A map projection is defined as “a geometrical transformation of the earth’s spherical or ellipsodial surface onto a flat map surface.” Although many things have been written about these projections, people still find this subject to be one of the most contraversial aspects of map use. Many professionals admit that they don’t completely understand map projections. This shortcoming unfortunately can have consequenes. First, it hinders their abilty to understand to understand the international relationships in the global society. Second, it can make easy prey for poliatcians, advertisers, and others who lack understanding or use the map projections in deceptive ways.
There are an infinate number of map projections, and each is better suited for a particular purpose. So the question arises, how to distinguish one from another. Two approaches are commonly used to classify the projections into different families based on their geometrical distortion properties, realting to shape, area, and direction. Also examing the nature of the surface that is used to make the projection, whether it is a cone, plane or cylinder. These two aproaches go hand in hand with what spatial properties are preserved, also with the pattern and level of distortion.
The two projections that will be compared in this essay will be a cylindrical projection (Mercator), and a conic projection (Lambers equal area).
The first projection that will be analyzed will be the cylyndrical projection, dealing specificly with the Mercator projection. The most common to project accuratly is the equtrial zone, and frequently the only true useful aspect of all cylindrical projections. All of the coordinate lines are straight parallels. Cross meridians are always at right angles...
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...r British Columbia and it is also used by the United States Geological Survey or USGS and the United States Census Bureau.
Coordinates from a spherical datum can be made into an Albers equal-area conic projection with coordinates from the following formulas: Where λ is the longitude, λ0 is the reference longitude, φ is the latitude, φ0 is the reference latitude and φ1 and φ2 are the standard parallels.
The comparison of the Mercator and the Albers equal area projections is somewhat like comparing apples to oranges. They are both good at describing one region on the earth; however neither is good for displaying the entire globe. The problem with modern society is that the mental map, thanks to uneducated citizens, is that of the Mercator. So many individuals have a flawed sense of the mapped world. Hopefully with a more informed public this can change for the better.
According to Roland Shearer (1992) the release of non-Euclidean geometries at the end of the 19th Century copied the announcement of art movements occurring at that time, which included Cubism, Constructivism, Orphism, De Stijl, Futurism, Suprematism and Kinetic art. Most of the artists who were involved in these beginnings of Modern art were directly working with the new ideas from non-Euclidean geometry or were at least exposed to it – artists such as Picasso, Braque, Malevich, Mondrian and Duchamp. To explain human-created geometries (Euclidean, non-Euclidean), it is a representation of human-made objects and technology (Shearer
Ken Jennings was a map nerd from a young age himself, you will not be surprised to learn, even sleeping with an old creased atlas at the side of his pillow, most kids his age were cuddling with a trusted blanket- Jennings was not. As he travels the world meeting people of kindred spirits--map librarians, publishers, geocachers, and the engineers behind google maps. Now that technology and geographic unknowing is increasingly insulting us from the space and land around us, we are going to be needing these people more than ever. Mapheads are the ones who always know exactly where they are and...
After 3rd century BC, Eratosthenes calculation about Earth's circumference was used correctly in different locations such as Alexandria and syene (Aswan now) by simple geometry and the shadows cast. Eratosthenes's results undertaken in 1ST century by Posidonius, were corroborated in Alexandria and Rhodes by the comparison between remarks is excellent.
Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen, Geometry, Houghton Mifflin Company. Boston, ©1988.
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.
Blij, H.J. de , Peter O. Muller, Jan Nijman, and Antoinette M.G.A WinklerPrins. The World Today Concepts and Regions in Geography. Fifth Edition ed. United States of America: John Wiley & Sons, Inc., 2011. Print.
In this essay the conic sections in taxicab geometry will be researched. The area of mathematics used is geometry. I have chosen this topic because it seemed interesting to me. I have never heard for this topic before, but then our math teacher presented us mathematic web page and taxicab geometry was one of the topics discussed there. I looked at the topic before and it encounter problems, which seemed interesting to explore. I started with a basic example, just to compare Euclidean and taxicab distance and after that I went further into the world of taxicab geometry. I explored the conic sections (circle, ellipse, parabola and hyperbola) of taxicab geometry. All pictures, except figure 12, were drawn by me in the program called Geogebra.
