Indian Mathematics :: India Math Education

Introduction: Indian, in particular, Hindu, mathematics has not been given the credit or recognition that it deserves. Many of the foundational concepts used in all mathematics were first discovered by the Hindu Indians. This paper will discuss many of these concepts and how they were used in the fifth through the eighth centuries. Apart from direct testimony on the point, the literature of the Hindus furnishes unmistakable evidence to prove that the ancient Hindus possessed astonishing power of memory and concentration of thought. The science of mathematics, the most abstract of all sciences, must have an irresistible fascination for the minds of the Hindus. Mathematics is the science to which Indians have contributed the most. Our decimal system, place notation, numbers one through nine, and the ubiquitous 0, are all major Indian contributions to world science. Without them, our modern world of computer sciences, satellites, microchips, and artificial intelligence would all have been impossible. The majority of my writing will focus on a specific area of math called the shulba sutras, which consists of the majority of the discoveries made in geometry. This geometry fascinates me because of their purpose and meaning that is connected with everything they do. Math although seemingly very concrete, right and wrong, can be explained in a spiritual sense as well. The meanings behind all the numerical calculations are the actual significant part according the Vedic literature. The Sulba Sutras The Sulba Sutras, is an important part of the Vedic literature, which consists of a detailed analysis explaining the importance and interrelation between various branches of Vedic texts. Mr. Maharihsi Mahesh Yogi, has completely restored the thousands of years-old scattered Vedic Literature for the total significance of its theory and practice, and has organized it in the form of a complete science of consciousness. The Vedic literature is compiled into forty parts, including the four Vedas plus six sections each with six parts. The four Vedas, the Brahamanas, the Vendangas, the Upa-Vedas, and the Pratishakhya each "express a specific quality of consciousness,"(1) which means that we need to look beyond the surface to find the deeper meanings. There are four main Sulba Sutras, the Baudhayana, the Apastamba, the Manava, and the Katyayna. One of the meanings of the Vedic Sulba Sutras is "string, cord or rope,"(1) which shows that the earliest geometrical and mathematical investigations among the Indians rose from the requirements of their religious rituals. "This could be a reference to the fact that measurements for the geometrical constructions are performed by drawing arcs with different radii and centers using a cord or sulba".

A Quality Leader Essay

Dr. Karoru Ishikawa is one of the world’s idolized leaders in quality control. His famous quote† Through total quality control with the participation of all employees, including the president, any company can create better products (or service) at a lower cost, increase sales, improve profit and make the company into a better organization† ( Dr. Kaoru Ishikawa) . Ishikawa joined the Union of Japanese Scientist and Engineers, a quality research group back in 1949. The Japanese was concerned about their industry sector since it was known that American manufacturing was producing cheap toys and defective cameras. This group took on the responsibility of Japan’s quality-improvement; that was when Ishikawa took the initiative to build on Feigenbaum’s concept of total quality and promoted greater involvement by all employees, from the top management to the front-line staff, by reducing reliance on quality professionals and quality departments. He advocated collecting and analyzing factual data using simple visual tools, statistical techniques, and teamwork as the foundations for implementing total quality. Like others, Ishikawa believed that quality begins with the customer and therefore, understanding customers’ needs is the basis for improvement, and that complaints should be actively sought. (Evans, 2010 pg 110) Background Kaoru Ishikawa was born in 1915 in Tokyo. He graduated from Tokyo University in 1939 with a degree in Applied Chemistry. In his brief tour in the military as a Naval Technical Officer In charge of 600 workers to construct a factory he quoted â€Å"This experience he says was invaluable to Quality Control activities later on. †, (Dr. Kaoru Ishikawa) He worked for Nissan Liquid Fuel Company from 1941-1947 before he was appointed associate Professor of the University of Tokyo. In 1949 He joined the Union of Japanese Scientist and Engineers because he wanted to change the way people thought about work and help management improve the quality of their product. In 1970 Dr. Ishikawa started conducting quality control training seminars. Around 1978 Dr. Ishikawa became the President of Musashi Institute of Technology. Upon Ishikawa’s 1989 death, Dr. Juran delivered this message: â€Å"There is so much to be learned by studying how Dr. Ishikawa managed to accomplish so much during a single lifetime. In my observation, he did so by applying his natural gifts in an exemplary way. He was dedicated to serving society rather than serving himself. His manner was modest, and this elicited the cooperation of others. † (Dr. Joseph M. Juran) Primary work and significant accomplishments Dr. Kaoru Ishikawa accomplishments have include helping thousands of companies, like IBM, Bridgestone, and Komatsu, to turn out higher quality products at considerable lower costs. His book,†What is Total Quality Control? The Japanese Way†, Prentice Hall, Inc. was a best seller in business books. He has been awarded the Deming Prize and the Nihon Keizai Press Prize, the Industrial Standardization Prize for his writings on Quality Control, and the Grant Award in 1971 from the American Society for Quality Control for his education programmer on Quality Control. Process Improvement Japan, 2012). His creation of the fishbone diagram, the user can see all possible root causes of process imperfections. There are many other accomplishments that Dr. Ishikawa has made, which you can find in books and online. These were deserving awards due to his unselfish work ethics and have truly made him a quality genius. Conclusion Through total quality control a company of any type can stay in business, make products at lower cost, and endure great productivity from its workers. Dr Ishikawa wanted to change the way workers and management do business. Quality should start with the customer and it can be done using his writings, fishbone diagram, and other tools like control charts, run charts, histogram, scatter diagram, Pareto charts, and flowcharts. His knowledge was needed in a time when people wanted a product that will last and was supported by the company who makes it. His many accomplishments and strong work ethics influenced many companies to change and many of those companies are still in business today. Dr. Ishikawa is truly a leader in quality control.

