1pi

1π refers to the quantity obtained by multiplying 1 by π. In practical terms it is equal to π, and in most mathematical contexts the expression 1π is simply π.

π is the constant that represents the ratio of a circle's circumference to its diameter in Euclidean geometry. It is the same ratio for any circle, and its use spans geometry, trigonometry, and analysis. The symbol π is a long-standing convention, with a history dating back to ancient civilizations and a modern formalization as a transcendental number.

Value and properties: π is an irrational number, meaning it cannot be expressed as a finite fraction, and its decimal expansion is non-repeating. It is also transcendental, a stronger property that implies it is not the root of any nonzero polynomial equation with rational coefficients. The decimal expansion begins 3.14159 and continues without repeating patterns.

Key formulas and relationships: The circumference of a circle is C = 2πr, and the area is A = πr^2. In radian measure, arc length is s = rθ, with θ in radians; a full circle corresponds to θ = 2π. π also appears in many areas of mathematics and physics, including series, integrals, and fundamental relations such as Euler's identity e^(iπ) + 1 = 0.

Usage and notation: In most contexts, 1π is simply another way to write π and is rarely used as a distinct symbol. It may appear in algebraic expressions or programming contexts where explicit multiplication by π is needed, but it denotes the same constant as π itself.