Make a project on the title “π - WORLD'S MOST MYSTERIOUS NUMBER”
class 9th
Answers
Step-by-step explanation:
We all learned that the ratio of the circumference of a circle to its diameter is called pi and that the value of this algebraic symbol is roughly 3.14. What we weren't told, though, is that behind this seemingly mundane fact is a world of mystery, which has fascinated mathematicians from ancient times to the present. Simply put, pi is weird. Mathematicians call it a "transcendental number" because its value cannot be calculated by any combination of addition, subtraction, multiplication, division, and square root extraction. In this delightful layperson's introduction to one of math's most interesting phenomena, Drs. Posamentier and Lehmann review pi's history from prebiblical times to the 21st century, the many amusing and mind-boggling ways of estimating pi over the centuries, quirky examples of obsessing about pi (including an attempt to legislate its exact value), and useful applications of pi in everyday life, including statistics.This enlightening and stimulating approach to mathematics will entertain lay readers while improving their mathematical
it will be help you
The pi digit is the ratio of the circumference to its diameter, the most famous and ancient mathematical constant. It is useful not only in geometry and engineering pi arises in all mathematical and physical theories; simply because the circle (the set of points equidistant from a given) is used even in fields that are far from the scientific fields of geometry in complex analysis, probability theory, digit theory.In most cases, scientists need to know only that pi is a positive digit. Some amazing features of this digit are much more interesting for mathematicians. For example, the fact that pi. an irrational digit. it can’t be represented as a fraction .in the decimal description of pi there is an infinite number of digits, and there are no periodic repetitions.Oddly enough, except that the decimal representation of pi is infinite and aperiodic, there is little we can say more about it. Often you can hear that in the description of pi on any sufficiently distant place there is a preassigned finite digit. Actually, it is unknown whether it is so. Moreover, we do not even know whether any digit is repeated in the description of the pi infinite digit of times: it is possible that starting from a very distant position in the description there will be, for example, only zeros and ones.
In ancient times, the length of the perimeter of polygons inscribed in a circle was calculated. Using this method, Archimedes correctly found the first three digits of this constant - 3.14. However, near the 15th century, people began to use a much more efficient way representation of pi as the sum of an infinite series, the addition of an increasing digit of the first members which gives the most accurate value of pi. Perhaps the simplest of these series is a series of Leibniz However, it "slowly converges" - to calculate the next digit is necessary to add more members. Over the past century there were many other - much faster converging series, allowing finding an approximate value of pi and calculating its regular digits; Race of Records in calculating of pi, as a result, turned into a race of inventing new formulas, and since the 1950s . it became even the race of processing powers of computers.
The last record was registered in October 2014: an anonymous enthusiast with the nickname houkouonchi found on a standard PC with a processor capacity of 2.6 GHz 13,300,000,000,000 (13.3 trillion) pi digits. The calculation itself took 208 days and 182 hours to check the result. Houkouonchi used to calculate the y-cruncher algorithm, invented by the American mathematician Alexander Yee.A rivalry peaked in the 1980s - 1990s: over the past two decades, a record of calculating pi increased from two million digits to 200 billion. The main competitors were Japanese Yasumasa Canada and American mathematician brothers David and Gregory Chudnovsky. At the same time, a professor from Tokyo University used industrial supercomputer Hitachi SR8000, while Chudnovsky brothers were doing calculations on a makeshift computer m zero. The car was built on the money of their wives, one of whom worked as a lawyer, and the second - an officer in the United Nations. The supercomputer took the whole room, it was cooled by 25 household fans and cost about 70 thousand dollars and worked faster than many commercial supercomputers that cost tens of millions of dollars.
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