Theodorus's Constant

There are (at least) two mathematical constants associated with Theodorus. The first Theodorus's constant is the elementary algebraic number , i.e., the square root of 3. It has decimal expansion

(1)

(OEIS A002194) and is named after Theodorus, who proved that the square roots of the integers from 3 to 17 (excluding squares 4, 9,and 16) are irrational (Wells 1986, p. 34). The space diagonal of a unit cube has length .

has continued fraction [1, 1, 2, 1, 2, 1, 2, ...] (OEIS A040001). In binary, it is represented by

(2)

(OEIS A004547).

Another constant sometimes known as the constant of Theodorus is the slope of a continuous analog of the discrete Theodorus spiral due to Davis (1993) at the point , given by

			(3)
			(4)
			(5)
			(6)

(OEIS A226317; Finch 2009), where is the Riemann zeta function.