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# Transcendental Numbers

Transcendental numbers may be defined as either real or complex numbers that are not the root of any rational polynomial equation. This means that they are not algebraic numbers and must be irrational numbers since all rational numbers are algebraic numbers by definition.

In this article, we''ll look at some common examples of transcendental numbers. Let''s get started!

## Examples of transcendental numbers

Two of the most common transcendental numbers are π, the ratio of a circle''s circumference to its diameter with a value of about 3.1416, and e, the base of natural logarithms with a value of about 2.718. However, there are an infinite number of transcendental numbers that we simply don''t deal with very often. Euler is the mathematician credited with defining transcendental numbers. Students typically study transcendental numbers for the first time in a college-level number theory course. There are actually more transcendental numbers than there are algebraic numbers!

## Practice Question

a. In your own words, what are the properties of transcendental numbers?

Transcendental numbers are irrational. They are not the solution to any rational polynomial equation. There are an infinite number of them, and we seldom work with them in mathematics.

## Topics related to the Transcendental Numbers

Powers of i

Logarithmic Functions

Solving Logarithmic Equations

## Flashcards covering the Transcendental Numbers

Algebra II Flashcards

College Algebra Flashcards

## Practice tests covering the Transcendental Numbers

Algebra II Diagnostic Tests

College Algebra Diagnostic Tests

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Many students find transcendental numbers too abstract to study. If this describes you, a 1-on-1 mathematics tutor could help out by pointing you toward branches of mathematics that work with them regularly. A tutor can also adapt lessons to your specific pacing needs, enhancing your study efficiency. Contact Varsity Tutors for more specific information including pricing details.

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