Happy Pi Day, notes on the mathematical expression π
March 14, 2010 by Cheap gift
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In the calendar there are two celebrations in honor of the mathematical expression Pi Day “Pi” and “Pi Approximation Day. This celebration was an occurrence of the physicist Larry Shaw in San Francisco, and has been gaining in popularity to the point of having in 2009 with a successful resolution of the House of Representatives of the United States in declaring March 14 as a national day of π.
By the way it is written in the format used in the United States, March 14 (3 / 14) has become an unofficial celebration for the “Pi Day”, derived from the approximation of three digits of pi : 3.14. Usually the conclusion is concentrated at 1:59 PM (in recognition of the six-digit approximation: 3.14159), although some people claim that they are actually from 13:59, so the right thing would be to hold the 1:59 possibly to be taken early evening hours to facilitate the conclusion.
Mathematicians and teachers from various schools around the world organize events and meetings on this date. Some groups meet to discuss and comment on the importance of pi in their lives, sharing stories or theorize as would be the world without the existence of pi. Other groups gather to watch the cult film, Pi, faith in chaos. It is also common to eat cakes with motifs on π, another play on words in the English language as well as foot pi (pie) have the same pronunciation. In fact, to celebrate the day of Pi , many netizens have created songs with the title song and Pi have videos uploaded to Youtube, singing or playing an instrument, a user has specifically used the melody of the American Pie films.
The point Pi “final” would have occurred on March 14, 1592 at 6:53 with 58 seconds (AM). This, written in U.S. format, it would be 3/14/1592 6:53.58, which would correspond to the value of pi expressed in twelve digits: 3.14159265358.
Pi Approximation Day
The “Pi Approximation Day” can be identified in any of these dates:
* 22 julio, 22 / 7 on the international date format. 22 / 7 \ simeq 3.14286 is an approximation of pi.
* 26 April (or April 25 in leap years), the day the earth completes two astronomical units of its annual orbit (ie, two radians). The total length of Earth’s orbit divided by the length covered to this day is equal to pi.
* December 21 (December 20 in leap years), which is day 355 of year, at 1:13 PM, coinciding with the approximate value of 355/113 \ simeq 3.141593; calculated by Zu Chongzhi.
* 10 November (November 9 in leap years), who is day number 314 of the year according to the Gregorian calendar.
On the mathematical Pi
π (pi) is the ratio between the length of a circle to its diameter in Euclidean geometry. It is an irrational number which is commonly used in mathematics, physics and engineering matters. The numerical value of π, truncated to its first digit is: \ pi \ approx 3 (,) 14159265358979323846 …
The value of π has been obtained with different approaches throughout history, being one of the more mathematical constants that appear in the equations of physics, along with the number e. Therefore, perhaps the most constant passion erupts between professional and amateur mathematicians. The relationship between the circumference and diameter is not constant in non-Euclidean geometry. Irrational numbers are the elements of the real line (whole, natural and rational) that can not be expressed by the quotient of two integers and are characterized by infinite decimals that do not follow a defined period, the irrational number is not an infinite decimal newspaper, I could never finish writing all places. As a result, the most well known irrational numbers are identified by special symbols.
Notation with the Greek letter π comes from the initial words of Greek origin “περιφέρεια” (periphery) and περίμετρον “(perimeter) of a circle, notation was first used by William Oughtred (1574-1660), and proposed use by the Welsh mathematician William Jones (1675-1749), although it was the mathematician Leonhard Euler, in his book “Introduction to Calculus” in 1748, who popularized it.
The search for the greater number of decimal places the number π has been a constant effort of many scientists throughout history. In ancient Egypt, a scribe Ahmes in 1800 a. C., approaches described in the Rhind papyrus, which employs an approximate value of π by saying that: the area of a circle is similar to that of a square whose side equals the diameter of the circle down to 1 / 9, ie equal to 8 / 9 of the diameter.
Of the eight mathematical documents found in ancient Egyptian culture, talking about two circles. One is the Rhind papyrus and the other is the Moscow papyrus. Only in the first speech of the approximate value of the number π. The Rhind papyrus shows the Egyptian numbering system as well as an organization of arithmetic and geometry problems, was bought by a Scotsman in 1858 during a visit to Luxor.
Archimedes (third century before our era) was able to determine the value of π between the interval by 3 10/71, as the minimum value, and 3 1 / 7, the maximum value. With this approximation of Archimedes gets a value with an error of between 0.024% and 0.040% on the actual value. The method used by Archimedes was simple and consisted circumscribe and inscribe regular polygons of n-sided circles and calculate the perimeter of these polygons. Archimedes started with hexagons circumscribed and inscribed, and was doubling the number of sides to reach 96-sided polygons.
More information about mathematical methods to achieve approximations to a larger number of digits of Pi, from millennia before our era, to modern computer and stage, Wikipedia.
