Theodorus' constant, also known as the square root of 2 or the Pythagoras constant, is a fundamental mathematical constant denoted by the symbol √2. Its value is approximately equal to 1.41421356237 when expressed as a decimal, but its exact value cannot be represented as a finite decimal because √2 is an irrational number.
Theodorus of Cyrene, an ancient Greek mathematician, is often associated with discovering that the square root of 2 is an irrational number. Legend has it that Theodorus encountered the irrationality of √2 when trying to express the diagonal of a square as a ratio of its side length.
Theodorus' constant (√2) has various applications in mathematics, particularly in geometry, trigonometry, calculus, and other fields of science and engineering. It appears in formulas related to the Pythagorean theorem, as well as in various mathematical proofs and calculations involving areas, volumes, and the relationships between the sides and diagonals of geometric figures.