Siege of Leningrad in World War II

The Siege of Leningrad took place from September 8, 1941 to January 27, 1944, during World War II. With the beginning of the invasion of the Soviet Union in June 1941, German forces, aided by the Finns, sought to capture the city of Leningrad. Fierce Soviet resistance prevented the city from falling, but the last road connection was severed that September. Though supplies could be brought across Lake Ladoga, Leningrad was effectively under siege. Subsequent German efforts to take the city failed and in early 1943 the Soviets were able to open a land route into Leningrad. Further Soviet operations finally relieved the city on January 27, 1944. The 827-day siege was one of the longest and costliest in history. Fast Facts: Siege of Leningrad Conflict: World War II (1939-1945)Dates: September 8, 1941 to January 27, 1944Commanders:AxisField Marshal Wilhelm Ritter von LeebField Marshal Georg von KÃ ¼chlerMarshal Carl Gustaf Emil Mannerheimapprox. 725,000Soviet UnionMarshal Georgy ZhukovMarshal Kliment VoroshilovMarshal Leonid Govorovapprox. 930,000Casualties:Soviet Union: 1,017,881 killed, captured, or missing as well as 2,418,185 woundedAxis: 579,985 Background In planning for Operation Barbarossa, a key objective for German forces was the capture of Leningrad (St. Petersburg). Strategically situated at the head of the Gulf of Finland, the city possessed immense symbolic and industrial importance. Surging forward on June 22, 1941, Field Marshal Wilhelm Ritter von Leebs Army Group North anticipated a relatively easy campaign to secure Leningrad. In this mission, they were aided by Finnish forces, under Marshal Carl Gustaf Emil Mannerheim, which crossed the border with the goal of recovering territory recently lost in the Winter War. Field Marshal Wilhelm Ritter von Leeb. Â  Bundesarchiv, Bild 183-L08126 / CC-BY-SA 3.0 The Germans Approach Anticipating a German thrust towards Leningrad, Soviet leaders began fortifying the region around the city days after the invasion commenced. Creating the Leningrad Fortified Region, they built lines of defenses, anti-tank ditches, and barricades. Rolling through the Baltic states, 4th Panzer Group, followed by 18th Army, captured Ostrov and Pskov on July 10. Driving on, they soon took Narva and began planning for a thrust against Leningrad. Resuming the advance, Army Group North reached the Neva River on August 30 and severed the last railway into Leningrad (Map). Finnish Operations In support of the German operations, Finnish troops attacked down the Karelian Isthmus toward Leningrad, as well as advanced around the east side of Lake Ladoga. Directed by Mannerheim, they halted at the pre-Winter War border and dug in. To the east, Finnish forces halted at a line along the Svir River between Lakes Ladoga and Onega in East Karelia. Despite German pleas to renew their attacks, the Finns remained in these positions for the next three years and largely played a passive role in the Siege of Leningrad. Cutting Off the City On September 8, the Germans succeeding in cutting land access to Leningrad by capturing Shlisselburg. With the loss of this town, all supplies for Leningrad had to be transported across Lake Ladoga. Seeking to fully isolate the city, von Leeb drove east and captured Tikhvin on November 8. Halted by the Soviets, he was not able to link up with the Finns along the Svir River. A month later, Soviet counterattacks compelled von Leeb to abandon