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The experiment of archimedes
The life and work of the great archimedes
The life and work of the great archimedes
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Pi, the most talked about yet the least known about, is the ratio of the circumference of a circle over the diameter, and is one of the most important numbers ever to be used in mathematics. The world of Pi is very interesting, detailed, and complex. There is a very large history of how pi was found and of different ways mathematicians and civilizations calculated Pi. A few of the many examples of the calculation of pi are from Archimedes, Ahmes, the Chinese, the ancient Babylonians, and also the ancient Egyptians. In today’s society there are also many real world uses of Pi.
Pi has a very rich and detailed history since it's creation long ago. It has been a well known ratio for around 4000 years. Many mathematicians have used different ways of calculating Pi but the first to make a huge breakthrough was a man by the name of Archimedes. To calculate the magical number of Pi, Archimedes used the Pythagorean Theorem to find the perimeter of two regular polygons. He used at first a Hexagon, but then thought is not a circle just a polygon with so many sides that you can’t count (He might not have actually said that). So he went on doubling the sides of these polygons (on the left), until he reached a 96-gon as we demonstrated in our model, knowing the more sides the more accurate the number. These polygons were inscribed and circumscribed
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After the ideas of mathematicians like Archimedes spread to China and other places on the east they started to make more advanced calculations as well. Zu Chongzhi one of the best chinese mathematicians of the time, was the first person to come up with accurate first six digits of Pi. He calculated it to 3.141592 also known as 355/113, sadly many of his books and works have been lost, therefore no one knows exactly how he actually came up with his
Squaring the circle with a compass and straightedge had been a problem that puzzled geometers for years. In his notes under the drawing he recognized that “if you open your legs enough that your head is lowered by one-fourteenth of your height and raise your hands enough that your extended fingers touch the line of the top of your head, know that the centre of the extended limbs will be the navel, and the space between the legs will be an equilateral triangle” . This excerpt alone shows that Da Vinci had an immense understanding of proportion, as well as geometry. On this page, Da Vinci also wrote the exact proportions that he used, based his own observations and the ones used in Vitruvius’s book. Da Vinci
By using the survival manual, Pi attempts to navigate his way, but he his unsuccessful. He decides to merely float.
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, short for Piscine Molitor Patel, is a young Indian boy growing up in South India in the 1970's. His father owns a zoo and, with increasing political unrest in India, decides to sell up and emigrate to Canada. They accompany the wild animals on board the ship on their journey to the new zoos in North America.
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
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.
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 real life situations, there are many applications of physics. Physics is applied in almost everything we do and everything around us from household chores, in school and in
Probability and Statistics most widespread use is in the arena of gambling. Gambling is big all over the world and lots of money is won and lost with their aid. In horse racing especially the statistics of a horse in terms of its physical condition and winning history sway numbers of persons into believing that the mathematical evidence that is derived can actually be a good indicator of a race’s outcome. Usually it is if the odds or probability are great in favor of the desired outcome. However the future is uncertain and races can turn out any of a number of different ways.
In addition, when Pi is in university and is introducing himself to each of his classes he uses repetition to explain his name. He says his name, writes it on the board, and underlines it. Pi uses ritual to get people in the habit of calling him Pi. This has significance to his past zoo life. Zoo animals need lots of care, this includes feedings, cleanings, and training. Pi is used to ritual, he knows that animals learn/live off of routine, and repetition, and so he has applied these skills to his classmates indicating a similarity between animals, and humans. Animals learn off of repetition, and routine, as do humans. Pi 's name has a mathematical link which has major symbolism to the entire novel. We all know that Pi is a large, and complicated number. Pi says in the novel, "That 's one thing I hate about my nickname, the way that number runs on forever." (Martel 316). I feel like the author included this quote to signify that Pi has been on a long journey, just like Pi says the numbers continue on. This quote was said towards the ending of the novel, and could represent the
A rectangle is a very common shape. There are rectangles everywhere, and some of the dimensions of these rectangles are more impressive to look at then others. The reason for this, is that the rectangles that are pleasing to look at, are in the golden ratio. The Golden Ratio is one of the most mysterious and magnificent numbers/ratios in all of math. The Golden Ratio appears almost everywhere you look, yet not everyone has ever heard about it. The Golden Ratio is a special number that is equal to 1.618. An American mathematician named Mark Barr, presented the ratio using the Greek symbol “Φ”. It has been discovered in many places, such as art, architectures, humans, and plants. The Golden Ratio, also known as Phi, was used by ancient mathematicians in Egypt, about 3 thousand years ago. It is extraordinary that one simple ratio has affected and designed most of the world. In math, the golden ratio is when two quantities ratio is same as the ratio of their sum to the larger of the two quantities. The Golden Ratio is also know as the Golden Rectangle. In a Golden Rectangle, you can take out a square and then a smaller version of the same rectangle will remain. You can continue doing this, and a spiral will eventually appear. The Golden Rectangle is a very important and unique shape in math. Ancient artists, mathematicians, and architects thought that this ratio was the most pleasing ratio to look at. In the designing of buildings, sculptures or paintings, artists would make sure they used this ratio. There are so many components and interesting things about the Golden Ratio, and in the following essay it will cover the occurrences of the ratio in the world, the relationships, applications, and the construction of the ratio. (add ...
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).
In conclusion, it is clear that while their ancient civilization perished long ago, the contributions that the Egyptians made to mathematics have lived on. The Egyptians were practical in their approach to mathematics, and developed arithmetic and geometry in response to transactions they carried out in business and agriculture on a daily basis. Therefore, as a civilization that created hieroglyphs, the decimal system, and hieratic writing and numerals, the contributions of the Egyptians to the study of mathematics cannot and should not be overlooked.
They constructed the 12-month calendar which they based on the cycles of the moon. Other than that, they also created a mathematical system based on the number 60 which they called the Sexagesimal. Though, our mathematics today is not based on their system it acts like a foundation for some mathematicians. They also used the basic mathematics- addition, subtraction, multiplication and division, in keeping track of their records- one of their contributions to this world, bookkeeping. It was also suggested that they even discovered the number of the pi for they knew how to solve the circumference of the circle (Atif, 2013).
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.