# Definition:Tribonacci Constant

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## 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

**, according to taste.**

*trib*-bo-*nar*-chiThe 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**: 203 – 214) www.jstor.org/stable/3620403