14142135623730951

14142135623730951 is a 17-digit integer formed by removing the decimal point from the decimal expansion of the square root of 2 (1.4142135623730951) up to 16 places. It represents sqrt(2) scaled by 10^16, equal to sqrt(2) multiplied by 10^16 when truncated to 16 digits after the decimal.

The square root of 2 is the positive solution to the equation x^2 = 2. It is an irrational number, meaning its decimal expansion does not terminate or repeat. The value 1.4142135623730951 is a commonly cited approximation used in a variety of contexts, including education, engineering, and computational work.

Geometric significance underpins its popularity: the diagonal length of a unit square is sqrt(2), a result central to the Pythagorean theorem. The irrational nature of sqrt(2) has historically motivated studies in number theory and approximation methods, producing many fractional and fixed-point representations for practical use.

In computing and numerical analysis, integers like 14142135623730951 are sometimes employed as fixed-point representations of irrational constants. By storing the scaled value as an integer, systems can perform arithmetic with a known precision without floating-point hardware, while still enabling recovery of the approximate real value by dividing by 10^16.

See also: square root of 2, fixed-point arithmetic, Pythagoras and the diagonal of a unit square, irrational numbers.