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Geometry in construction
Geometry in construction
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Believe it or not, Geometry is actually useful! All our lives we have been told that we would use this in our lives and we have thought “no we won't.” but we do use it in life. Geometry is used for home decorating. Also architects use it for home building.
The architects use the golden rule or Pie is the ratio found in all of life. Humans have incorporated it into everything from mathematics, to artwork, and music. Pie is 3.14159265359 and it continues on for ever. It is found in everything from the shape of our universe, the structure of clouds, and the even the proportions of the human body. It is found in everything from the shape of our universe, the structure of clouds, and the proportions of the human body. While there is some controversy
For me geometry is the most basic concern for artists. Roland Shearer quotes poet Apollinaire where he explains, “geometry is to the plastic arts what is to the art of the writer”. This is not to say that artists are geometers, because most of us are far from it (Shearer 1992:143).
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."
An example of the difference in the abstract geometry and the measurement geometry is the sum of the measures of the angles of a trigon. The sum of the measures of the angles of a trigon is 180 degrees in Euclidian geometry, less than 180 in hyperbolic, and more than 180 in elliptic geometry. The area of a trigon in hyperbolic geometry is proportional to the excess of its angle sum over 180 degrees. In Euclidean geometry all trigons have an angle sum of 180 without respect to its area. Which means similar trigons with different areas can exist in Euclidean geometry. It is not possible in hyperbolic or elliptic geometry. In two-dimensional geometries, lines that are perpendicular to the same given line are parallel in abstract geometry, are neither parallel nor intersecting in hyperbolic geometry, and intersect at the pole of the given line in elliptic geometry. The appearance of the lines as straight or curved depends on the postulates for the space.
Nevertheless, that day followed me, and I tried to understand more about fractals through the resources I already had at my disposal-- through courses I was taking. Sophomore year, through my European History and Architecture courses, I learned about many ancient architectural feats-- Stonehenge, the Pyramids of Giza, the Parthenon, many Gothic Cathedrals, and the Taj Mahal-- and that they all somehow involved the use of the golden ratio. I will come back to how this relates to fractals later in the article, but for now know that each of these buildings use different aspects of their design to form the golden ratio. I was intrigued by the fact that fractals, what seemed to be something only formed by the forces of nature, were being constructed by human hands. Although I wanted badly to find out more, I waited until that summer, when I discovered a YouTube account by the name of Vihart. Vihart’s videos are not tutorials on how to do math, however Vihart’s ramblings about the nature and the concepts of the mathematical world have a lot of educational value, especially on topics that are more complicated to understand then to compute. Her videos on fractal math and their comparability to nature, helped to show me that...
Geometry is used in Auto Mechanics in many ways; for example, cam and crankshaft, oil pump, fuel delivery, rings, valves, piston, and speed.
I also learned that mathematics was more than merely an intellectual activity: it was a necessary tool for getting a grip on all sorts of problems in science and engineering. Without mathematics there is no progress. However, mathematics could also show its nasty face during periods in which problems that seemed so simple at first sight refused to be solved for a long time. Every math student will recognize these periods of frustration and helplessness.
The ancient Egyptians and ancient Greeks knew about the golden ratio, regarded as a number that can be found when a line or shape is divided into two parts so that the longer part divided by the smaller part is also equal to the whole length or shape divided by the longer part. The Ancient Greeks and Romans incorporated it and other mathematical relationships, such as the triangle with a 3:4:5 ratio, into the design of monuments including the Great Pyramid, the Colosseum, and the Parthenon. Artists who have been inspired by mathematics and studied mathematics include the Greek sculptor Polykleitos, who created a series of mathematical proportions for carving the ‘perfect’ nude male figurine. Renaissance painters such as Piero della Francesca an...
While studying the golden mean it becomes evident just how relevant this number is in the world. Many architects and artists have used this ratio as a scale and proportion sequence. The sequence is also relevant in music, nature and even the human body. Ancient mathematicians were so fascinated in the ratio because of its frequency in geometry. The first person to provide a written definition was Euclid. He stated “A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less” this has been studied thoroughly by many mathematicians but the most relevant was the studies of Leonardo Fibonacci. Fibonacci is famous for the work he put in to come up with the Fibonacci sequence.
are how to follow lines of reasoning, how to say precisely what is intended, and
is convergent and ends up converging to φ, the golden ratio [2]. This curious quantity is just a ratio, so what makes it so special? Why is it so mystifying? While the other major constant in mathematics, pi, is a ratio between a circle's circumference and its diameter, phi (φ) considers a rectangle with height, h, and width, w, and forms the following ratio:
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...
Fields that use trigonometry or trigonometric functions include astronomy (especially for locating apparent positions of celestial objects, in which spherical trigonometry is essential) and hence navigation (on the oceans, in aircraft, and in space), music theory, audio synthesis, acoustics, optics, analysis of financial markets, electronics, probability theory, statistics, biology, medical imaging (CAT scans and ultrasound),pharmacy, chemistry, number theory (and hence cryptology), seismology, meteorology, oceanography, many physical sciences, land surveying and geodesy, architecture, phonetics, economics, electrical engineering, mechanical engineering, civil engineering, computer graphics, cartography, crystallography and game
A triangle is a shape with a total of three sides. The triangle to me looks like one side of “ The Great Pyramid”. A triangle is a two dimensional figure. In a three-dimensional form, it is a pyramid. I strongly believe that the triangle is the most unique shape of all of the shapes.