The deep recesses of the number line are not as forbidding as they might seem. That’s one consequence of a major new proof about how complicated numbers yield to simple approximations.

Pi belongs to a huge mathematical group called irrational numbers, which go on forever and cannot be written as fractions. Scientists have calculated pi to 105 trillion digits, although most of us ...

Numbers comprise a string of digits that are used to represent various quantities and amounts. Each number designates the size of some quantity that is either large or small. Numbers can be of ...

Most people rarely deal with irrational numbers—it would be, well, irrational, as they run on forever, and representing them accurately requires an infinite amount of space. But irrational ...

The deep recesses of the number line are not as forbidding as they might seem. That's one consequence of a major new proof about how complicated numbers yield to simple approximations. The proof ...

Real numbers are, in fact, pretty much any number that you can think of. This can include whole numbers or integers, fractions, rational numbers and irrational numbers.

It’s that the golden ratio, among all irrational numbers, is the most irrational one. What can that mean? Either a number is the ratio of two whole numbers or it isn’t*.

Because every transcendental number is irrational, any proof showing that pi is transcendental also proves that pi is irrational.