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.

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

After an infinite number of days, all kinds of numbers are created, from fractions to irrational numbers to infinities and infinitesimals. Credit: Lukáš Lánský/Wikimedia Commons (CC BY-SA 3.0) ...

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 ...

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 ...

Why do irrational numbers exist? originally appeared on Quora: the place to gain and share knowledge, empowering people to learn from others and better understand the world.

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 ...

But irrational constants such as π and √2—numbers that cannot be reduced to a simple fraction—frequently crop up in science and engineering.

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 ...

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