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: ...
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 ...
Originally defined as the ratio between the circumference of a circle and its diameter, pi — written as the Greek letter π — appears throughout mathematics, including in areas that are completely ...
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 ...
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 ...
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. Answer by Alon Amit, PhD ...
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 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 ...
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 ...
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