Irrational numbers are numbers that cannot be expressed as the ratio of two whole numbers. This is opposed to rational numbers, like 2, 7, one-fifth and -13/9, which can be, and are, expressed as the ...

Mathematics students face challenges with rational and irrational numbers. Understanding the principles and patterns simplifies this concept. Rational numbers can be fractions of integers. Irrational ...

Katie has a PhD in maths, specializing in the intersection of dynamical systems and number theory. She reports on topics from maths and history to society and animals. Katie has a PhD in maths, ...

When you hear the words "rational" and "irrational," they might bring to mind the relentlessly analytical Spock in "Star Trek." If you're a mathematician, however, you probably think of ratios between ...

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 constants ...

The proof resolves a nearly 80-year-old problem known as the Duffin-Schaeffer conjecture. In doing so, it provides a final answer to a question that has preoccupied mathematicians since ancient times: ...

When my students grow too dependent on their calculators, I ask them to find a number that, when multiplied by itself, gives them 2. Students quickly see that since 1² = 1 and 2² = 4, the answer has ...

The ancient Greeks wondered when “irrational” numbers can be approximated by fractions. By proving the longstanding Duffin-Schaeffer conjecture, two mathematicians have provided a complete answer. The ...