Take a tread ( L is the thread's length) and then make a circle. Measure the D diameter of the circle, and then your experimental Piex = L/D. The more accurately measured L and D, the less % deviation will be between Pi and Piex.
Take a tread ( L is the thread's length) and then make a circle. Measure the D diameter of the circle, and then your experimental Piex = L/D. The more accurately measured L and D, the less % deviation will be between Pi and Piex.
Whatever the size of a circle, the ratio of its circumference to its diameter will always be 22/7 = 3.14. There;s really nothing more to it. It is a constant and will remain so. Like Len Leonid Mizrah said, the slight deviations you might notice are just a function of differences in measurement accuracy.
Pi is actually ratio of circumference to diameter of a circle. ... This value 22/7 is an irrational number - which means the decimals of pi are neither repetitive nor they are terminating. 2. The value of pi - 22/7 is an approximation..
The number π (/paɪ/) is a mathematical constant. Originally defined as the ratio of a circle's circumference to its diameter, it now has various equivalent definitions and appears in many formulas in all areas of mathematics and physics. It is approximately equal to 3.14159. It has been represented by the Greek letter "π" since the mid-18th century, though it is also sometimes spelled out as "pi". It is also called Archimedes' constant.
The mathematical constant is common from the circle and its equivalent to 180 degree or named to pi this value is equal 3.14 in radian this is a short brefly
Check for more info: http://mathworld.wolfram.com/Pi.html
...
A brief history of notation for pi is given by Castellanos (1988ab). π is sometimes known as Archimedes' constant or Ludolph's constant after Ludolph van Ceulen (1539-1610), a Dutch π calculator. The symbol π was first used by Welsh mathematician William Jones in 1706, and subsequently adopted by Euler.
In Measurement of a Circle, Archimedes (ca. 225 BC) obtained the first rigorous approximation by inscribing and circumscribing 6·2n-gons on a circle using the Archimedes algorithm. Using n = 4 (a 96-gon), Archimedes obtained
3+ 10/71 < π < 3 + 1/7
(Wells 1986, p. 49; Shanks 1993, p. 140; Borwein et al. 2004, pp. 1-3).
The approximation π ≈ 22/7 seems to have been inspired by the heptagonal division of the circle ― It can be remarked that:
I. The approximation π ≈ 22/7 equals 2·11/7; where 2, 7, 11 are (three) distinct prime numbers. Their product is 154, for that called a sphenic number. It is the volume of a rectangular parallelopiped of sides 2, 7, and 11; called a sphenic brick. It is also a 9-gonal (or enneagonal, or nonagonal) number: a(n) = n·(7·n - 5)/2, with n = 7.
II. A regular heptagon can be represented by a dot at the centre, and by other dots around that central dot, disposed in successive heptagonal layers. That gives the sequence of centered heptagonal numbers, which includes 22.
III. 22/7 = 3 + 1/7; where 1/7 is an 'Egyptian fraction', i.e., either unit fraction (reciprocal of a positive integer) or sum of unit fractions. This splitted form may possibly have inspired the division of the circle in seven parts.
IV. Archimedes found that 3 + 10/71 < π < 22/7; 71 is also a centered heptagonal number.
V. Babylonians are said to have found that π ≈ 3 + 1/8; where 8 is a centered heptagonal number. It was early recognized that 3 + 1/8 < π < 3 + 1/7. The approximation π ≈ 3 + 1/7 may have been inspired by this Babylonian approximation.
VI. The approximation π ≈ 3 + 15/106 was claimed to be ancient (rabbinic) by a few scholars; 106 is a centered heptagonal number.
VII. The notably accurate approximation π ≈ 355/113 = 3 + 16/113 has been attributed to Zu Chongzhi (China; c. 429-500 AD). It can be noticed that 16/113 = 25·p/(2·p·113), where the denominator is a centered heptagonal number for either p = 46 or p = 53.
VIII. Accepting that π ≈ 22/7, the area of a circle of radius r = 7 is π·r2 ≈ 154 (cf. §I). Its perimeter is 2·π·r ≈ 2·(22/7)·7 = 44, that of a square of side 11.
IX. A regular heptagon of side s and perimeter 7·s = 44, has side s = 4·11/7. Its area is given by a = 7·s·r*/2 = 22·r*, where r* is the radius of the inscribed circle. For r* = 7; a = 154.
X. A knotted rope of length 44 ― can be bended as a regular heptagon of side 4·11/7. Let us acept that: (i) the same rope can be also bended as a circle of radius close to 7, inscribed on that heptagon; (ii) both the perimeter and area of that heptagon closely match those of the circle. It can be then coherently accepted that π ≈ 22/7.
XI. According to reputed authors, the π ≈ 22/7 approximation was introduced by the ancient Egyptians, for whom seven seemingly symbolized the eternal life or 'the complete cycle' ― that could visually suggest a circle.
XII. Each of the four lunar phases takes around 7.4 days, what can explain the calendar division in weeks of seven days. This may have inspired the heptagonal division of the circle.
XIII. Many ancient cultures recognized seven moving astronomical bodies; those that the naked eye could see moving relative to the fixed stars: Sun, Moon, Mercury, Venus, Mars, Jupiter, and Saturn; which were as well perceived as deities by many ancient mythologies. They are cornerstones of astrology, occultism, and alchemy; and may also have inspired the mentioned circle division.
XIV. We also find 22 at this very accurate approximation, found by Ramanujan (1914): π ≈ (92 + 192/22)1/4.
XV. It is witty to remember that in the typewriter era, the lowercase π was occasionally typed with two letters 7T (7 and T). Here, the uppercase letter even seems to evocate 'Three', the first digit of π!
Egyptians like Ahmes in 1650 BCE corrected round granary estimates of pi = 256/81, used since the old kingdom, by subtracting 22/7 in RMP 38 , and p!acing.double entry bookkeeping corrections in 1/320 of a hekat units..