Who was the earliest among these mathematicians to give a method to calculate pi?

Archimedes wrote nine treatises that survive. In On the Sphere and Cylinder, he showed that the surface area of a sphere with radius r is 4π r 2 and that the volume of a sphere inscribed within a cylinder is two-thirds that of the cylinder. (Archimedes was so proud of the latter result that a diagram of it was engraved on his tomb.) In Measurement of the Circle, he showed that On Floating Bodies, he wrote the first description of how objects behave when floating in water. Siege of SyracuseLearn more about the siege of Syracuse. Archimedes, (born c. 287 bce, Syracuse, bce, Syracuse), the most famous mathematician and inventor in His life Archimedes probably spent some time in Egypt early in his career, but he resided for most of his life in bce by constructing war machines so effective that they long delayed the capture of the city. When Syracuse eventually fell to the Roman general bce, Archimedes was killed in the sack of the city. Study how turning a helix enclosed in a circular pipe raises water in an Archimedes screw Far more details survive about the life of Archimedes than about any other ancient scientist, but they are largely Heurēka!” (“I have found it!”) is popular embellishment. Equally According to ce), Archimedes had so low an opinion of the kind of practical Method Concerning Mechanical Theorems shows that he used mechanical reasoning as a There are nine On the Sphere and Cylinder (in two books) are that the surface area of any r is four times that of its gre...

The number represented by pi (π) is used in calculations whenever something round (or nearly so) is involved, such as for circles, spheres, cylinders, cones and ellipses. Its value is necessary to compute many important quantities about these shapes, such as understanding the relationship between a circle’s radius and its circumference and area (circumference=2πr; area=πr 2). Pi also appears in the calculations to determine the area of an ellipse and in finding the radius, surface area and volume of a sphere. Our world contains many round and near-round objects; finding the exact value of pi helps us build, manufacture and work with them more accurately. Historically, people had only very coarse estimations of pi (such as 3, or 3.12, or 3.16), and while they knew these were estimates, they had no idea how far off they might be. The search for the accurate value of pi led not only to more accuracy, but also to the development of new concepts and techniques, such as limits and iterative algorithms, which then became fundamental to new areas of mathematics. Finding the actual value of pi Between 3,000 and 4,000 years ago, people used trial-and-error approximations of pi, without doing any math or considering potential errors. The earliest written approximations of pi are The first rigorous approach to finding the true value of pi was based on geometrical approximations. Around 250 B.C., the Greek mathematician Archimedes drew polygons both around the outside and within the in...

I am very interested in the history of $\pi$. I am first trying to find out who calculated it. Many sources have different answers, from the ancient Egyptians, to Archimedes, to the Babylonians. I still can't find an answer to who first discovered $\pi$, or found a way to calculate it to any degree of accuracy. So who, or which group of people, were the first one(s) to discover/calculate $\pi$? It depends on the meaning of "calculate", since $\pi$ is a transcendental number it can not be "calculated" in the usual meaning of the word. The first analytic formula (in the form of an infinite series) that in principle can calculate $\pi$ to any required accuracy is probably due to medieval Indian mathematician A semi-geometric "calculation" procedure capable in principle of producing arbitrary accuracy is much older. It consists of approximating a circle by inscribed and circumscribed polygons, and can be traced to ancient Greek orator Approximating the circumference with polygon perimeters is much simpler than approximating the circle area with polygon areas as Antiphon suggested. Using $96$-gons, Archimedes obtained what is now presented as the double estimate $3\frac<\pi<3\frac17$, although to Archimedes $\pi$ was not a number, and the result was phrased geometrically in terms of However, ancient Greeks also had a different concept of calculation, a purely geometric one, that was dominant in their time. A geometric magnitude was considered "calculated" if one could give a ge...

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There is an old adage that “research informs teaching;” this is a story about its converse – how “teaching informs research” and how a routine topic covered in a Wittenberg University mathematics course started me on a search to track down the story behind an overlooked milestone in the history of mathematics and computer science. The course was Math 460: Senior Seminar, and the topic was the number π and how and why in 1949 the ENIAC , the first electronic computer, was used to compute π to over 2000 digits. The end result was a paper “The ENIAC’s 1949 Determination of π,” which was eventually accepted for publication. Math 460: Senior Seminar for mathematics majors is a selective history of mathematics where we look at some the great theorems in mathematics the mathematicians who proved them. We use a text by William Dunham called Journey through Genius – The Great Theorem of Mathematics, which is a history of 12 famous theorems. One of the themes covered is the history of determining π – the ratio of the circumference of a circle to its diameter; that is getting a good approximation to a number that is irrational, meaning it cannot be expressed as a simple ratio of two integers. So why is the history of π interesting and how is it connected with the ENIAC ? The origins of π can be traced back to antiquity in early attempts to find a formula for the area of a circle. At this point π as a number did not “figure into the equation”. For example the Egyptian Rhind Papyrus wh...

