Aryabhata I and How He Influenced Math Essay Example for Free

Aryabhata I and How He Influenced Math Essay Aryabhata I was born in Kerala, India, but moved to Kusumapura early in life. His contribution to mathematics and science is vast, from approximating Pi better than anyone in his time period to deducing the Earth is round. He had many scientific and mathematic discoveries, which he wrote about in his book, the Aryabhatiya. He declared that the Earth rotates on its own axis and used logic to determine that this is what created night and day. (Jain) Part of Aryabhata’s fame was brought by his debunking myths of both religious and general varieties. Instead of the previously believed â€Å"fact† distributed by the Hindu priests that it was a demon’s head named Rahu swallowing the sun and moon, Aryabhata proved them wrong by driving the theory that eclipses happen because of the shadow given off by the earth and moon in place of the Hindu myth. Another myth he disproved by declaration was the thought that the moon gave off its own light, giving it the glow that dominated the night sky. In 499 A.D., at age 23, he wrote Aryabhatiya, which would be known as his famous astronomical opus. As a result of his paper, the Gupta dynasty ruler, Buddhagupta, gave him the title of Head of the Nalanda University to recognize his intellect (Kumar). Later, it is believed that he wrote another book, called the Aryabhata-siddhanta, but it is now lost (Jain). The book is split into three parts: the Ganita, which translates to Mathematics; the Kala-Kriya, which contains Time Calculations; and the Gola, which is mainly sphere mathemati cs. The Ganita is astonishing because of its lack of proof concerning the 66 rules it provides (â€Å"Aryabhata I†). Aryabhata’s mind is also the basis of algebra, geometry, and trigonometry. He created the equation for finding the circumference of a circle using the radius instead of the diameter, like the Greeks used. For  this equation, C = 2Ï€r2, he had to have a close value for Ï€, which he successfully approximated somehow, and shared his discovery in Aryabhatiya: â€Å"’Add four to one hundred, multiply by eight and then add sixty-two thousand. The result is approximately the circumference of a circle of diameter twenty thousand. By this rule the relation of the circumference to diameter is given.’ In other words, n = 62382/20000 = 3.1416, correct to four rounded-off decimal places† (Jacobs). The advancements on finding the numerical value of Ï€ have dramatically increased since then, having calculated numbers on the upside of 5 trillion. His contributions to the mathematical world are still vast, and his discoveries are the foundation for modern algebr a and through that, most of math overall. Aryabhata I calculated the length of a sidereal rotation and year in his book as well. As for the sidereal rotation, he used the stars to determine that the time per day was 23 hours, 56 minutes, and 4.1 seconds. The present value is 23 hours, 56 minutes, and 4.091 seconds. For the sidereal year, he found it to be 365 days, 6 hours, 12 minutes, and 30 seconds, when the modern calculation is a mere 3 minutes and 20 seconds less than Aryabhata’s value. Aryabhata also impacted Trigonometry by his definitions of sine (jya), cosine (kojya), versine (utkrama-jya), and inverse sine (otkram jya). â€Å"He was the first to specify sine and versine (1-cos x) tables, in 3.75 ° intervals from 0 ° to 90 °, to an accuracy of 4 decimal places† (Kumar). The modern names â€Å"sine† and â€Å"cosine† are also believed to be mistranslations of the words introduced by Aryabhata, Jya and Kojya. In the field of Algebra, he provided results for the summation of series of squares: He did not disappoint the series of cubes: As for remembering the great Aryabhata, he has many colleges named after him, such as the Aryabhata Knowledge University in Bihar and the Aryabhata Research Institute of Observational Sciences (ARIOS) near Nainital, India. India’s first satellite also shared his name. (Kumar) Works Cited Aryabhata I. Medieval History. About.com, 2014. Web. 27 Apr. 2014. . Jacobs, James Q. The Àryabhatà ­ya of Àryabhata. The Àryabhatà ­ya of Àryabhata by J. Q. Jacobs. J.Q. Jacobs, 1997. Web. 15 Mar. 2014. . Jain, Ankur. Aryabhatta Biography. Aryabhatta Scientists | Biography. Study Helpline, 2011. Web. 27 Apr. 2014. . Kumar, Amit. Aryabhatta- The Great Indian Mathematician. The Braves and Smarts. Web. 10 Mar. 2014. . OConnor, J.J., and E.F. Robertson. Aryabhata the Elder. School of Mathematics and Statistics University of St. Andrews, Scotland. Nov. 2000. Web. 10 Mar. 2014. .