The map was developed by the CIPD in conjunction with professionals and organisations around the world and is made up of the following 3 sections:
"The Foundations of Geometry: From Thales to Euclid." Science and Its Times. Ed. Neil Schlager and Josh Lauer. Vol. 1. Detroit: Gale, 2001. Gale Power Search. Web. 20 Dec. 2013.
Historical geographer JB Harley wrote an essay on Map Deconstruction in 1989, in which Harley argues that a map is more than just a geographical representation of an area, his theory is that we need to look at a map not just as a geographical image but in its entire context. Harley points out that by an examination of the social structures that have influenced map making, that we may gain more knowledge about the world. The maps social construction is made from debate about what it should show. Harley broke away from the traditional argument about maps and examined the biases that govern the map and the map makers, by looking at what the maps included or excluded. Harley’s “basic argument within this essay is that we should encourage an epistemological shift in the way we interpret the nature of cartography.” Therefore Harley’s aim within his essay on ‘Deconstructing the Map’ was to break down the assumed ideas of a map being a purely scientific creation.
The six concepts of geography are location, region, spatial pattern, spatial interaction, human/ environmental interaction, and culture. The location is everything; it is the starting point in geography. The region is the area of the land with consistent recognizable features, it has variations in its physical features. There are mountains, hills, valleys, plains, plateaus, oceans, lakes, deserts and wilderness, variations occur in its social and cultural features too. The spatial pattern is when a pattern is found in places that are far apart. Spatial interaction is when geographers believe one event can lead to a change in another location that is far away. Managing change is a key aspect of geography, geographers learn from past changes and predict and future ones. Human/ environmental interaction is the impact humans have on the environment. Interaction is closely linked to change. Again, in both physical and human aspects of the subject, geographers want to find out how things are linked together and how one aspect affects another. Lastly culture has different impacts on the environment, natural resources, concern issues of how people think about the world and how they communicate that thinking to
Mathematicians, engineers and scientists encounter numerous functions in their work: polynomials, trigonometric and hyperbolic functions amongst them. However, throughout the history of science one group of functions, the conics, arise time and time again not only in the development of mathematical theory but also in practical applications. The conics were first studied by the Greek mathematician Apollonius more than 200 years BC. Essentially, the conics form that class of curves which are obtained when a double cone is intersected by a plane. There are three main types: the ellipse , the parabola and the hyperbola . From the ellipse we obtain the circle as a special case, and from the hyperbola we obtain the rectangular hyperbola as a special case. These curves are illustrated in the following figures. cone-axis
Euclidean Geometry is the study of plane and solid figures based on the axioms and theorems outlined by the Greek mathematician Euclid (c. 300 B.C.E.). It is this type of geometry that is widely taught in secondary schools. For much of modern history the word geometry was in fact synonymous with Euclidean geometry, as it was not until the late 19th century when mathematicians were attracted to the idea of non-Euclidean geometries. Euclid’s geometry embodies the most typical expression of general mathematical thinking. Rather than simply memorizing basic algorithms to solve equations by rote, it demands true insight into the subject, cleaver ideas for applying theorems in special situations, an ability to generalize from known facts, and an
as if I were to do this, then I would be plotting 2366 datum points
...h tech tools that are now used a lot of the final measurements are determined by the human eye. In the Industrial Age surveying became very important to deal with taxes and this is where the two methods came into play because geodetic were effective for a large area and took the terrain into account which was helpful for maps but plane surveying was more helpful in equally dividing up the land. Surveying became even more prominent as population grew and construction began to expand surveying for roads and bridges to just collect data as travel began to increase and ensure that the establishments could handle the new load that the increased population could handle and thus the tools began to advance dramatically from rod measurement to GPS to give more detailed reading to get further intelligence on the ground and distance more accurately using the new equipment.