• v • t • e γεωμετρία; Classic geometry was focused in In modern times, geometric concepts have been generalized to a high level of abstraction and complexity, and have been subjected to the methods of calculus and abstract algebra, so that many modern branches of the field are barely recognizable as the descendants of early geometry. (See Early geometry [ ] The earliest recorded beginnings of geometry can be traced to early peoples, such as the Egyptian geometry [ ] Main article: The ancient Egyptians knew that they could approximate the area of a circle as follows: Area of Circle ≈ [ (Diameter) x 8/9 ] 2. Problem 50 of the π is 4×(8/9) 2 (or 3.160493...), with an error of slightly over 0.63 percent. This value was slightly less accurate than the calculations of the Ahmes knew of the modern 22/7 as an approximation for π, and used it to split a hekat, hekat x 22/x x 7/22 = hekat; [ citation needed] however, Ahmes continued to use the traditional 256/81 value for π for computing his hekat volume found in a cylinder. Problem 48 involved using a square with side 9 units. This square was cut into a 3x3 grid. The diagonal of the corner squares were used to make an irregular octagon with an area of 63 units. This gave a second value for π of 3.111... The two problems together indicate a range of values for π between 3.11 and 3.16. Problem 14 in the V = 1 3 h ( a 2 + a b + b 2 ) where a and b are the base and top side lengths of the truncated pyramid and h is the height. Babylo...

Pi (π) has been known for almost 4000 years—but even if we calculated the number of seconds in those 4000 years and calculated π to that number of places, we would still only be approximating its actual value. Here’s a brief history of finding π. The ancient Babylonians calculated the area of a circle by taking 3 times the square of its radius, which gave a value of pi = 3. One Babylonian tablet (ca. 1900–1680 BC) indicates a value of 3.125 for π, which is a closer approximation. The Rhind Papyrus (ca.1650 BC) gives us insight into the mathematics of ancient Egypt. The Egyptians calculated the area of a circle by a formula that gave the approximate value of 3.1605 for π. The first calculation of π was done by Archimedes of Syracuse (287–212 BC), one of the greatest mathematicians of the ancient world. Archimedes approximated 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 π but only an approximation within those limits. In this way, Archimedes showed that π is between 3 1/7 and 3 10/71. A similar approach was used by Zu Chongzhi (429–501), a brilliant Chinese mathematician and astronomer. Zu Cho...

The history of the constant ratio of the circumference to the diameter of any circle is as old as man's desire to measure; whereas the symbol for this ratio known today as π ( pi) dates from the early 18th century. Before this the ratio had been awkwardly referred to in medieval Latin as: quantitas in quam cum multiflicetur diameter, proveniet circumferencia (the quantity which, when the diameter is multiplied by it, yields the circumference). It is widely believed that the great Swiss-born mathematician Leonhard Euler (1707-83) introduced the symbol π into common use. In fact it was first used in print in its modern sense in 1706 a year before Euler's birth by a self-taught mathematics teacher William Jones (1675-1749) in his second book Synopsis Palmariorum Matheseos, or A New Introduction to the Mathematics based on his teaching notes. Before the appearance of the symbol π, approximations such as 22/7 and 355/113 had also been used to express the ratio, which may have given the impression that it was a rational number. Though he did not prove it, Jones believed that π was an irrational number: an infinite, non-repeating sequence of digits that could never totally be expressed in numerical form. In Synopsis he wrote: '... the exact proportion between the diameter and the circumference can never be expressed in numbers...'. Consequently, a symbol was required to represent an ideal that can be approached but never reached. For this Jones recognised that only a pure platoni...

Pi (π) has been known for almost 4000 years—but even if we calculated the number of seconds in those 4000 years and calculated π to that number of places, we would still only be approximating its actual value. Here’s a brief history of finding π. The ancient Babylonians calculated the area of a circle by taking 3 times the square of its radius, which gave a value of pi = 3. One Babylonian tablet (ca. 1900–1680 BC) indicates a value of 3.125 for π, which is a closer approximation. The Rhind Papyrus (ca.1650 BC) gives us insight into the mathematics of ancient Egypt. The Egyptians calculated the area of a circle by a formula that gave the approximate value of 3.1605 for π. The first calculation of π was done by Archimedes of Syracuse (287–212 BC), one of the greatest mathematicians of the ancient world. Archimedes approximated 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 π but only an approximation within those limits. In this way, Archimedes showed that π is between 3 1/7 and 3 10/71. A similar approach was used by Zu Chongzhi (429–501), a brilliant Chinese mathematician and astronomer. Zu Cho...

Archimedes wrote nine treatises that survive. In On the Sphere and Cylinder, he showed that the surface area of a sphere with radius r is 4π r 2 and that the volume of a sphere inscribed within a cylinder is two-thirds that of the cylinder. (Archimedes was so proud of the latter result that a diagram of it was engraved on his tomb.) In Measurement of the Circle, he showed that On Floating Bodies, he wrote the first description of how objects behave when floating in water. Siege of SyracuseLearn more about the siege of Syracuse. Archimedes, (born c. 287 bce, Syracuse, bce, Syracuse), the most famous mathematician and inventor in His life Archimedes probably spent some time in Egypt early in his career, but he resided for most of his life in bce by constructing war machines so effective that they long delayed the capture of the city. When Syracuse eventually fell to the Roman general bce, Archimedes was killed in the sack of the city. Study how turning a helix enclosed in a circular pipe raises water in an Archimedes screw Far more details survive about the life of Archimedes than about any other ancient scientist, but they are largely Heurēka!” (“I have found it!”) is popular embellishment. Equally According to ce), Archimedes had so low an opinion of the kind of practical Method Concerning Mechanical Theorems shows that he used mechanical reasoning as a There are nine On the Sphere and Cylinder (in two books) are that the surface area of any r is four times that of its gre...