Final answer:
In mathematics, the term transcendental refers to numbers that are not solutions to any polynomial equation with rational coefficients. Pi is a transcendental number, meaning that it cannot be expressed as the root of such an algebraic equation, and is an extension of the Pythagorean understanding of numbers defining the universe.
Step-by-step explanation:
In mathematics, transcendental means that a number is non-algebraic; that is, the number is not a root of any non-zero polynomial equation with rational coefficients. When we say that pi (π) is transcendental, we mean that it cannot be expressed as the solution to any such algebraic equation. Pi is the Greek letter used to represent the mathematical constant that is the ratio of a circle's circumference to its diameter, an irrational number that extends to infinity, commonly approximated as 3.14.
Calling a number transcendental implies it's not just irrational (can't be written as a simple fraction), but it also lies beyond the scope of being the solution to any polynomial equation with rational number coefficients. This concept goes back to the Pythagorean theorem and the notion in ancient Greek mathematics that numbers and their relationships define the universe. Pythagoras emphasized that reason and mathematical principles are fundamental to understanding truth and reality.
The recognition of pi as a transcendental number informs us about the deep relationship between mathematics and the natural world, something that has been a point of contemplation since the days of Pythagoras. In essence, when we discuss transcendental numbers, we delve into the heart of mathematics being the language of nature, a sentiment echoed by Renaissance thinkers and beyond.