Question

The number π (/paɪ/) is a mathematical constant. Originally defined as the ratio of a circle's circumference to its diameter, it now has various equivalent definitions and appears in many formulas in all areas of mathematics and physics. It is approximately equal to 3.14159. It has been represented by the Greek letter "π" since the mid-18th century, though it is also sometimes spelled out as "pi". It is also called Archimedes’ constant.[1] Being an irrational number, π cannot be expressed exactly as a common fraction (equivalently, its decimal representation never ends and never settles into a permanent repeating pattern). Still, fractions such as 22/7 and other rational numbers are commonly used to approximate π. The digits appear to be randomly distributed. In particular, the digit sequence of π is conjectured to satisfy a specific kind of statistical randomness, but to date, no proof of this has been discovered. Also, π is a transcendental number; that is, a number that is not the root of any non-zero polynomial having rational coefficients. This transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge. Is this true or false

Answer 1

The assertion that number pi (π) can't be expressed as a simple fraction, is not the root of any non-zero polynomial with rational coefficients, and is transcendent, thus making it impossible to square the circle with just a compass and a straightedge, is indeed accurate.

In terms of real numbers, an irrational number, like pi, can't be expressed as a fraction of two integers. Even though we often use 3.14 or 22/7 as approximations, the true value of pi is an infinite un-repetitive decimal, signifying that it's irrational.

Moreover, pi is a transcendental number, which means it's not algebraic; it can't be a root of any non-zero polynomial equation with rational coefficients. Even though it may seem abstract, this has practical implications. Since ancient times, mathematicians attempted to "square the circle". The nature of pi as a transcendental number proves this to be impossible using basic geometric tools: a compass and a straightedge.

In conclusion, the statement is true: pi is irrational and transcendental, and you can't square a circle with a compass and straight-edge alone.

Answer: True