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
(OEIS A226317 ; Finch 2009), where is the Riemann zeta
function .
See also Irrational Number ,
Pythagoras's Constant ,
Square Root ,
Theodorus's
Constant Digits ,
Theodorus Spiral
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References Davis, P. J. Spirals from Theodorus to Chaos. Wellesley, MA: A K Peters, 1993. Finch,
S. "Constant of Theodorus." http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.440.3922&rep=rep1&type=pdf . Gautschi,
W. "The Spiral of Theodorus, Numerical Analysis, and Special Functions."
https://www.cs.purdue.edu/homes/wxg/slidesTheodorus.pdf . Jones,
M. F. "Approximations to the Square Roots of the Primes Less Than 100."
Math. Comput. 22 , 234-235, 1968. Sloane, N. J. A.
Sequences A002194 /M4326, A004547 ,
A040001 , and A226317
in "The On-Line Encyclopedia of Integer Sequences." Uhler,
H. S. "Approximations Exceeding Decimals for , , , and Distribution of Digits in Them." Proc.
Nat. Acad. Sci. USA 37 , 443-447, 1951. Wells, D. The
Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England:
Penguin Books, pp. 34-35, 1986. Referenced on Wolfram|Alpha Theodorus's Constant
Cite this as:
Weisstein, Eric W. "Theodorus's Constant."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/TheodorussConstant.html
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