Pi (π) is an irrational and transcendental number that represents the ratio of the circumference of a circle to its diameter. It is a mathematical constant because it is a fixed value that is inherent in the geometry of circles and appears in many mathematical formulas and calculations.

One of the reasons that pi is called a mathematical constant is that its value does not change, regardless of the size of the circle. This is because pi is defined as the ratio of the circumference of a circle to its diameter, and this ratio remains constant for all circles, regardless of their size.

In mathematical terms, pi is defined as the ratio of the circumference (C) of a circle to its diameter (d), expressed as π = C/d. This ratio is always the same for any given circle, regardless of its size, and it is approximately equal to 3.14159.

Another reason that pi is considered a mathematical constant is that it appears in many mathematical formulas and calculations, including those used in trigonometry, geometry, calculus, and physics. For example, the area of a circle can be calculated using the formula A = πr², where r is the radius of the circle. Pi also appears in the formula for the surface area and volume of a sphere, as well as in many other mathematical equations.

Furthermore, pi is an irrational number, which means that its decimal expansion goes on infinitely without repeating. This property makes pi an important mathematical constant because it cannot be expressed as a simple fraction, and its value can only be approximated. In fact, mathematicians have calculated the value of pi to trillions of digits, and yet its decimal expansion continues infinitely without any discernible pattern.

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