Essay PreviewMore ↓
The ancient Egyptians and Babylonians discovered abstract Geometry. They developed these ideas that were used to build pyramids and help with reestablishing land boundaries. While, the Babylonians used abstract geometry for measuring, construction buildings, and surveying. Abstract geometry uses postulates, rules, definitions and propositions before and up to the time of the Euclid.
Abstract geometry is deductive reasoning and axiomatic organization. Deductive reasoning deals with statements that have already been accepted. An example of deductive reasoning is proving the sum of the measures of the angles of a quadrilateral is 360 degrees. Another example of deductive reasoning is proving the sum of the angles of a trigon is equal to 180 degrees. From this we get, any quadrilateral can be divided into two trigons. Axioms, which are also called postulates, are statements that can be proved true by using deductive reasoning.
Measurement geometry contains theories that exist and can have supporting ideas to back them up, and cannot be disproved. Hyperbolic geometry and elliptic geometry are two examples of measurement geometry. Non-Euclidean geometry can be considered measurement geometry, since it is a branch in which the fifth postulate of Euclidean Geometry is replaced by one of the two alternative postulates. Mathematicians in the nineteenth century showed that it is possible to create consistent geometries with Euclid's postulates.
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.
At the present time mathematics is trying to figure out which of the three is the best representation of the universe.
How to Cite this Page
"Abstract Geometry." 123HelpMe.com. 21 Aug 2018
Need Writing Help?
Get feedback on grammar, clarity, concision and logic instantly.Check your paper »
- The Application of Fractal Geometry to Ecology Abstract New insights into the natural world are just a few of the results from the use of fractal geometry. Examples from population and landscape ecology are used to illustrate the usefulness of fractal geometry to the field of ecology. The advent of the computer age played an important role in the development and acceptance of fractal geometry as a valid new discipline. New insights gained from the application of fractal geometry to ecology include: understanding the importance of spatial and temporal scales; the relationship between landscape structure and movement pathways; an increased understanding of landscape structures; and the abil... [tags: essays research papers]
3415 words (9.8 pages)
- There are generally two types of paintings- representational and abstract. While representational painting portrays recognizable objects, abstract painting does not look like a particular object. Instead, abstract art is made up of designs, shapes and colors. (http://www.harley.com/art/abstract-art/ ) The meaning of abstract art is, in its most simplified form, art that relies on the emotions of the artist and the elements of design rather than exact representation. This broad definition allows artists almost unlimited freedom of expression.... [tags: essays research papers]
1099 words (3.1 pages)
- Fractal Geometry The world of mathematics usually tends to be thought of as abstract. Complex and imaginary numbers, real numbers, logarithms, functions, some tangible and others imperceivable. But these abstract numbers, simply symbols that conjure an image, a quantity, in our mind, and complex equations, take on a new meaning with fractals - a concrete one. Fractals go from being very simple equations on a piece of paper to colorful, extraordinary images, and most of all, offer an explanation to things.... [tags: essays papers]
1448 words (4.1 pages)
- “Always,” created by Clement Meadmore, is a sculpture located in front of the Carlson Center entrance at Johnson County Community College. This sculpture of approximately 20 feet is full round because it can be walked around on all sides. “Always” is composed of welded aluminum that is painted black and therefore, the method of execution used for this sculpture is addition. Abstract geometric shapes are easily seen in “Always.” The subject of geometry is apparent from any angle. This sculpture has a unitary form of a long and large rectangular shape that bends several times in different directions and angles before springing into space.... [tags: carlson center, geometry, biography]
739 words (2.1 pages)
- Geometry Geometry was actually first used in ancient Egypt and Babylon at around 2000 BC in both cases. In order for the Egyptians to build such massive structures as the pyramids they had to have made plans for them prior to the actually building, in these plans geometry had to be used. On ancient Babylonian tablets there is evidence that they understood the Pythagorean theorem. The so-called "father" of Geometry is Euclid a Greek mathematician. He wrote The Elements, books of postulates and theorems, which paved the way for modern Geometry.... [tags: Papers]
362 words (1 pages)
- As you begin the course of geometry students are generally familiarized with frequently used formulas in mathematics. These formulas include finding the perimeter and area of two-dimensional figures and finding the volume and surface area of three-dimensional figures. For every diverse shape there is a related formula for finding its perimeter, area, volume, or surface area. Therefore, we will only focus on four formulas for four singular shapes or figures. We will find the perimeter of a square, the area of a triangle, the volume of a right circular cylinder and the total surface area of a sphere.... [tags: Geometry]
649 words (1.9 pages)
- 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.... [tags: Mathematics, Geometry, Taxicab Geometry]
1769 words (5.1 pages)
- According to J. Dee, (1608), an English scholar, “There is nothing which so much beautifies and adorns the soul and mind of man as does knowledge of the good arts and sciences. ... Many ... arts there are which beautify the mind of man; but of all none do more garnish and beautify it than those arts which are called mathematical, unto the knowledge of which no man can attain, without perfect knowledge and instruction of the principles, grounds, and Elements of Geometry.” Geometry was derived from the Greek word meaning earth measurement which focuses on the study of shapes, sizes, relative configuration, and spatial properties.... [tags: geometry, construction, topography]
1227 words (3.5 pages)
- Analysis of The Abstract Wild by Jack Turner Jack Turner's The Abstract Wild is a complex argument that discusses many issues and ultimately defends the wild in all of its forms. He opens the novel with a narrative story about a time when he explored the Maze in Utah and stumbled across ancient pictographs. Turner tells this story to describe what a truly wild and unmediated experience is. The ideas of the aura, magic, and wildness that places contain is introduced in this story. Turner had a spiritual connection with the pictographs because of the power, beauty, and awe that they created within him upon their first mysterious contact.... [tags: The Abstract Wild Jack Turner Essays]
3431 words (9.8 pages)
- Abstract The topic of year round schooling is quite controversial and greatly misconceived by the public. Most school systems tend to steer clear of the idea due to lack of support and academic success. Year-round schooling is not for everyone. Benefits however, include downsizing of schools, the reduction of building construction, and the ability to effectively meet the demands of the community. Students and teachers are typically placed on a multi-track schedule instead of the general nine month school calendar.... [tags: essays papers]
1685 words (4.8 pages)
Alder, Irving, A New Look at Geometry, John Day Co. (1996)
Bake, H. F., Principles of Geometry, university Press (1922)
Euclid's Fifth Postulate, D.E.Joyce, Clark University