PiYesMathematicsA well-known and mysterious constant, which is defined as the ratio of the circumference of any circle to its diameter. However, no matter how hard we try,PiIt seems like it's never enough. As early as ancient times, people began to try to calculatePiand continue to break new ground over the centuries. But are we really able to count it all?IfPiWhat are the unbelievable consequences of being really poor?In this article, we will ** these questions and explore the mysteries of them.
Humans forPiThe exploration goes back a long way. In 2000 BC years ago ancient Babylon andAncient India, people have calculated the approximate according to the actual needsPiValue. However, these values are not the same as those known today as 314159··· It's a slight difference, but it's accurate enough for the ancients.
withMathematicsThe development of peoplePiThe calculations have become more precise. In the 18th centuryMathematicsHome has proven itPiis oneIrrational numbers, i.e., an infinite and non-cyclic decimal. But even so, people are constantly trying to calculate it in different waysPimore digits. From ancient GreeceArchimedesto Liu Hui during the Wei, Jin, Southern and Northern Dynasties in ChinaZu ChongzhiMathematicsThe family is constantly refining the calculations to makePiThe value of tends to be exact.
In recent years, advances in computing technology have allowed us to calculate at breakneck speedsPimore digits. In 2019, Google Cloud will:PiGot itDecimal pointAfter 314 trillion bits, but this record was soon taken by a Swiss supercomputer to 628 trillion bits exceeded. However, in 2022, Google Cloud Server once again broke the record, calculated it:Decimal pointAfter 100 trillion bitsPi。These breakthroughs are already going to bePiThe amount of computation has been pushedAstronomyNumeric level, thoughPiIt seems that he has never been counted poor.
1. The irrationality of pi
of the 18th centuryMathematicsHome provesPiis oneIrrational numbers, i.e., an infinite and non-cyclic decimal. This means that no matter what we calculatePiWe can never count the number of digits. Because of this,PiDeemed to beMathematicsa miracle and a challenge.
PiThe irrationality also givesMathematicsBrings a lot of confusion and thinking. Although we have no way of knowingPi, but we can use approximations for practical applications. in the everydaylife, we will generallyPiThe approximation is 314. That's enough for our needs. Ancient BabyloniansAncient IndiaApproximations have also been used to make discs and wheels, and they have not been greatly affected.
2. The supernumber and complexity of pi
In addition to being irrational,MathematicsIora also notedPiProbably a supernumber, i.e. more than averageIrrational numbersMore complex and incomprehensible**. This means:PiInMathematicsThe place in research is even more special and important.
PiThe supernumber property further adds to the calculationsPidifficulty. Although we can try to use a different oneMathematicsmethods and algorithms to calculatePibut each bit requires a huge amount of computation and time. It also explains why people have been struggling with calculationsPibecause it's a big impact on computer performance andMathematicsAn important challenge to theory.
1. The subversion of geometry and calculus
Historically, people have always thought of a circle as a smooth curve. However, ifPiTo be poor, then a circle is actually a collection of polygons. Even in geometry, such a discovery would cause great confusion and subversion. Calculation of the area covered by the curve and based on the theory of limit accumulationCalculuswill be challenged, modernMathematicsTheories may also need to be revisited and adjusted.
In addition,CalculusIt has a wide range of applications in modern science and engineering, especially in the field of modern science and engineeringAstronauticsField. CalculusThe subversion of theories will have a huge impactSpaceshipTracksRocket enginesthrust and flight trajectory calculations, thereby givingAstronauticsTechnological developments pose enormous challenges.
2. The subversion of real technology
PiThe calculation of poverty will be on realityTechnologyMake a far-reaching impact. First, calculatePimethods and technologies will be completely upended. At present, it is calculated by methods such as the circumcision methodPiis a common strategy that doesn't exhaust it all, but gives an approximation. OncePiOnce exhausted, we will no longer need to use these methods, as the concept of a circle will be redefined as a polygon. This will have a profound impact on the disciplines of geometry and numerical computing.
Secondly, utilizationCalculusTheoryIntegrated circuitswill no longer apply. All usePiAnd the curves of the calculations of the electronic devices will become invalid, as they are based onMathematicsThe theory will no longer apply. This is important for modern timesTechnologyThe development and application will bring great challenges, as we will have to redesign and evolve based on differencesMathematicsModel of electronic devices.
3. Influence on the universe and cosmology
PiThe calculation of poverty will be on our part of the universe andCosmologyhas a significant impact. IfPiIf it can be calculated, then it means that our understanding of the trajectories of stars and galaxies will change radically. In addition, the orbits of microscopic particles such as atoms and electrons as we know them will be redefined as polygons. This will revolutionize our perception of the universe and matter, challenging our understanding of the real world.
However, some believe thatPiWhether or not you can be considered poor does not affect the everydaylifewithTechnologyDevelopment has too much of an impact. Whether the circle is a smooth curve or made up of polygons, it is normal for uslifewithTechnologyThe impact of the app is not significant. AlthoughPiThe exact value is important for research and applications in some fields (such as cryptography and system bug detection), but for most people, it is knownPiApproximate value of 314 is enough.
PiThe computational journey is amazing and fascinating. Although we have made great progress, butPiThe exact value remains a mystery. Even in the future, we may not be able to truly do the math outPiPiThe irrationality and complexity that makesMathematicsBecome an eternal challenge and development area. PiThe arithmetic impoverishment can bring some disruption and challenges, especially when it comes to geometryCalculus, modernTechnologyand the perception of the universe. However, for most people, the existing approximations are sufficient for the needs, and we don't need to worry too muchPiThe exact value of the problem.