Comparing Euclidean, Spherical Geometry, And

Longitude by Dava Sobel was a book that explained in great detail the struggle to find longitude at sea and way it was so necessary. Sobel talked about the tragedies that followed with not finding longitude at sea and then the discoveries and trials that had occurred to find a final solution. Throughout the book, you understand the urgent need to find longitude why it was so hard, and what it really took in order to come to the final discovery. As you read through this paper you will get an understanding of the topics Sobel talked about in her book such as, the shipwrecks and tragedies that occurred without longitude at sea, the two competing methods to find longitude and the man who discovered it.

suspected it consisted of a single curved line and a single straight one. For my retests, I studied it

S- together the angles make a coordinate that can pinpoint any geographic position on the surface of the Earth, or any other

I only prove that $E\hat{H}G = 90^{\circ}$, for the reason that the prove of the other angles will be similar. When I was asked to prove if the inscribed rhombus is a square, I simply say to myself, ``it means I have to prove that the corners of the rhombus are right angled ($90^{\circ}$)" since the properties of a rhombus are such that opposite angles are equal, all sides are equal, and opposite sides are parallel, the diagonals bisect the angles, and the diagonals are perpendicular bisectors of each other. Therefore, the inscribed rhombus can only be a square if the angles are right angles. I observe that all four triangles are congruent by SSS, therefore from $A\hat{E}H + E\hat{H}A = 90^{\circ}$ and $E\hat{H}G + A\hat{H}E + D\hat{H}G = 180^{\circ}$ and $G\hat{H}D = A\hat{E}H$, it follows that $A\hat{H}E + D\hat{H}G = 90^{\circ}$, hence $E\hat{H}G = 90^{\circ}$. There is a need to draw the picture since it gives more logical reasoning and the understanding of how the angles and sides are defined, without drawing the picture we may not understand what is happening, therefore it is very crucial that as teachers we make use of pictures when we dealing with this kind of

The Law of ellipses, which means that each planet travels around the sun in an ellipses.

4) This line is much like a line on a geologic topo map. Explain the similarity.

One of Thales’ most renounced findings include his discovery in geometric studies in the area reading the rules of triangles. He came to the conclusion that if the base angles of an isosceles triangle are equal, the sum of the angles of a triangle are equivalent to two right angles. With the application of “geometric principles to life situations, Thales was able to calculate the height of a pyramid by measuring its shadow, and the distance of a boat to the shore, by using the concept of similar triangles” (pg. 5, Muehlbauer). Realizations such as these helped shape the beginning for the formation of natural law based on observations of the world through explanation.

Chapter 1- This is a second-dimentional world filled with lines and edges so everything here is completely flat. It is impossible to view anything other than a line becuse everything is viewed from one angle. Edwin Abbott uses a penny to explain this, loking down on it you would see a circle but if you lowered your gaze to the side, you would onle see a line.

4) This line is much like a line on a geologic topo map. Explain the

Lines are paths or marks left by moving points and they can be outlines or edges of shapes and forms. Lines have qualities which can help communicate ideas and feelings such as straight or curved, thick or thin, dark or light, and continuous or broken. Implied lines suggest motion or organize an artwork and they are not actually seen, but they are present in the way edges of shapes are lined up.

The concept of linear perspective is simple to understand. There is a horizon line, which is the point where the sky meets the ground. There is a vanishing point, which is where all the lines of the painting run inward to meet the horizon line (Exploring Linear Perspective).

Line: There are smooth lines such as those lining the babies and the ladies. There are also zigzag lines, for instance, the downside of the groove.

Burgess’s concentric zone theory was presented in 1924. He presented a descriptive urban land use model that divided cities in a set of concentric circles expanding from downtown to the suburbs. His representation came from Burgess’ observations of various American cities, especially Chicago. Burgess model assumes a relationship between the socio-economic status of households and the distance from the Central Business District. The further from the district, the better the quality of housing, but the longer the commuting time. Making this Accessing better housing is done at the expense of longer commuting times and costs as well. According to Burgess, urban growth is a process of expansion and reconversion of land uses, with a tendency of each inner zone to expand in the outer zone. According to Burgess’ theory, a large city is divided in six concentric zones, Burgess’s model has its cons according to critics. It is said to be a product of its time. That is, it won’t work the same with present cities. The model was developed when American cities were growing very fast and when motorized transportation was still uncommon as most people used public transit. Thus the concept cannot be applied to those from the second half to the twentieth century where highways have enabled urban development to escape the reconversion process and to take place directly in the suburbs. The model in this case was developed for American cities and is limited elsewhere.

This description is then matched against those stored in memory. According to Biedermann, geons are detected on the basis of non-accidental properties such as collinearity, symmetry and parallelism. Like Marr and Nishihara, Biedermann sustains that primitives are invariant under changes in viewpoint.

Euclid’s assumptions about his postulates have set the groundwork for geometry today. He provided society with definitions of a circle, a point, and line, etc and for 2000 was considered “the father of geometry.” His postulates proved to be a framework from which mathematics was able to grow and evolve, from two thousand years ago, till Newton and even to all our classrooms today.