History of Mathematics Essay Example for Free

History of Mathematics Essay If D is between A and B, then AD + DB = AB (Segment Addition Postulate). And segment AB has exactly one midpoint which is D (Midpoint Postulate). The midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle. Midsegment Theorem states that the segment that joins the midpoints of two sides of a triangle is parallel to the third side and has a length equal to half the length of the third side. In the figure show above (and below), DE will always be equal to half of BC. Given ? ABC with point D the midpoint of AB and point E the midpoint of AC and point F is the midpoint of BC, the following can be concluded: Since the tangent of circle is perpendicular to the radius drawn to the tangency point, both radii of the two orthogonal circles A and B drawn to the point of intersection and the line segment connecting the centres form a right triangle. If and are the equations of the two circles A and B, then by Pythagorean theorem, is the condition of the orthogonality of the circles. A Saccheri quadrilateral is a quadrilateral that has one set of opposite sides called the legs that are congruent, the other set of opposite sides called the bases that are disjointly parallel, and, at one of the bases, both angles are right angles. It is named after Giovanni Gerolamo Saccheri, an Italian Jesuit priest and mathematician, who attempted to prove Euclids Fifth Postulate from the other axioms by the use of a reductio ad absurdum argument by assuming the negation of the Fifth Postulate. In hyperbolic geometry, since the angle sum of a triangle is strictly less than radians, then the angle sum of a quadrilateral in hyperbolic geometry is strictly less than radians. Thus, in any Saccheri quadrilateral, the angles that are not right angles must be acute. Some examples of Saccheri quadrilaterals in various models are shown below. In each example, the Saccheri quadrilateral is labelled as ABCD, and the common perpendicular line to the bases is drawn in blue. For hundreds of years mathematicians tried without success to prove the postulate as a theorem, that is, to deduce it from Euclid’s other four postulates. It was not until the last century or two that four mathematicians, Bolyai, Gauss, Lobachevsky, and Riemann, working independently, discovered that Euclid’s parallel postulate could not be proven from his other postulates. Their discovery paved the way for the development of other kinds of geometry, called non-Euclidean geometries. Non-Euclidean geometries differ from Euclidean geometry only in their rejection of the parallel postulate but this single alteration at the axiomatic foundation of the geometry has profound effects in its logical consequences. The Lobachevsky geometry is therefore consists of these statements: ? There are lines that are parallel which are everywhere equidistant. ? In any triangle the sum of the three angles is two right angles which is 180 degrees. ? Straight lines parallel to the same line are parallel to each other. ? There exist geometric figures similar with same shape but of different size to other geometric figures. ? Given three points, there is a circle that passes through all three. ? If three angles of a quadrilateral are right angles, then the fourth angle is a right angle. ? There is no triangle in which all three angles are as small as we please. ? There exist squares or equilateral quadrilaterals with four right angles.

Ogden Nash: An Amazing Poet Essay -- essays research papers

  Ã‚  Ã‚  Ã‚  Ã‚  Ogden Nash was a poet that used nonsensical and humorous verse to draw people into reading his poems. Then, he would slip in insightful poems that speak a lot about life. His light verse even earned him a place on a postage stamp. His poems contain uneven lines that all rhyme, and he even made up spellings to words to achieve the best effect.   Ã‚  Ã‚  Ã‚  Ã‚  Frederick Ogden Nash was born August 19, 1902, in New York. His family thought that education was very important, and this was the basis for his love of languages and writing. At the age of seven, he got an eye infection, so he had to stay in a darkened room for almost a year. During this time, his mother schooled him, and this helped him develop his incredible memory. By the tender age of 10, he was already writing the humorous poetry that he became famous for.   Ã‚  Ã‚  Ã‚  Ã‚  He went to Harvard briefly, but his family didn’t have much money, so he had to quit and get a job. His first job was as a high school teacher, then as a bond salesman, then as an advertising copy-writer, then as an editor, and finally as a writer for the â€Å"New Yorker.† He published many of his poems in books, but he also made sure to do lecturing, even though he hated it. The lecturing ensured that he would make enough money to support his family. He died May 19, 1971, in Baltimore, Maryland. His tombstone says that he was a master of light verse. Archibald MacLeish contests that, saying that his poetry is so much more than that. Sure, some of his poems are lig...

