Geometry is the math of the world. It has developed through art and architecture and is an integral part of society. It has helped develop security systems. However, one of the most important parts of Geometry is the Pythagorean Theorem. The Pythagorean Theorem is the most important because it is one of the most commonly used theorems in Geometry and in all of math. The Pythagorean Theorem is as old as Geometry itself. It was developed by the Egyptians and Chinese and finalized by a Greek philosopher Pythagoras. It can also help solve many real world problems. The Pythagorean Theorem is fascinating because of who developed it, how it has affected influential people, and how it has improved art and architecture.
The Pythagorean Theorem is the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse. It is more commonly known as x2+y2=z2. What is important is the triangle must have a 90 degree angle to make this theorem true. Within this are special values that are called Pythagorean Triples. The Pythagorean Theorem is only useful if one follows the rules that come with it.
Many people believe that Pythagoras of Samos was alone the author of the Pythagorean Theorem. Pythagoras was a Greek Philosopher from Samos and lived approximately from 570 BC to 495 BC. During his life time he founded the Pythagoreanism which was a type of cult that was religious and scientific but was very secretive. Evidence from other nations shows Pythagoras was not the only one to have developed this type of theorem. Historians have found evidence that proves that the Egyptians and Chinese had a very similar theorem. From this evidence many believe that Pythagoras was influenced by either nation. Still others believe ...
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...ythagorean Theorem is incredible and will still be in the future because of everything that can be discovered in math.
Works Cited
A. Bogomolny, Pythagorean Theorem and its many proofs from Interactive Mathematics
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Huffman, Carl, Pythagoras, The Stanford Encyclopedia of Philosophy (Spring 2014 Edition),
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Maor, Eli, The Pythagorean Theorem: A 4,000-year History, Princeton University Press, 2007
Maor, Eli, The Pythagorean Theorem: A 4,000-year History, Princeton University Press, 2007
Pythagoras Theorem Used in Real Life Experiences, Bright Hub Education, Trent Lorcher (ed.)
URL= http://www.brighthubeducation.com/homework-math-help/36639-applications-of-pythagoras-theorem-in-real-life/, 11/20/2012
Study of Geometry gives students the tools to logical reasoning and deductive thinking to solve abstract equations. Geometry is an important mathematical concept to grasp as we use it in our life every day. Geometry is the study of shape- and there are shapes all around us. Examples of geometry in everyday life are- in sport, nature, games and architecture. The game Jenga involves geometry as it is important to keep the stack of tiles at a 90 degrees angle, otherwise the stack of tiles will fall over. Architects use geometry everyday- it is essential when designing buildings- shape, angles and area and perimeter are some of the geometry concepts architects
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.
Euclidean Geometry has been around for over thousands of years, and is studied the most in high school as well as college courses. In it's simplest form, Euclidean geometry, is concerned with problems such as determining the areas and diameters of two-dimensional figures and the surface areas and volumes of solids. Euclidean Geometry is based off of the parallel postulate, Postulate V in Euclid's elements, which states that, "If a straight line meets two other straight lines so as to make the two interior angles on one side of it together less than two right angles, the other straight lines, if extended indefinitely, will meet on that side on which the angles are less than two right angles."
...st important scientists in history. It is said that they both shaped the sciences and mathematics that we use and study today. Euclid’s postulates and Archimedes’ calculus are both important fundamentals and tools in mathematics, while discoveries, such Archimedes’ method of using water to measure the volume of an irregularly shaped object, helped shaped all of today’s physics and scientific principles. It is for these reasons that they are remembered for their contributions to the world of mathematics and sciences today, and will continue to be remembered for years to come.
Pythagoras held that an accurate description of reality could only be expressed in mathematical formulae. “Pythagoras is the great-great-grandfather of the view that the totality of reality can be expressed in terms of mathematical laws” (Palmer 25). Based off of his discovery of a correspondence between harmonious sounds and mathematical ratios, Pythagoras deduced “the music of the spheres”. The music of the spheres was his belief that there was a mathematical harmony in the universe. This was based off of his serendipitous discovery of a correspondence between harmonious sounds and mathematical ratios. Pythagoras’ philosophical speculations follow two metaphysical ideals. First, the universe has an underlying mathematical structure. Secondly the force organizing the cosmos is harmony, not chaos or coincidence (Tubbs 2). The founder of a brotherhood of spiritual seekers Pythagoras was the mo...
Carl Friedrich Gauss is revered as a very important man in the world of mathematicians. The discoveries he completed while he was alive contributed to many areas of mathematics like geometry, statistics, number theory, statistics, and more. Gauss was an extremely brilliant mathematician and that is precisely why he is remembered all through today. Although Gauss left many contributions in each of the aforementioned fields, two of his discoveries in the fields of mathematics and astronomy seem to have had the most tremendous effect on modern day mathematics.
Mathematics is part of our everyday life. Things you would not expect to involve math
Trigonometry is one of the branches of mathematical and geometrical reasoning that studies the triangles, particularly right triangles The scientific applications of the concepts are trigonometry in the subject math we study the surface of little daily life application. The trigonometry will relate to daily life activities. Let’s explore areas this science finds use in our daily activities and how we use to resolve the problem.
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).
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.
Trigonometry basics are often taught in school either as a separate course or as part of a precalculus course. The trigonometric functions are pervasive in parts of pure mathematics and applied mathematics such as Fourier analysis and the wave equation, which are in turn essential to many branches of science and technology.Spherical trigonometry studies triangles on spheres, surfaces of constant positive curvature, in elliptic geometry. It is fundamental to astronomy and navigation. Trigonometry on surfaces of negative curvature is part of hyperbolic
1) Do both 5, 12, 13 and 7, 24, 25 satisfy a similar condition of :
The 17th Century saw Napier, Briggs and others greatly extend the power of mathematics as a calculator science with his discovery of logarithms. Cavalieri made progress towards the calculus with his infinitesimal methods and Descartes added the power of algebraic methods to geometry. Euclid, who lived around 300 BC in Alexandria, first stated his five postulates in his book The Elements that forms the base for all of his later Abu Abd-Allah ibn Musa al’Khwarizmi, was born abo...
However, between 1850 and 1900 there were great advances in mathematics and physics that began to rekindle the interest (Osborne, 45). Many of these new advances involved complex calculations and formulas that were very time consuming for human calculation.
Euclid, also known as Euclid of Alexandria, lived from 323-283 BC. He was a famous Greek mathematician, often referred to as the ‘Father of Geometry”. The dates of his existence were so long ago that the date and place of Euclid’s birth and the date and circumstances of his death are unknown, and only is roughly estimated in proximity to figures mentioned in references around the world. Alexandria was a broad teacher that taught lessons across the world. He taught at Alexandria in Egypt. Euclid’s most well-known work is his treatise on geometry: The Elements. His Elements is one of the most influential works in the history of mathematics, serving as the source textbook for teaching mathematics on different grade levels. His geometry work was used especially from the time of publication until the late 19th and early 20th century Euclid reasoned the principles of what is now called Euclidean geometry, which came from a small set of axioms on the Elements. Euclid was also famous for writing books using the topic on perspective, conic sections, spherical geometry, number theory, and rigor.