...geometry have on subsequent developments in mathematics? Word Count: 1912 Euclidean geometry is the everyday “flat” or parabolic geometry which uses the axioms from Euclid’s book The Elements. Non-Euclidean geometry includes both hyperbolic and elliptical geometry [W5] and is a construction of shapes using a curved surface rather than an n-dimensional Euclidean space. The main difference between Euclidean and non-Euclidean geometry is the nature of parallel lines. There has been much investigation into the first five of Euclid’s postulates; mainly into proving the formulation of the fifth one, the parallel postulate, is totally independent of the previous four. The parallel postulate states “that, if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.” [W1] Many mathematicians have carried out extensive work into proving the parallel postulate and into the development of non-Euclidean geometry and the first to do so were the mathematicians Saccheri and Lambert. Lambert based most of his developments on previous results and conclusions by Saccheri. Saccheri looked at the three possibilities of the sum of the angles in a triangle. He found the first to be <180°, one being =180° and the final being >180°. He showed that the first, that the angles total <180°, was viable but only through...
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...Alternatives to Euclidean Geometry and Its Applications Negations to Euclid’s fifth postulate, known as the parallel postulate, give rise to the emergence of other types of geometries. Its existence stands in the respective models which their originators have imagined and designed them to be. The development of these geometries and its eventual recognition give humans some mathematical systems as alternative to Euclidean geometry. The controversial Euclid’s fifth postulate is phrased in this manner, to wit: “If a straight line crossing two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if extended indefinitely, meet on that side on which is the angles less than the two right angles.” which has been rephrased, and what is known as the parallel postulate as follows: “Given a line L and an external point P not on L, there exists a unique line m passing through P and parallel to L.” With the sphere as its model, is spherical (also called reimannian or elliptic) geometry being advanced by German mathematician, Bernhard Riemann who proposes the absence of a parallel line with Euclid’s fifth postulate as reference. His proposition is as follows: “ If L is any line and P is any point not on L, then there are no lines through P that are parallel to L” It contradicts Euclid’s fifth postulate mainly because no matter how careful one in constructing a line with a straightedge- as straight as it is- that line...
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...Euclid’s research findings had been earlier stated by Greek Mathematicians, Euclid has received a lot of recognition for developing the very first comprehensive deductive systems. Euclid’s approach to mathematical geometry involved providing all the theorems from a finite number of axioms (postulates). Euclidean Geometry is basically a study of flat surfaces. Geometrical concepts can easily be illustrated by drawings on a chalkboard or a piece of paper. A number of concepts are known in a flat surface. These concepts include, the shortest distance between points, which is known to be one unique straight line, the angle sum of a triangle, which adds up to 180 degrees and the concept of perpendicular to any line.( Johnson, 2013, p.45) In his text, Mr. Euclid detailed his fifth axiom, the famous parallel axiom, in this manner: If a straight line traversing any two straight lines forms interior angles on one side less than two right angles, the two straight lines, if indefinitely extrapolated, will meet on that same side where the angles smaller than the two right angles. In today’s mathematics, the parallel axiom is simply stated as: through a point outside a line, there is only one line parallel to that particular line. Euclid’s geometrical concepts remained unchallenged until around early nineteenth century when other concepts in geometry started to emerge. The new geometrical concepts are majorly referred to as non-Euclidean geometries and are used as the alternatives...
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...one determine our physical space rather than inferring because of past experiences, or in this instance postulates of geometry. Euclidean geometry studies planes and solid figures based on a number of axioms and theories. This is explained using flat spaces, hence the usage of paper, and dry erase boards in classrooms, and other flat planes to illustrate these geometrical standards. Some of Euclid’s concepts are 1. The shortest distances between two points is a straight line. 2. The sum of all angles in a triangle equals one hundred eighty degrees. 3. Perpendicular lines are associated with forming right angles. 4. All right angles are equal 5. Circles can be constructed when the point for the center and a distance of the radius is given. But Euclid is mostly recognized for the parallel postulate. This states that through a point not on a line, there is no more than one line parallel through the line. (Roberts, 2012) These geometries went unchallenged for decades until other forms of geometry was introduced in the early nineteen hundreds, because Euclid’s geometry could not be applied to explain all physical spaces, this gave rise to non- Euclidean geometry. Non Euclidean geometry are in correspondence with axioms when metric geometry or the parallel postulate is replaced, in other words non Euclidean geometry negates Euclid’s parallel postulate. Some popular non Euclidean geometry is hyperbolic or the saddle which states If L is any line and P...