New paradigms for health care delivery

Changes occurring in Health care delivery and Medicine are the result of social, economical, technological, scientific forces that have evolved in the 21st century. Among the most significant changes are shift in disease patterns, advanced technology, increased consumer expectations and high costs of health care. These factors have redefined medical practices to fit into the changing health delivery system. Many health care professionals have come to the conclusion and belief that they will be compelled to explore new paradigms for health care delivery in the future like electronic medical record keeping, telemedicine, computer-based diagnostics and health monitoring to keep pace with the changing scenario. This is due to the accountability of the medical profession today and changing disease patterns. Doctors are under increasing pressure to keep up to date and to base their decisions more firmly on evidences as opposed to anecdotal information of the past. Patients are much more informed than they were 10 years ago. No doctor can tell a patient what to do without being questioned today. Further, with the advent of concepts like informed consent and advance directives, such scientific changes gain relevance. ELEMENTS OF THE NEW PARADIGM The use of electronic documentation is becoming increasingly prevalent in terms of convenience. The National Academy of Sciences report states that the US health care industry spent between $10 and $15 billion on information technology in 1996. Much of this expenditure is attributed to creating electronic records systems and converting conventionally stored data to electronic formats.   There are many software programs specially developed for electronic record keeping. This includes ‘Doctors partner’, an advanced Electronic Medical Records (EMR) System with Integrated Appointment Scheduling Billing, Prescription Writer, Transcription Module, Document Management and Workflow Management built to meet HIPAA standards. ‘Practice Partner Patient Records’ is an award winning electronic medical records (EMR) system, allowing practices to store and retrieve patient charts electronically. There are innumerable such branded medical record softwares available today. The standards in practice for EMR include ASTM International Continuity of Care Record , ANSI X12 (EDI) CEN , EN13606, HISA, DICOM , HL7 ,ISO   and openEHR . (Ringold et.al.,2000). The American Medical Association and 13 other medical groups representing 500,000 physicians have signaled their intention to go electronic with the AMA formed   Physicians' â€Å"Electronic Health Record Coalition† to recommend affordable, standards-based technology to their constituents. President Bush has also promoted a nationwide computerized medical records system in a recent visit to a children's hospital at Vanderbilt University. Scientific innovations have found a niche in complicated medical procedures as well. A recent study successfully has evaluated a bar code patient identification system, which involves a hand-held computer for sample collection and for compatibility testing administration of blood. (Turner et.al, 2003). A recent research article (Sandler et.al, 2000) reports of a solid phase and micro titer plate hemagglutination method for pretransfusion compatibility tests. This I-TRAC is an automated process of blood matching with improved serological sensitivity and standardized compatibility testing supporting electronic record keeping and linking to a bar code identification system. San Raffale Hospital in Milan, Italy, has recently collaborated with Intel and CISCO systems to use wireless-enabled infrastructures and Radio frequency identification (RFID) technologies. The system uses RFID-radio frequency identification technology to address the sources of   human and systems error in blood transfusion supply chain. This pilot programme has been   implemented at the 1,100 bed San Raffale hospital where more than 15000 blood transfusions are done every year. The CAT (Computer Aided Tomography) is yet another revolution in medicine which combines the X-ray technology with computer signal processing to generate images of tissues of the body obscured by other organs. Magnetic Resonance Imaging (MRI) is a common technique used to scan pathological or physiological status of living tissues. Much is known about the computer aided continuous ECG monitoring with a play back facility for assessing the cardiac status of the patient. Today we are in a wonderful situation where we will be able to develop a drug based on computer analysis skipping a few phases of clinical testing. PERSPECTIVES ON THE PARADIGM SHIFT Thus, scientific innovations are part of the evolutionary process of the medical science. The basic instrument of a physician, the Stethoscope, the Sphygmomanometer used for monitoring the patient blood pressure, the Catheter, Radiotherapy, Chemotherapy, the EEG, ECG, EMG, Echocardiogram, Ultrasonic scan, to name a few were nothing but such scientific innovations integrated into the field of medicine in the nineteenth and twentieth century. Thus, Computer based telemedicine, medical record system, and diagnostic procedures are scientific innovations of the twenty-first century. Hence, it is nothing but a natural and moral obligation of the health care sector to integrate them into the field of medicine. Changes in financial incentives and health care delivery structures are producing new threats to health care quality (A.Brennan, 1991). The retributive measures are cumbersome and expensive. Hence, there is a need for more accountable health delivery system, which will enable application of modern scientific approaches to quality health care system. In this context, quality of the medical care depends on promotion of quality medical care by managed care organizations. REFERENCE Brennan, T, et.al, â€Å"Incidence of adverse events and negligence in hospitalized patients: the results of the Harvard Medical Practice Study†, New England Journal of Medicine 324: 370-76, 1991. Là ¦rum Hallvard, MD, Tom H. Karlsen, MD, and Arild Faxvaag, MD, PhD . â€Å"Effects of Scanning and Eliminating Paper-based Medical Records on Hospital Physicians' Clinical Work Practice†. Journal of the American Medical Informatics Association 10: 588-595.2003. Ringold DJ , JP Santell, and PJ Schneider , â€Å"ASHP national survey of pharmacy practice in acute care settings: dispensing and administration–1999†. American Journal of Health-System Pharmacy 57 (19): 1759-75. 2000. Sauer et.al, â€Å"Errors in transfusion medicine† Lab Med. 32(4): 205-207, 2001. Turner et.al, â€Å"Bar code technology: its role in increasing the safety of blood transfusion†, Transfusion, 43(9): 1200:2003.