A New Road to Transportation Essay -- Hybrid Electric Car, Smart Car

The United States goes through about 19,600,000 barrels of oil a day, and a barrel of oil is around a $100. In a day, just for oil, we spend $1.96 billion dollars worth of oil, and yes that was with a â€Å"b†. Gas is now up to $3.65 per gallon and is rising. I pay $120 for insurance for one month and I use 8 gallons of gas a week average. That means I spend almost $3,000 a year! I’m only sixteen and that is not even adding all the costs. I could add oil, tires, air filters, battery, and windshield wiper fluid. The list could continue on forever. A person who is auto dependent spends 25% of their income on their transportation (Boelte 2). This shows we need to cut our spending on transportation. On the news I saw that people were buying electric cars and cars that get 40mpg. What people need to do is find a transportation that is suitable for them. When a traveler is traveling a far distance, it gets really pricey. I could pay $600 for a round trip flight and be there in an hour or drive 600miles. In a car with 40mpg, that would only be only $146. More people would rather fly though because they will get there and back. What we really need is something cheap, suitable, and fast. Having bullet trains, car pools, and bike lanes will provide cheaper transportation. People seem to be amazed when they see a high performance car roar down a street. Yes, it may seem like the car is amazing, but when the price comes at hand a driver wouldn’t want to pay for it. I paid $800 for my car because it was reposed. It’s a 1996 dodge neon with only 70,000 miles on it, and gets 32.9 mpg highway at 75mph. Not everyone can get a deal like that, but we need to make a way for transportation to be like the deal I got. A hybrid, electric car, and cars that ... ...th a carpool lane at hand these cars would be saving a ridiculous amount of money. By adding just one lane to the highway Americans will cut spending in half by taking someone with them. Another way to cut spending is by creating a system of super trains. The system would run through each capital. The price of this would be hefty but in time it would pay for itself. Super trains are extremely same and never have had any fatal accidents ever. Speaking of safety, biking on the road isn’t very safe. By adding a bike lane to separate a rider from the road will be safe. A person can ride a bike to any place close and still save money. If a rider rides their bike 5miles a day they can save $600 or more on gas. The rider will stay in shape and save money at the same time. There are many ways to save money and help the environment. So stop wasting money and get to saving.