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...What are the different approaches to system installation? Which is the most costly and least expensive? What re the risk with each method? When all tests have been successfully completed the system can be installed in to a working environment. A company can choose from four different methods of implementation; Direct, Parallel Installation, Pilot and Phased. The parallel installation is the most secure method of the four. However, it is the most costly because you are running two systems and there is the possibility the company may want to rely on the old system. In this instance the old and new system is still fully operational. Users are able to use the old system as well as the new system. This is safe because if there are any problems with the new system, the old system is still accessible. The old system will stay in use until the new system has all the data input and functioning without any problems. Later the old system will be expired. The direct installation is and over night or two day conversation from one system to another. The other system is in use on until the new is installed. Then the old system is immediately terminated. This method has to be carefully planned as there is no back up. This plan is risky and the less expensive. The pilot installation allows live testing of the new system in a group environment. This system is installed in a small area and users are able to test it in a live working environment while providing feedback. ...
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...Parallel Structures Exercise 1 2. “genius” and “lunatic” 4. “work fast”, “ask few questions”, and “keep a low profile” Exercise 2 2. As part of his accounting business, Rick has private clients, corporations, and does some pro bono work. 4. A new job is likely to cause a person anxiety, but working extra hours is likely to make a good impression. Exercise 3 2. “Caught in” and “tied in”. King used two parallel verb phrases followed by an abstract idea. The parallelism creates a wise tone in the sentence which keeps them awake, alert, and listening. 4. “Collection of the facts to determine whether injustices exist; negotiation; self-purification; and direct action”. King uses parallel phrases that all relate back to a nonviolent campaign. His use of parallelism appeals to logos, as he provides the audience with a list of action. 6. “extremist for love”, “extremist for justice”, and “extremist for the Christian gospel: "I bear in my body the marks of the Lord Jesus?" Was not Martin Luther an extremist”. King paralleled the phrase “extremist for…” followed by a cause and preceded by a famous example. He then used a quote to prove the point he was making. The parallel structures provides a lot of emphasis, which supports the point King was trying to make. The parallelism attributes to a great deal of logos as well. Exercise 5 2. “Alas, art is long and life is short” Type: Antithesis Effect:Franklin’s use of anaphora conveys to the audience the obvious length...
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...Doppelganger. Parker s 2006 Dystopian novel illustrates the ideas of thirst for power and darkness within humanity as the protagonist Andrew is placed in a dystopian parallel of his own world. These ideas reflect the major concerns of late 20th century Australian society. Parker examines deeper issues and illuminates universal aspects of the human condition. Parker exposes the potential for the darker side of humanity in Doppelganger, reflecting issues of his context. Cleary derived from themes in modern literature, such as Golding's "Lord of Flies" which examines the conflict between two competing impulses in all human beings, the instinct to live by rules, act peacefully and follow moral commands opposed to acting selfishly to gratify ones immediate desires. The darker side of humanity is introduced through Andrew’s character, an ordinary Australian teenager governed by his philosophy "don’t disturb the world and it won’t disturb you”. Andrew finds himself incapable of standing up for what he knows is right and this is exemplified early in the novel when Josh in an act of unprovoked evil, tears apart miss swains photograph. Andrew, convinced he is “hardwired” to be compliant with josh, aids his vindictive nature as it is easier than standing up for what he knows to be right. Andrew discovers his own darkness in the parallel Sydney, under the influence of mind altering drugs when he murders another boy in a response to his primitive urges. Incited by the chanting “Kill boy, kill boy”...
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...to identify more with her inner self rather than conforming to her outer self increases; Edna begins to devote more time towards her paintings and furthermore, moves out from her residency with her husband. However, in the process of accepting her inner self, Edna is no longer able to fit in as a functioning member of society. She as a result becomes frustrated and depressed. Furthermore, not even those who are closest to her (for example, Robert) are able to understand her needs and desires. As a result comes the ending: Edna’s ultimate death in a search for independence (her swim out to the sea). Such ending comes as a shock with no real solution for Edna other than death. However, such ending is conclusive because of its realistic parallels to society that Chopin is trying to highlight. Chopin’s ending of the book serves as a commentary of society’s expectations of women. Chopin’s main message, as highlighted through the ending, is the expectations society places onto women is an ultimatum forcing women to either conform to its norms or to reject its norms, but face rejection as well. Because of the present society, women are unable to balance both lending to women’s continued subordination and lack of expression. The setting of the ending of the novel takes place at the sea. Edna has gone out for a swim to the sea and has swum so far that she loses her strength to return. The sea, throughout the novel, is representative of...