Movie Review Astray By Amy Christine Parker - 1488 Words

Novel Evaluation: Astray Selection: I selected the novel Astray by Amy Christine Parker for our novel analysis. I decided to read Astray after reading the series’s first book, Gated. I first read Gated because it is on the 2015-16 SC YABA nominee list, and I wasn’t disappointed. It kept me on the edge of my seat throughout the entire book. When I saw Astray in the library, I really wanted to know what happened to all the characters, and if this sequel was as good as Gated, so I chose it. I would recommend this series to anyone interested in finding a novel with lots of suspense and plot twists to read. Genre: Astray falls under the genre of realistic fiction. It is set in modern times, and all the people have up to day amenities. The†¦show more content†¦Character Relations: There are not many characters in Astray that I relate to. I do not face the conflicts and the same circumstances as the characters in the novel. However, I can relate to Lyla Hamilton and Taylor, the sheriff’s daughter and Cody’s sister. I relate to Lyla because she must make decisions that affect her future, and how occasionally, she must convince herself on what to think or do. I too execute decisions that affect my future; in fact, I do this every second of the day. A second way I relate to Lyla is when I periodically convince myself to at attention in school, or clean my room. Similarly, another character I can identify with is Taylor. Taylor expressed an opinion, and instantly regretted it, and I have done that too. Though I cannot relate to many characters in Astray, I can relate to at l east two: Lyla Hamilton and Taylor. Literary Strengths / Weaknesses: Astray by Amy Christine Collins is the sequel to the book Gated. Lyla Hamilton is a 17 year old girl that joined a gated community that is prepared for the apocalypse. After her sister was kidnaped from her family’s front yard in New York 12 years ago, the leader of the Community, Pioneer, contacted them and they joined the Community. Life was perfectly in place with Pioneer’s visions from the ancient aliens called the Brethren, until Lyla meets an