 1998: John Sharp: Have You Seen This Number? (The Mathematical Gazette Vol. 82: pp. 203 – 214)  www.jstor.org/stable/3620403