Prove the Circumference Formula
Introduction:
Archimedes is credited to be the creator of the circumference formula, but more importantly to find the first theoretical calculation of Pi. Pi is an irrational number and the digits are continuous and never come to an end. Archimedes knew he had only found an approximation of pi, he found that pi is between 3 1/7 and 3 10/71. “Pi is a name given to the ratio of the circumference of a circle to the diameter. That means, for any circle, you can divide the circumference (the distance around the circle) by the diameter and always get exactly the same number. It doesn't matter how big or small the circle is, Pi remains the same. Pi is often written using the symbol  and is pronounced "pie", just like the dessert”(math.com).
The circumference formula we use to this day is:

Pi is abbreviated to 3.14 when being written, but calculators use a much more accurate version of the number.
I chose to investigate this topic because the origin of formulas interests me. Somehow these letters are created and it works under any conditions and never seems to fail. Prior to this investigation I have learned what the circumference formula is and how to apply it.
Statement of Purpose:
The main purpose of this investigation is to prove the circumference formula to be correct. Through this investigation I will use different processes of math to prove this formula correct. This will show that the formula holds true in multiple settings.
Plan of Investigation:
I will derive the formula and work it in multiple ways to prove that the formula we have used for the past centuries to be correct. I will also look at the history of pi.
Math:

The above picture shows all the parts you need to know for this ex...
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...en surpassed until 1429, when astronomer Jamshid Al-Kashi of Samarkand found  Correct to sixteen decimal places. Western mathematicians did not surpass the Tsus approximation until around 1600.
Works Cited
“Circumference of a Circle - Derivation." Derivation of the Formula for the Circumference of a Circle. Math Open Refrence, n.d. Web. 28 Oct. 2013..
"PI." PI. Math.com, n.d. Web. 28 Oct. 2013. .
"Johann Heinrich Lambert." The world of π. N.p.. Web. 11 Nov 2013. .
"The "Jewish" or "Bible" Value of "pi"." Purplemath. Elizabeth Stapel, n.d. Web. 11 Nov 2013. http://www.purplemath.com/modules/bibleval.htm.
Howard, Eves. An Introduction to the History of Mathematcis. Fifth Edition. New York: The Saunders Series, 1983. Print.
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This shows that there is a difference of 2cm between A and B, and B
So using this formula but with the data we collected from our first attempt, this is what it would look like; Tan(60°) x 23m = 39m. As you can tell this answer collected from our first attempt is very well incorrect, but at the time, our group did not know this.
Geometry, a cornerstone in modern civilization, also had its beginnings in Ancient Greece. Euclid, a mathematician, formed many geometric proofs and theories [Document 5]. He also came to one of the most significant discoveries of math, Pi. This number showed the ratio between the diameter and circumference of a circle.
» Part 1 Logarithms initially originated in an early form along with logarithm tables published by the Augustinian Monk Michael Stifel when he published ’Arithmetica integra’ in 1544. In the same publication, Stifel also became the first person to use the word ‘exponent’ and the first to indicate multiplication without the use of a symbol. In addition to mathematical findings, he also later anonymously published his prediction that at 8:00am on the 19th of October 1533, the world would end and it would be judgement day. However the Scottish astronomer, physicist, mathematician and astrologer John Napier is more famously known as the person who discovered them due to his work in 1614 called ‘Mirifici Logarithmorum Canonis Descriptio’.
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Ever wonder how scientists figure out how long it takes for the radiation from a nuclear weapon to decay? This dilemma can be solved by calculus, which helps determine the rate of decay of the radioactive material. Calculus can aid people in many everyday situations, such as deciding how much fencing is needed to encompass a designated area. Finding how gravity affects certain objects is how calculus aids people who study Physics. Mechanics find calculus useful to determine rates of flow of fluids in a car. Numerous developments in mathematics by Ancient Greeks to Europeans led to the discovery of integral calculus, which is still expanding. The first mathematicians came from Egypt, where they discovered the rule for the volume of a pyramid and approximation of the area of a circle. Later, Greeks made tremendous discoveries. Archimedes extended the method of inscribed and circumscribed figures by means of heuristic, which are rules that are specific to a given problem and can therefore help guide the search. These arguments involved parallel slices of figures and the laws of the lever, the idea of a surface as made up of lines. Finding areas and volumes of figures by using conic section (a circle, point, hyperbola, etc.) and weighing infinitely thin slices of figures, an idea used in integral calculus today was also a discovery of Archimedes. One of Archimedes's major crucial discoveries for integral calculus was a limit that allows the "slices" of a figure to be infinitely thin. Another Greek, Euclid, developed ideas supporting the theory of calculus, but the logic basis was not sustained since infinity and continuity weren't established yet (Boyer 47). His one mistake in finding a definite integral was that it is not found by the sums of an infinite number of points, lines, or surfaces but by the limit of an infinite sequence (Boyer 47). These early discoveries aided Newton and Leibniz in the development of calculus. In the 17th century, people from all over Europe made numerous mathematics discoveries in the integral calculus field. Johannes Kepler "anticipat(ed) results found… in the integral calculus" (Boyer 109) with his summations. For instance, in his Astronomia nova, he formed a summation similar to integral calculus dealing with sine and cosine. F. B. Cavalieri expanded on Johannes Kepler's work on measuring volumes. Also, he "investigate[d] areas under the curve" ("Calculus (mathematics)") with what he called "indivisible magnitudes.
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The Scientific Revolution was sparked through Nicolaus Copernicusí unique use of mathematics. His methods developed from Greek astr...
Piscine Molitor Patel, this name carries great significance throughout the novel Life Of Pi. Associations of Pi 's name with water is very clear to the reader. Pi was named after a pool in Paris, Piscine Molitor, Mr. Adirubasamy 's favourite pool, Mr. Adirubasamy also taught Pi how to swim. He then became a skilful swimmer. I believe that the author has incorporated this connection to make Pi 's story of the shipwreck seem more realistic, because Pi is a good swimmer, then he has a skill to aid him in living on an ocean. This is used to enhance the authors credibility and make the fantasized story feel more realistic. Another thing that is interesting about the name Pi, is that it is a very unusual name, we don 't regularly see people with
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