1414213562373095

1414213562373095 is a 16-digit integer that encodes the decimal expansion of the mathematical constant sqrt(2) (the square root of two) up to 15 fractional digits. Specifically, the decimal form of sqrt(2) begins 1.414213562373095..., and removing the decimal point from the first 16 digits yields 1414213562373095. This number can be viewed as sqrt(2) scaled by 10^15 and truncated to an integer.

sqrt(2) is an irrational number, the positive solution to x^2 = 2. It is also the value used to describe the diagonal of a unit square, illustrating its geometric origin. The decimal expansion never terminates or repeats, a property that underpins many number-theory and computational concepts. In mathematics, sqrt(2) has a continued fraction representation [1; 2, 2, 2, ...], with well-known rational convergents such as 3/2, 7/5, 17/12, 99/70, and 577/408, which provide progressively accurate approximations.

In computing, representations like 1414213562373095 appear in fixed-point arithmetic and data encoding when a truncated decimal expansion of sqrt(2) is stored without a decimal point. The true value of sqrt(2) cannot be exact in finite precision, but modern floating-point formats (for example, IEEE 754 double precision) store it as approximately 1.4142135623730951. This makes the integer a useful reference for testing fixed-point and precision-related routines.

As a fundamental irrational, sqrt(2) and its digit patterns continue to be of interest in numerical analysis, geometry, and algorithms that rely on precise irrational approximations.