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...Six Thinking Hats Anngellet Jones Dallas Baptist University Creative Problem Solving/Marketing Decisions MRKT 6301 Professor Toni McNutt November 2, 2012 Six Thinking Hats Introduction Six Thinking Hats, is authored by Edward de Bono. Mr. de Bono comes from a well-educated family from Malta. De Bono’s parents were Joseph and Josephine de Bono. Mr. de Bono graduated at the age of 15, and was nicknamed genius. Mr. de Bono has several degrees, including a couple of doctorates. Mr. de Bono is a physician, author, inventor, and a consultant. The phase lateral thinking as a term was introduced by Mr. de Bono. Mr. de Bono is widely known for his development of lateral thinking as a skill. De Bono used his medical experience as his inspiration for understanding the brain as a self-organizing system, which allowed de Bono to create practical tools for thinking (Powell, 2007). Mr. de Bono is an activist for teaching lateral thinking as a subject in schools. Development of Lateral Thinking The development of Mr. de Bono’s theory was a result of his path from medicine during the 1960’s. Mr. de Bono’s path lead to the use of a system for solving health problem but related it to the thinking process, but more specifically creativity thinking. Mr. de Bono’s was researching the glands and kidney system at the time of developing the thinking process as a result of recognizing they were self-organizing glands. Mr. de Bono related his research of the self-organizing systems to the...
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...points) Give an example from real life of busy waiting 4. (2 points) Describe the purpose of a buffer and give an example from your own experience where its use clearly benefits system response. 5. (2 points) Compare and contrast the critical region and working set. 1. The master/slave multiprocessing configuration the slave processors access the main memory directly but the master processor speak to the printer and other I/O , whereas the symmetric configuration use homogeneous processors which all communicate with the main memory and the printer and other I/O devices in a synchronized manner 2. Implicit parallelism is the automatic detection by the compiler of instructions that can be performed in parallel is called. Creating knowing when to implement the algorithm for the complier is the role of the programmer 3. Busy waiting: a method by which processes, waiting for an event to occur, continuously test to see if the condition has changed and remain in unproductive, resource consuming wait loops. Real life example would be cars waiting at a stop light waiting for light to turn green. 4. A buffer is an interim storage area that works as a temporary holding place before being used by the computer. Example while steaming music videos on You tube the system first gathers a certain amount of data in its buffer before allowing the video to be played. 5. Working set is a collection of processers...
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...and bottom of platter * Never expose to magnet * Data loss my result * 137GB Limit * Hard drive size limited to 137GB * Not a physical limit * Limited by addresses system can support * 28-bit communications * Limit to 268,435,555 addresses * Equates to 137GB * Flash Bios to upgrade * Hard Drive Interfaces * PATA, SATA, SCSI, USB, and Fire wire * Most common is PATA inter faces * Sometimes referred to as IDE or EIDE * IDE describes drive standard * Not the connector * Refers to hard drives, CD drive, DVD drives and tape drives * Now used inter changeably with PATA * PATA- Parallel ATA * IDE (PATA) cable has two connections * Master and Slave * Motherboard supports two cables * Primary and secondary * Four devices total * Primary master and primary slave * Secondary master and secondary slave * Motherboard Connectors * Blue=primary channel * Black=secondary channel * Cable connectors * Blue=plugs to motherboard * Black=first device * Gray=second device * Master/Slave designation * Not determined by position on cable * Determined by jumpers on drive * Check documentation or labels * Master, slave, cable select * Best-hard drive installation * Master on primary * Only...