Tikhvin and retreat behind the River Volkhov. Unable to take Leningrad by assault, German forces elected to conduct a siege. The Population Suffers Enduring frequent bombardment, the population of Leningrad soon began to suffer as food and fuel supplies dwindled. With the onset of winter, supplies for the city crossed the frozen surface of Lake Ladoga on the Road of Life but these proved insufficient to prevent widespread starvation. Through the winter of 1941-1942, hundreds died daily and some in Leningrad resorted to cannibalism. In an effort to alleviate the situation, attempts were made to evacuate civilians. While this did help, the trip across the lake proved extremely hazardous and saw many lose their lives en route. Trying to Relieve the City In January 1942, von Leeb departed as commander of Army Group North and was replaced by Field Marshal Georg von KÃ ¼chler. Shortly after taking command, he defeated an offensive by the Soviet 2nd Shock Army near Lyuban. Beginning in April 1942, von KÃ ¼chler was opposed by Marshal Leonid Govorov who oversaw the Leningrad Front. Seeking to end the stalemate, he began planning Operation Nordlicht, utilizing troops recently made available after the capture of Sevastopol. Unaware of the German build-up, Govorov and Volkhov Front commander Marshal Kirill Meretskov commenced the Sinyavino Offensive in August 1942. Marshal Leonid Govorov. Public Domain Though the Soviets initially made gains, they were halted as von KÃ ¼chler shifted troops intended for Nordlicht into the fight. Counterattacking in late September, the Germans succeeded in cutting off and destroying parts of the 8th Army and 2nd Shock Army. The fighting also saw the debut of the new Tiger tank. As the city continued to suffer, the two Soviet commanders planned Operation Iskra. Launched on January 12, 1943, it continued through the end of the month and saw the 67th Army and 2nd Shock Army open a narrow land corridor to Leningrad along the south shore of Lake Ladoga. Relief at Last Though a tenuous connection, a railroad was quickly built through the area to aid in supplying the city. Through the remainder of 1943, the Soviets conducted minor operations in an effort to improve access to the city. In an effort to end the siege and fully relieve the city, the Leningrad-Novgorod Strategic Offensive was launched on January 14, 1944. Operating in conjunction with the First and Second Baltic Fronts, the Leningrad and Volkhov Fronts overwhelmed the Germans and drove them back. Advancing, the Soviets recaptured the Moscow-Leningrad Railroad on January 26. On January 27, Soviet leader Joseph Stalin declared an official end to the siege. The citys safety was fully secured that summer, when an offensive began against the Finns. Dubbed the Vyborg–Petrozavodsk Offensive, the attack pushed the Finns back towards the border before stalling. Aftermath Lasting 827 days, the Siege of Leningrad was one of the longest in history. It also proved one of the costliest, with Soviet forces incurring around 1,017,881 killed, captured, or missing as well as 2,418,185 wounded. Civilian deaths are estimated at between 670,000 and 1.5 million. Ravaged by the siege, Leningrad had a pre-war population in excess of 3 million. By January 1944, only around 700,000 remained in the city. For its heroism during World War II, Stalin designed Leningrad a Hero City on May 1, 1945. This was reaffirmed in 1965 and the city was given the Order of Lenin.