Criminal Law Foundations Essay

The United States Constitution has been amended since its origination. These amendments are meant to help our Nation adjust to the ever changing times. Our Bill of Rights is contended in the first ten amendments. The Bill of Rights is instilled into our constitution to protect the citizens of the United States from unfair and unjust treatment by their own government. Our government is protected and enforced through local police departments and our Bill of Rights gives certain freedoms to the citizens and suspect of the police prior to and during prosecution by the criminal justice system. From arrest to sentencing, the Bill of Rights protects us. This paper will specifically discuss the fourth, fifth, and sixth amendments of the Bill of Rights and how they pertain to both juvenile and adult court proceedings. The Bill of Rights also governs the government by placing limits to the extent of their reach, or power, and how that power is used against its own citizens. The Bill of Rights, or ten amendments, took adoption into our Constitution in 1789 by the efforts of James Madison. Fourth Amendment Our Fourth Amendment guarantees protection from unreasonable or unlawful search and seizure. This particular amendment is a component of the Bill of Rights that gives citizens the right to secure their persons, belongings and homes; each of which are protected under the Fourth Amendment from any unreasonable or unlawful search and seizure. The bill strongly states that this right shall never be violated as well no warrants shall be issued, unless there is a probable cause, which has approval by an oath of affirmation and the description of the place under inspection, the affected person or the possessions to be seized. In both juvenile and adult courts, the constitutional safeguard is applied (Emanuel 2009). Both juvenile and  adults are afforded this right by our Constitution to be free from harassment that is not been approved by the law with stated warrants specifying the desire and description of objects to be seized. If this right is violated in any way it is most likely the v iolator would face criminal charges or consequences due to their actions for denying citizens their Fourth Amendment right. Fifth Amendment Our Fifth Amendment discusses due process, self-incrimination, double jeopardy and eminent domain. Consider this Amendment as a safeguard stating no person shall be under pressure to answer for any crime, unless he or she is under the indictment of a grand jury (Abadinsky, 2008). The only exception to the Fifth Amendment would be the cases involving any military or militia presently servicing or during war times. Our Fifth Amendment also states; No person shall be put in jeopardy of limb or life twice. No one shall be put under pressure to testify against himself. No one shall face depletion of liberty, life or property, unless the same has approval by the law. No private property shall be in for public use, unless the owner gets due compensation. This is the so called Miranda bill. In adult and juvenile courts, persons have the right to stay silent and not to plead guilty of any offence. No one is free to make the suspect reveal anything, unless in front of a jury and within the pro tection of a counsel. The juveniles are immature and may not know their rights. Owing to this law the minors have constitutional protection from any illegal exploitation (Hartley & Rabe, 2008). Sixth Amendment Our sixth amendment discusses the right of trial by jury, the rights of the accused, the right to a speedy trial, the right to an attorney, and the right to a public trial. The Sixth Amendment states that any subject suspected of criminal activity resulting in prosecution will have the absolute right to a speedy trial by public and of a jury of their peers (Abadinsky, 2008). All subjects or suspects shall be informed of the charges against him/her regarding any arrest of criminal activity, witnesses are also available to testify for and against the accused according to the Sixth Amendment and the accused will be given witnesses prior to jury trial,  this right is afforded to citizens under the Sixth Amendment of our Constitution. The suspect will have the right to have his/her own witness as well as a presentation of defense by his/her attorney in order to conflict with prosecutor evidence given against him/her. Our constitution affords the right to be given a fair, speedy and public trial in both juvenile and adult criminal court proceedings. Not only do they have the right to a fair, speedy, and public trial; but they are afforded the right to legal representation for any offense brought to the criminal justice system. This ensures the rights of the accused to place defense upon any mistaken identities or statements of the facts regarding the crime in which they have been charged. The right to a speedy trial gives the accused the ability to precede with his/her normal life without undergoing a long drawn out process of the court system inflicting undue influence on their lives. Delay of justice may bring a lot of frustrations to the accused, thus, the speedy and public trial is a great variant (Wilkerson 1973). Impacts of the Safeguards on day to day Operations in the Court All of the Amendments that have been added to our Constitution have guaranteed a well needed transformation of our criminal justice system. The Amendments allow the citizens of the United States to be informed of their rights. By doing so a better understanding is gained between the relationship of our government and our citizenship accordingly, thus harmonizing the relationship between government and citizenship bringing a sense of understanding and relief for individuals. Having the right to an attorney gives the accused an equal stance in the courtroom to defend against an accusation of criminal activity with a fair and just trial. This ensures that the citizens of the United States involved with criminal activity or accused of criminal activity have proper representation and rebuilds trust that the government cannot abuse their power against them (Champion, 2010). Imagine a juvenile without these rights, they would h ave no way to argue their innocence without legal knowledge, thus falling to the will of the government. The hiring of an attorney can come through private methods or be available through the state with no charge, at any rate, ensuring counsel for defense. The inclusion of the Miranda warnings protects all accused of criminal activity from self-incrimination due to pressure or undue  influence. Law enforcement adjusts their tactics by moderating their power to gather information through unwarranted measures, deceit, and playing subjects against each other is a common method to gain a voluntary confession. With the Miranda warnings, subjects can have the right to remain silent and refrain from stating incriminating statements against themselves (Abadinsky, 2008). They are afforded an attorney who can guide them with legal knowledge the extent of the statements they should make. This protects the accused from unfair and illegal questioning in interrogation from unwarranted authority figures. The right to a fair and speedy trial allows justice to come at a reasonable pace, delivering a sense of comfort to the accused by eliminating long drawn out trials that may play on their ability to remain a sane in normal life experiences. Delaying the justice system is often expensive and comes with stress that plays into the accused everyday lives thus, creating more chaos than is due for the circumstance. Our Constitutional rights ensure fair treatment and the rights of citizens to know their course of action is readily available. The safeguards against unlawful search and seizure ensures citizens their dignity and privacy is not disregarded and their lives are protected affording a sense of stability and comfort against the force of the Nation’s government (Hartley & Rabe, 2008). This changes the view of law enforcement and the communities they serve and opens the door for acceptance of their position and an understanding of the job they are doing through community actions and other theoretical methods of law enforcement. Conclusion Thus the Fourth, Fifth, and Sixth Amendments of the Bill of Rights are in place to secure the rights of the citizens of the United States. Following these Amendments can afford our Nation the right to boast of fairness and justice being served without conflicting with personal rights giving our government an admirable placement regarding the criminal justice process. It is the hope of our Constitution, and the Amendments that every citizen of the United States is educated to their rights and utilizes the Constitution to protect themselves from unfair treatment and prevents the government from exerting their brute force to bully a conviction of an innocent citizen, or placing improper sentencing on a guilty party. All these laws and rights are a product of the people for the people and therefore should work in  favor of the people, with all do influence of the government it is nice to know they are governed as well. References Hartley, R. D., & Rabe, G. A. (2008). Criminal Courts: Structures, Process, and Issues (2nd ed.). : Prentice Hall Inc.. Champion, D. J. (2010). The Juvenile Justice System: Delinquency, Processing, and the Law (6th ed.). : Prentice Hall Inc.. Abadinsky, H. (2008). Law and Justice: An Introduction to the American Legal System (6th ed.). : Prentice Hall Inc..

Public Health Concerns The Health Of A Whole Population

Public health concerns the health of a whole population, and spans a variety of issues that include the processes necessary to â€Å"developing effective interventions† (Childress 170). This means that public health policy will scientifically evaluate the issues that may lead to an unhealthy population, and then act accordingly for the sake of the population’s well-being. The topics that public health addresses can be anything that can make an impact on the health of our population – which we can individually define as a public health issues. Yet, we must not group medicine into public health because our goal is not to find a way to treat individual effects of public health issues, but understand what causes them in the first place. It’s simply a way to prevent large societal health problems by defining and suggesting regulations to either eliminate or lessen the medical problem. An effective system requires communication among members of the community and a strong regulating body to ensure the best chance of health as a society (Childress 171). Furthermore, The Institute of Medicine defines public health as â€Å"what we, as a society, do collectively to assure the conditions in which people can be healthy† (Childress 170). This definition reveals that public health is a society’s own actions to create effective â€Å"conditions† to live healthily. Public health is a community effort and requires a regulatory body of its own to set standards. In our own society, our government andShow MoreRelatedUnderstanding Evidence-Based Public Health Strategies Essay1213 Words   |  5 Pagesexplaining what public health is and describing the key aspects of public health strategies. P1 Public health is all about preventing disease and prolonging life through the use of promotions of services which are provided by the government to ensure the publics health. 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