Transcendental number facts for kids
A transcendental number is a special kind of number or complex number. It's a number that cannot be the answer to a simple algebra problem (called an algebraic equation) if that problem only uses integers (whole numbers) for its parts. Think of it this way: if you have an equation like `2x + 3 = 0` or `x^2 - 5 = 0`, the solutions to these are not transcendental numbers. Transcendental numbers are much harder to find using these kinds of equations.
Every transcendental number is also an irrational number. This means it cannot be written as a simple fraction (like 1/2 or 3/4). Its decimal form goes on forever without repeating.
Contents
Discovering Transcendental Numbers
The idea of transcendental numbers first appeared with mathematicians like Gottfried Wilhelm Leibniz and Leonhard Euler. They were among the first to think that such numbers might exist.
Who Proved Their Existence?
The first person to actually prove that transcendental numbers exist was a mathematician named Joseph Liouville. He did this important work in 1844. His proof showed that there are indeed numbers that cannot be solutions to algebraic equations with integer coefficients.
Famous Transcendental Numbers
Some of the most well-known numbers in mathematics are transcendental. Here are a few examples:
- e: This number is often called Euler's number. It's about 2.71828 and is very important in areas like calculus and finance.
- π: This is the famous number pi, which is about 3.14159. It's used to calculate the circumference and area of a circle.
- ea: If you take Euler's number (e) and raise it to the power of any non-zero algebraic number (a number that *can* be a solution to an algebraic equation), the result is also a transcendental number.
- 2√2: This number, which is 2 raised to the power of the square root of 2, is another example of a transcendental number.
See also
In Spanish: Número trascendente para niños
