Archimedes of Syracuse discovered, by considering the perimeters of 96-sided polygons inscribing a circle. When a circle's diameter is 1, its circumference is π.
He estimated the area of a circle by using the Pythagorean Theorem to find the areas of two regular polygons: the polygon inscribed within the circle and the polygon within which the circle was circumscribed. Since the actual area of the circle lies between the areas of the inscribed and circumscribed polygons, the areas of the polygons gave upper and lower bounds for the area of the circle. Archimedes knew that he had not found the value of pi but only an approximation within those limits.
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“And he made a molten sea, ten cubits from the one brim to the other: it was round all
about and his height was five cubits: and a line of thirty cubits did compass it about.” (I Kings 7, 23)
And it gives the value of Pi equal to 3. Rabbi Nehemiah explained this in his 'Mishnat ha -
Middot' (the earliest known Hebrew text on geometry, 150 AD) by saying that the diameter was
measured from the outside of the brim while the circumference was measured along the inner rim. The stated dimensions would be exact if measured this way on a brim about four inches wide.
This is disputed, however, and other explanations have been offered, including that the measurements are given in round numbers (as the Hebrews tended to round off measurements to whole numbers), or that the basin may not have been exactly circular or that the brim was wider than the bowl itself. Many reconstructions of the basin, in fact, show a wider brim extending outward from the brim itself by several inches, which might account for the discrepancy.
According to Galileo – a famous scientist once said:
'Mathematics is the language with which God created the universe'.
Knowledge of pi then bogged down until the 17th century. Pi was then called the Ludophian number, after Ludolph van Ceulen, a German Mathematician. The first Person to use the Greek letter Pi for the number was William Jones, a Welsh mathematician, who coined it in 1706.
19 – The Secret Code of God Page 184 most medieval scholars. The compass in this 13th Century manuscript is a symbol of God's act of Creation, as many believed that there was something intrinsically "divine" or "perfect" that could be found in circles
Johann Heinrich Lambert proved that pi is an irrational number and it is a lie to look for
rational pi in 1761 because it cannot be written as the ratio of two integers.
In 1882, Ferdinand von Lindemann showed that pi is also transcendental number, which
means that there is no polynomial with rational coefficients of which Pi is a root. An important consequence of the transcendence of Pi is the fact that it is not constructible. Because the
coordinates of all points that can be constructed with compass and straightedge are constructible numbers, it is impossible to square the circle: that it is impossible to construct using compass and straightedge alone, a square whose area is equal to the area of a given circle.
The Indiana, USA - Pi Bill:
The 'Indiana Pi Bill' of 1897 AD , which never passed out of committee, has been claimed to imply a number of different values for Pi, although the closest it comes to explicitly asserting one is the wording, ' the ratio of the diameter and circumference is as five-fourths to four' which would make Pi = 3.2
Pi = 3.2 (as proposed by Indiana Pi Bill in 1897 AD in USA).
Goodwin's model circle as described in section 2 of the bill. It has a diameter of 10 and a circumference of 32; the chord of 90° has length 7
Although the bill has become known as the "pi bill", its text does not mention the name pi at all, and Goodwin appears to have thought of the ratio between the circumference and diameter of a circle as distinctly secondary to his main aim of squaring the circle. Yet towards the end of Section 2 appears the following passage:
Furthermore, it has revealed the ratio of the chord and arc of ninety degrees, which is as seven to eight, and also the ratio of the diagonal and one side of a square which is as ten to
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seven, disclosing the fourth important fact, that the ratio of the diameter and circumference is as five-fourths to four ...
which comes close to an explicit claim that π = 4/1.25 = 3.2, as well as .
This quote is often read as three mutually incompatible assertions, but they fit together well if the statement about is taken to be about the inscribed square (with the circle's diameter as diagonal) rather than the square on the radius (with the chord of 90° as diagonal). Together they describe the circle shown in the figure, whose diameter is 10 and circumference is 32; the chord of 90° is taken to be 7. Both of the values 7 and 32 are within a few percent of the true lengths for a diameter-10 circle which, of course, does not justify Goodwin's presentation of them as exact.
Squaring the circle
was the dream of all Greek mathematicians for more than 4000 years but as the great mathematicians proved and showed that pi is an irrational number, a transcendental number so the effort to square the circle was stopped and discouraged by almost all mathematicians of the world till today. The quest to prove whether circle can be squared was stopped by the scientists and mathematicians 120 years ago because of the irrationality and transcendental properties of Pi.Pi is approximately 3.1415926….. the number of times that a circle’s diameter will fit around the circle. Pi goes on forever. The exact value of Pi has an infinite decimal expansion of various numbers: its decimal expansion never ends and does not repeat, since Pi is accepted and proved as an irrational and transcendental number.
This infinite sequence of digits has fascinated mathematicians and laymen alike, and much effort over the last few centuries has been put into computing more digits and investigating the number’s properties.
“To ask for the system in pi is like asking, “Is there life after death?” When you die, you’ll find out.”
---Richard Preston, The Mountains of Pi
The Pi was also calculated by taking the square root of Number – 10 as:
Pi = √10 = 3.16227766…………
In the book, ‘Introduction to Pi’, L.Berggren, J.Borwein and P.Borwein write about the calculation of Pi as:
“The computation of Pi is virtually the only topic from the most ancient stratum of mathematics that is still of serious interest to modern mathematical research. And to pursue this topic as it
19 – The Secret Code of God Page 186 developed throughout the millennia is to follow a thread through the history of mathematics that winds through geometry, analysis and special functions, numerical analysis, algebra and number theory. It offers a subject which provides mathematicians with examples of many current mathematical techniques as well as a palpable sense of their historic development.”
'God exists since mathematics is consistent, and the devil exists since we cannot prove it.'
Andre' Weil, French Mathematician
(Reference:http://en.wikipedia.org/wiki/User:Piledhigheranddeeper)