Renaissance A New Way Of Gathering Ideas - 1169 Words

Renaissance means a rebirth and a new way of gathering ideas, which changed the life of many individuals. In European civilization, Renaissance was the period following the medieval period. Renaissance was basically a rebuilding phase after a long period of cultural degeneration and stagnation. People had lost their faith in church and were more focused on each other. In the15 centaury many great things were happening throughout England and other part of Europe. It was beginning of an era where people discovered new ways of learning and thinking by looking back at the ancient Greek and Rome for their inspiration. It was the era of artists, scientist, philosopher, and painter. The Renaissance also perceived the discovery and exploration†¦show more content†¦In the Renaissance era, there was an increase in new educated middle class, who demanded books in their language instead of Latin. In Renaissance books are affordable by middle class. As a humanist in Western Europe I un derstood this as an opportunity to spread the awareness. As a scholar in 15ht century, I would have not known or even think about the problems at the time. Knowing the information now I would like to use a printing press as a newspaper to create awareness about some of the problems people in the Renaissance were dealing with. Throughout this paper I will be discussing three major topics that were important in Western Europe at the beginning of the Renaissance to increase awareness. First gender, which was a method regarding the domination of women. Second social and economic difference between poor and wealthy. Finally spice trade, which made a big impact in the Renaissance. In the 15th century the Renaissance has changed a lot in Western Europe and part of England. Women had lost more power from their economic freedom due more men were getting educated and they were going out to work to make more money. Slowly women stared becoming housewives who stayed home and did unpaid work. W omen were mostly uneducated because a lot of people thought that it was unnecessary, rather they were taught how to do housework so once they get married they could be housewives. In 15th centaury Europe women’s pride and self worth depended

The Blue Eyed Boy With Autism Essay - 1201 Words

How often have you heard the question â€Å"What Color is Monday?† I would personally have to say, I have never. It’s a unique question that is told by someone who views life through a different pair of lens. More importantly, it is someone who sees the days of the week as colors, extremely gifted in remembering everyone’s birthdays, and memorizing the name and details of every car he sees throughout his daily life. The question â€Å"What Color is Monday?† comes from a young boy with autism named Jack Cariello. Author and mother, Carrie Cariello, allows the reader to understand why â€Å"the blue-eyed boy† with autism is similar to a snowflake; no two are exactly alike, unique and beautiful in their own ways. With the help of jack’s mother and father, brothers and sister, the reader can envision how far Jack has come and the impact it has had on his family. Thereby allowing them to learn more about his diagnosis of Autism Spectrum Disorder ( ASD) and Pervasive Development Disorder (PDD), helping them find ways to tackle Jack’s challenges, his areas of disability, while telling us his unique gifts and strengths that he has developed along his journey. Everyone has their own quirks, just like Jack. However, it makes me wonder if each and every one of us has a form of Autism, some more than others. According to the DSM-5 criteria, children diagnosed with Autism Spectrum Disorder has some range of conditions classified as neurodevelopmental disorders, whether it is Asperger syndrome,Show MoreRelatedThe Best Decision Ive Ever Made1030 Words   |  5 Pageslife. To understand why this changed his life for the better you need to know what he has been through. Gannon is a nine year old beautiful blond hair blue eyed little boy whose eyes sparkle when he smiles. He has this knack for making people fall in love with him in an instant. For the first two years of his life he was a healthy little boy, but there was something not quite right with him. He wasn’t developing normally for his age. Then in June of 2006 it all became clear why. This was a normalRead MoreGump Notes Essay7299 Words   |  30 PagesForrest struggles through childhood in small-minded Greenbow, Alabama. Due to his mental disabilities, Forrest becomes the victim of academic discrimination, which his mother fights desperately to resolve. He might be a bit on the slow side, but my boy Forrest is going to get the same opportunities as everyone else, she stated to the principal of Greenbow County Central School. Hes not going to some special school to learn to how to re-tread tires. (Gump 1995) Forrests mother was determined.Read MoreStephen P. Robbins Timothy A. Judge (2011) Organizational Behaviour 15th Edition New Jersey: Prentice Hall393164 Words   |  1573 PagesMotivate Everyday People to Deliver Extraordinary Results (Capstone, 2011) Winnie-the-Pooh on Management: In Which a Very Important Bear and His Friends Are Introduced to a Very Important Subject (Penguin, 2011) Chicken Lips, Wheeler-Dealer, and the Beady-Eyed M.B.A.: An Entrepreneurs Wild Adventures on the New Silk Road (Wiley, 2011) Bodybuilders in Tutus: and 35 Other Obscure BusinessBoosting Observations (Robinwood Press, 2011) I’ll Make You an Offer You Can’t Refuse: Insider Business Tips from a Former

