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To start off, pi is the ratio of a circle’s circumference to its diameter (Bennet, Burton, & Nelson, 2012). This is approximately equal to 3.14159. In equation form it is calculated like this: π = C/d (Shell, 2013). Pi is also an irrational and transcendental number. This means that it will continue infinitely without any repetition or pattern. It also cannot be expressed accurately as a fraction and the decimal never ends (Shell, 2013).
The history of pi is a very confusing one. No one knows exactly who discovered it; they just know assumptions and possible coincidences. Many believe that the Babylonians were the first to find pi (Shell, 2013). They calculated the circumference of a circle and then they took three times the square of its radius. This gave them the sum of the earliest idea of pi=3 (Shell, 2013). Most reports have said that it’s extremely hard to pinpoint the exact person who became conscious of the constant ratio between circumference and diameter but it is said that humans became aware of it around 2550 BC.
The Great Pyramid of Giza was built between 2550 and 2500 BC with a perimeter of 1760 cubits and 280 cubits in height (Shell, 2013). This gives the ratio of 22/7, which is commonly used in estimating pi. Egyptologists believe that these proportions were chosen because of pi, but many other experts believe that it was completely accidental.
Archimedes has been credited as being the first to actually calculate an accurate estimate of pi by finding the areas of two polygons. Inside the polygons was an inscribed circle. An example is in the picture shown below (Shell, 2013):
Archimedes was born in 287 BC in Syracuse, Sicily. Much like the history of pi, his life is very obscure. His friend, Heracleides, wr...
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Discovering the Magical Pi (Lesson Plan) - TeacherVision.com. (2014). Retrieved March 25, 2014, from https://www.teachervision.com/math/lesson-plan/3430.html
Learn About Pi · Pi Day. (2014). Retrieved March 25, 2014, from http://www.piday.org/learn-about-pi/ Neuschwander, C., & Geehan, W. (1999). Sir Cumference and the dragon of pi: A math adventure. Watertown, MA: Charlesbridge.
Rollins, K. (2014). Retrieved March 25, 2014, from https://www.superteacherworksheets.com/songs/pi-song.pdf
Shell, B. (2013). Discovering Pi. Retrieved March 25, 2014, from http://www.learnnc.org/lp/pages/3970?ref=search
(“Learn About Pi Day, 2014)
Wolchover, N. (2012, August 9). What Makes Pi So Special? | What Does Pi
Mean? | LiveScience. Retrieved March 25, 2014, from
http://www.livescience.com/34132-what-makes-pi-special.html
Review of " On the irrationality of π4 and π6 " by Md. Reza Yegan
He found areas and volumes of spheres, cylinders and plain shapes. He showed that the volume of a sphere is two-thirds of the volume of the smallest cylinder that can contain the sphere. Archimedes was so proud of this concept that he requested that a cylinder enclosed a sphere, with an explanation of this concept, be engraved on his grave. Archimedes also gave a method for approximating pi. He was able to estimate the value of pi between 3 10/71 and 3 1/7. Math wasn’t as sophisticated enough to find out the exact pi (3.14). Archimedes was finding square roots and he found a method based on the Greek myriad for representing numbers as large as 1 followed by 80 million billion zeros.
...ct, the rest of the mathematical world doesn’t dare question their founding mathematicians, and that they alone, the cyclometer, have discovered the true value of Pi. One circle squarer even went so far as to submit a law in his home state of Indiana that his value of Pi be used as the legal value of Pi. It was passed, but to this day awaits further legislation in regard to its factuality.
Greek mathematics began during the 6th century B.C.E. However, we do not know much about why people did mathematics during that time. There are no records of mathematicians’ thoughts about their work, their goals, or their methods (Hodgkin, 40). Regardless of the motivation for pursuing mathematical astronomy, we see some impressive mathematical books written by Hippocrates, Plato, Eudoxus, Euclid, Archimedes, Apollonius, Hipparchus, Heron and Ptolemy. I will argue that Ptolemy was the most integral part of the history of Greek astronomy.
Pi, short for Piscine, meaning a rational source of water, is a rational man living in the irrational world, who believes in not one, but three religions, which some may say is irrational. Pi, whose family owned a zoo, faced many hardships
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.
In about 200 BC the Greek Eratosthenes devised an algorithm for calculating primes called the Sieve of Eratosthenes.
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.
Pi is an indian, but except Hinduism, he also believes in Christianity and Islam. It is pretty unusual. However, these three religions save his life when he meets storm on the sea. Religion is a key component in Pi’s survival because it lets him understand that he has to coexist with other creatures, it leads Pi to accept that even if he did not survive he would be redeemed, and it gives Pi the hope for survival.
for coming as a fish to save him. “Even when God seemed to have abandoned me … indifferent to my suffering, He was watching; and when I was beyond all of hope of saving, He gave me rest, and gave me a sign to continue my journey.” This quote portrays how Pi felt that God was with him every time, and that is why he is willing to live and not give up. He prayed and prayed as he believes that it is one of the keys to
Steinburg, D. H. (2012). Baker's math: Essential calculations for working with dough. Dim Sum Thinking, Inc.
Historically speaking, ancient inventors of Greek origin, mathematicians such as Archimedes of Syracuse, and Antiphon the Sophist, were the first to discover the basic elements that translated into what we now understand and have formed into the mathematical branch called calculus. Archimedes used infinite sequences of triangular areas to calculate the area of a parabolic segment, as an example of summation of an infinite series. He also used the Method of Exhaustion, invented by Antiphon, to approximate the area of a circle, as an example of early integration.
There are many people that contributed to the discovery of irrational numbers. Some of these people include Hippasus of Metapontum, Leonard Euler, Archimedes, and Phidias. Hippasus found the √2. Leonard Euler found the number e. Archimedes found Π. Phidias found the golden ratio. Hippasus found the first irrational number of √2. In the 5th century, he was trying to find the length of the sides of a pentagon. He successfully found the irrational number when he found the hypotenuse of an isosceles right triangle. He is thought to have found this magnificent finding at sea. However, his work is often discounted or not recognized because he was supposedly thrown overboard by fellow shipmates. His work contradicted the Pythagorean mathematics that was already in place. The fundamentals of the Pythagorean mathematics was that number and geometry were not able to be separated (Irrational Number, 2014).
The history of math has become an important study, from ancient to modern times it has been fundamental to advances in science, engineering, and philosophy. Mathematics started with counting. In Babylonia mathematics developed from 2000B.C. A place value notation system had evolved over a lengthy time with a number base of 60. Number problems were studied from at least 1700B.C. Systems of linear equations were studied in the context of solving number problems.
The Golden Ratio also appears in the Parthenon in Athens. It was built about 440 B.C.; it forms a perfect Golden Rectangle. The exterior dimensions form Golden Rectangle. The Golden Ratio also appears in the front face, which is found to be Phi times as wide as it is tall, so therefore it is a Golden Rectangle. The height of the roof is Phi times the space between the tops of the columns and the bottom of the roof.