👉 In mathematics, a non-imperial number is an irrational number that cannot be expressed as a ratio of two integers. These numbers include pi (π), e, and many other transcendental constants such as square roots of 2, square roots of -3, and the golden ratio phi. Non-imperial numbers are often used in mathematical analysis and in the study of complex numbers to represent quantities that cannot be expressed as ratios of two integers. They are also useful in the construction of algorithms for computing