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...on “what can be” versus “what is”. Traditional thinking was defined 2300 years ago by the “Greek Gang of Three” Plato, Socrates and Aristotle. Their thinking was based on an argumentative model which is fine but not complete. Six thinking hats uses constructive, or parallel thinking model using the analogy of six hats to represent each perspective. The six hats are: - The white hat – facts and figures - The red hat - emotions and feelings - The black hat – cautious and careful - The yellow hat – Speculative and positive - The green hat - creative thinking - The blue hat – control of thinking This method is an excellent technique for making sure a problem is analyzed from all directions. It is a process that makes case analysis simple. It succeeds for several reasons: Power: The technique allows members of a group to go in one direction rather than defending a position. The experience and knowledge from all members is directed at the case. Time Saving: following the process and eliminating the argumentative method decisions are made more quickly, less time arguing. Removal of Ego: presenting and defending an idea can be become a defense of your ego versus real problem solving. With parallel thinking the team is collecting and discussing ideas. One thing at a time: In this world where ADD seems to enter the boardroom and ideas are going from one topic to another, this method defines the focus and direction of the thinking process, allowing for real outcomes...
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...commodity hardware, such as personal computers. They also use free open source software such as Linux, to serve as their operating system. Clusters achieve multi-instruction-multi-data multiprocessing by using multiple systems, known as nodes, which are joined together. These nodes are connected via a local area network, which allows them to communicate with one another. These systems are capable of running an application simultaneously on all nodes of the cluster, which in turn, significantly increases performance of the system. However, applications have to be specifically written to utilize all of the computers of the cluster. This is done through parallelization, which is a program that is divided into separate components that run in parallel on individual node of the cluster. Beowulf clusters also yield high availability since each node of the cluster can monitor another over LAN. If one computer fails, another can take over whatever task that computer was performing without much of an interruption. In closing, I have learned how Beowulf clusters can offer supercomputer performance, as well as high-availability to the user at a fraction of the cost of a modern supercomputer. Works Cited Abraham Silberschatz, Peter Baer Galvin, Greg Gagne. Operating Systems Concepts. John Wiley & Sons. Inc., 2010. Meeker, Ralph D. Comparative...
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...havirdhara@gmail.com ABSTRACT: In this age of super-computing, the demand for the extremely high speed processors is surging. This ever-increasing demand forces us to go for the high speed Multi-core processors. Multi-core processors are no longer the future of computing-they are the present day reality. With the rise of multi-core architectures the question of the hour is: how to program massively parallel processors. Nvidia, the pioneer in GPU design, has come up with an advanced user-friendly architecture, “THE CUDA” that enables dramatic increases in computing performance by harnessing the power of the GPU (graphics processing unit). CUDA (an acronym for COMPUTE UNIFED DEVICE ARCHITECTURE) reduces the complexity of the parallel programming to a great extent. The best feature of CUDA is that we can program the GPUs using C, JAVA and other high level programming environments. In this paper, we present the basics of CUDA programming with the need for the evolution of the same. This paper also presents the different applications of CUDA, which tells us why and how CUDA scores over other parallel programming architectures. Introduction: Parallelism is the age old technique used for the efficient data processing. The same technique re-emerging into TLP i.e., Thread Level Parallelism and in combination with some finely developed manufacturing technologies provided the world with huge benefits in the form of multi cores. Generally a GPU (Graphical Processing Unit) consists of multiple...
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...06-1.08 the video summers talked about Hardware device connections, Connections including IO ports and RAM (Random Access Memory). • 1.06 discussed PATA, SATA, SCSI, USB and Firewire and connections to and from the motherboard. • 1.07 discussed Io ports including USB, VGA, DVI Parallel ports, Game ports, and as well as IO for monitors, keyboards and mouse. • 1.08 discussed different types of RAM also known as (Random Access Memory) and their different kind of significant including notches on DRAM, witch includes SIMM, DIMM and RIMM. • PATA- also known as (Parallel Advanced Technology Attachment) is a type of internal computer port that attaches to hard drives and other devices. It has been replaced by the faster port technology known as Serial ATA, or SATA. • SATA- also known as (Serial Advanced Technology Attachment) is an IDE standard for connecting devices like optical drives and hard drives to the motherboard. • Serial Port- Used to connect devices that contained DB9 pin connections usually mouse’s and keyboards. In todays computers Serial Ports have all been upgraded to USB ports. • Parallel Port- Used to connect printers or external devices such as hard disk drives. Parallel Parts are unique with a DB25 pin connection. They call it DSUB or DB25 cause the connection looks like a D • SRAM- also known as (Static random access memory) is a type of semiconductor memory where the word static indicates that, unlike dynamic ram or DRAM, it doesn’t need to be periodically...
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