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Scientists have created sophisticated new pieces of pie while building simpler models of how particles interact.
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The representation of pi allows scientists to use values that are closer to reality without having to store millions of digits.
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Creating the new Pi involved the use of a series, a structured set of terms that can either converge or diverge into a single equation.
In the new study, physicists Quantum mechanics They constructed a new model for the abstract concept of pi. Or, more accurately, they accidentally constructed a new model for the abstract concept of pi. include It’s a cool new representation for pi. But what does it mean, and why do we need a different representation for pi?
Quantum mechanics looks at the tiniest particles one by one, so even simple questions can yield complex answers that require vast amounts of computing power. high tech Video games, movies, etc. Avatar It could take several days or more, and that’s still not realistic. In this new paperPublished in a peer-reviewed journal Physics Review LetterPhysicists Arnab Priya Saha and Aninda Sinha describe a new version of the quantum model that reduces complexity but maintains accuracy.
This is called optimization. Think of early internet videos buffering in blocks of similar color, or of animators of old drawing individual moving parts on top of stationary objects, or of carving away the corners of a square sidewalk to make a dirt road. ShortcutsWe are surrounded by optimization and optimizing behavior.
As detailed in their paper, Saha and Sinha combined two existing ideas from mathematics and science: particle Euler beta function for scattering and string theory. The result is a sequence of numbers, represented in mathematics by the Greek letter Σ surrounded by parameters.
Series may ultimately generalize into an overall equation or expression, but that doesn’t have to be the case, and some series will diverge, meaning the terms continue to move away from each other, while others will converge to one approximate, concrete result. Pi The digits of pi go on forever, and because pi itself is an irrational number, it cannot be expressed exactly as a whole number fraction (the 22/7 we often learn in school is not very accurate by the standards of 2024).
But this can be expressed very quickly and elegantly in a series, because it allows you to build up values to the smallest possible decimal place. When mathematicians put the terms of a series together, they can use the resulting abstraction to say, Math This isn’t possible with the approximation of pi, which is rounded down to 10 digits on a standard desk calculator. Refined approximations make it possible to study nanoscale particles like those that first inspired scientists.
“The early 1970s,” Sinha says. In a statement From the Indian Institute of Science,scientist I briefly explored this area of research but quickly abandoned it as it was too complex.”
But such mathematical analysis has come a long way since the 1970s. Today, Sinha and Saha are model They then reconstruct it with the changed terms. They can build a sequence and see that it converges to the value of pi with many fewer terms than expected. This makes it easier for scientists to run the sequence and use it for further research.
All of this requires decades of fundamental research in the field and a huge body of work showing that certain mathematical techniques don’t work with others – a comment on the ongoing and collaborative nature of mathematics. theoryEven if the result is a working model that might be useful to scientists. Our ability to find meaningful approximations has grown hand in hand with our ability to solve complex problems completely.
“This kind of work may not produce immediate results, but application “Putting theory into practice in everyday life gives me pure joy,” Sinha said in a statement.
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