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 ...

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, ...

Imagine being asked to pick a number from 1 to 10. You are quite likely to pick a whole number; I have never seen someone do otherwise. But you could also pick the number pi, whose decimal expansion ...

Originally defined as the ratio between the circumference of a circle and its diameter, pi — written as the Greek letter π — ...

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 ancient scholar Hippasus of Metapontum was punished with death for his discovery of irrational numbers—or at least that’s the legend. What actually happened in the fifth century B.C.E. is far from ...

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 ...

IN the first of these tracts Prof. Dedekind gives a theory of irrational numbers and of the arithmetical continuum which is logically perfect, and in form, perhaps, more simple and direct than any ...

The golden ratio is an almost mythical number that you may have heard of in various areas of architecture or design. For example, many claim the ancient Greek Parthenon has numerous examples of the ...

It’s surprisingly difficult to prove one of the most basic properties of a number: whether it can be written as a fraction. A broad new method can help settle this ancient question. In June 1978, the ...