Berghuis V. Thompkins free essay sample

Thompkins was charged with multiple charges. He moved to suppress his statements made during the interrogation. He was found guilty on all charges by a jury of his peers and sentenced to life in prison without parole. His appellate counsel filed a motion for a new trial which was rejected by the trial court. He appealed the ruling to the Michigan Court of Appeals and the trial courts original refusal to suppress his pre-trial statements made during interrogation claiming his Miranda rights were violated. His claims were rejected ruling that he failed to invoke his right to remain silent therefore he waived it. He then filed a petition for a writ of habeas corpus in United States District Court for the Eastern District of Michigan; they also rejected his claim and upheld the previous court rulings. However, the United States Court of Appeals for the Sixth Circuit reversed the previous rulings for Thompkins regarding the Miranda claim. We will write a custom essay sample on Berghuis V. Thompkins or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page The court believed that the state court did not reasonably apply clearly established federal laws, basing its decision on an unreasonable determination of the facts. Legal Issue Are officers required to obtain an express Miranda waiver before questioning suspects? Or are implied waivers sufficient? Facts of Case Thompkins was arrested for murder after he shot a man outside a mall in Michigan. Before being questioned in a police interview room, he was given a written copy of the Miranda warnings and an officer who determined that he could read English, gave him time to read them. Thompkins was also provided with a supplemental warning that stated he had the right to decide at any time before or during questioning to use his right to remain silent or his right to speak with an attorney during questioning. That being said, the officer did not ask him if he wanted to waive those rights. During the interview, Thompkins did not admit anything and gave limited verbal and non verbal responses. About three hours in, he was asked, â€Å"Do you pray to God to forgive you for shooting that boy down? He answered, â€Å"yes†. This admission was used against him at trial where he was convicted and sentenced. Statement of Rule There are two types of waivers: express and implied. An express waiver occurs when the suspect is advised of his or her Miranda rights and thereafter responds affirmatively. An implied waiver occurs when the suspect responds to questioning after having been advised of his or her rights and by word or conduct, indicated that he or she understood his rights. Policy The circumstances under which a waiver will be implied are as follows: * Mirandized: The suspect must be correctly informed of their Miranda rights. * Rights understood: There must be reason to believe the suspect understands their rights. * No invocation: The suspect does not thereafter invoke their rights. * No coercion: The suspect’s subsequent statement was not coerced. Reasoning There was no invocation of silence as Thompkins did not invoke his right to remain silent by not saying anything for nearly three hours. There was no waiver of right to silence as the prosecution showed that Miranda warnings were given and understood and the suspect’s uncoerced statement established an implied waiver of the right to remain silent. There was no express waiver needed as the Miranda only requires that a suspect be given his warnings, understand them, and then have an opportunity to invoke them. Holding A suspect who receives and understands his or her Miranda warnings, and fails to invoke his or her Miranda rights, waives the right to remain silent when offering an uncocerced statement to the police. Therefore, an implied Miranda will suffice.

Justice is Blind free essay sample

This paper discusses the debate on Justice between three philosophers Plato, Socrates and Polemarchus. This paper discusses Platos works The Republic, a discussion before three very famous thinkers. It carefully analyzes how the apparent weaknesses of each presented theory concerning Justice are exploited. It details the views of these philosophers Thrasymachus, Socrates, Plato and Polemarchus and compares and contrasts between them. Perhaps one of Platos most influential political works, The Republic, opens on a series of dialogues between Socrates and three of his more outspoken companions. These three interlocutors present very different opinions of the definition and value of justice, and each makes valid points. Socrates, in return, questions every presupposition, twisting analogies and definitions until his opponents end up disagreeing with their own theories. In most cases, a careful analysis can show how the apparent weaknesses of each presented theory are exploited, and how they could be shored up against the prodding of Socrates and made stronger. We will write a custom essay sample on Justice is Blind or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page