The Pythagorean Theorem Essay Example for Free

The Pythagorean Theorem Essay In the world of mathematics, the Pythagorean Theorem is one of the most popular theorems and is widely applied in many problems and applications because of its basic and simple concept. It is a relation in Euclidean geometry relating the three sides of a right triangle. The theorem is named after the Greek mathematician and philosopher, Pythagoras, who lived in the 6th century B.  C.   It is one of the earliest theorems known since the ancient civilizations. The Pythagorean Theorem states that: â€Å"In any right angle triangle, the area of the square   of   the side opposite the right angle i. e. whose side is the hypotenuse   is equal to the sum of the areas of the squares of the two sides that meet at a right angle i.e. whose sides are the two legs.† In other words, â€Å"The square on the hypotenuse is equal to the sum of the squares on the other two sides.† Consider a right triangle ∆ABC with right angle at A. BAC = 90 degrees Then, the square drawn on BC opposite the right angle is equal to the two squares together on BA and AC. Thus,   the sides of a right triangle are related by the squares drawn on them. The Pythagorean Theorem is a statement about triangles containing a right angle. It states that: The area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides.          Illustratation by numbers Let the sides of the right angle triangle be 3, 4, and 5.    Then the square drawn on the side opposite the right angle is 25, which is equal to the squares on the sides that make the right angle:   9 + 16. The side opposite the right angle is called the hypotenuse.   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   Thus the theorem can be expressed as the equation: 32 + 42  Ã‚   = 52. This proves the earlier statement which is â€Å"The square on the hypotenuse is equal to the sum of the squares on the other two sides.†    Proofs    This is a theorem that may have more known proofs than any other. Consider a right triangle with sides a, b, and c as hypotenuse.                         Let a, b, and c arrange four of those triangles to form a square whose side is a  +  b as shown above in Fig.  1. Now, the area of that square is equal to the sum of the four triangles, plus the interior square whose side is c. Two of those triangles taken together, however, are equal to a rectangle whose sides are a, b.   The area of such a rectangle is a times b:   ab.   Therefore the four triangles together are equal to two such rectangles.   Their area is 2ab. As for the square whose side is c, its area is simply c ².   Therefore, the area of the entire square is c ² + 2ab   .   .   .   .   .   .  (1) At the same time, an equal square with side a + b (Fig. 2) is made up of a square whose side is a, a square whose side is b, and two rectangles whose sides are a, b.   Therefore the area of that square is a ² + b ² + 2ab But this is equal to the square formed by the triangles, line  (1): a ² + b ² + 2ab = c ² + 2ab. Therefore, on subtracting the two rectangles 2ab from each square, we are left with a ² + b ² = c ². This is the Pythagorean Theorem Works Cited Bell, John L. The Art of the Intelligible: An Elementary Survey of Mathematics in its Conceptual Development. USA: Kluwer, 1999. Dunham, W. Euclids Proof of the Pythagorean Theorem. Journey through Genius: The Great Theorems of Mathematics. New York: Wiley, 1990. Maor, Eli. The Pythagorean Theorem: A 4,000-Year History. Princeton. New Jersey: Princeton University Press, 2007. Morris, Stephanie J. â€Å"The Pythagorean Theorem.† 2008. The University of Georgia Department of Mathematics Education.   1 May 2008 http://jwilson.coe.uga.edu/emt669/Student.Folders/Morris.Stephanie/EMT.669/Essay.1/Pythagorean.html. Spector, Lawrence. â€Å"The Pythagorean Thoerem.† The Math Page. 2008. 30 April 2008 http:// www.themathpage.com/aTrig/pythagorean-theorem.htm. Weisstein, Eric W. â€Å"Pythagorean Theorem.† MathWorld. 1 May 2008. Wolfram Web Resource. 3 May 2008 http://mathworld.wolfram.com/Pythagorean Theorem.html.

Illegal Street Racing Essay -- essays research papers fc

One of the fastest growing sports in the world is racing. Racing in general can consist of many different types such as: Drag Racing, NASCAR, Indy, Motor Cross, Truck Rally. The topic of racing that I am chose was street racing. Street racing originated from drag racing on the quarter-mile strip. The concept of drag racing is when two racers in different cars would line up at a white line, and in the middle of the two cars would be a light post, called the Christmas tree for its red, yellow and green bulbs. The tree does what a stoplight does, except backwards, it starts from red, then to yellow, then to green. On the quarter-mile strip, when the light hits green, the two racers are supposed to try to go as fast as they can before the end of the quarter-mile, which would then set off a electronic board showing their electronic times (E.T.) and their speeds. As the sport of street racing began to boom around the early ‘90s, people couldn’t really afford to go to a legal track and race their cars, because of the price that it cost and the rules that they had. So there was a street track that was created on Terminal Island, called the Brotherhood Raceway. The Brotherhood Raceway or Brotherhood for short was basically a quarter-mile drag strip that was put down on a closed off street, where street racers could go and find out their quarter-mile times and speeds for the price of nothing. This was a quarter-mile drag strip to keep racers off of normal streets and highways. Around time of the mid-90s, the Brotherhood was then closed down, forcing street racers to take their racing to another legalized track, or to the streets and highways. People say that street racing is bad, illegal and dangerous to everyone. There is another side which thinks that street racing is ok, and safe. All street racers know that street racing is illegal and can be dangerous, but in their minds they will think they won’t hurt people around them but accidents do happen. When it comes to racing on streets, racers an open or deserted street and line two cars up, and basically race off of the line and see who stays ahead of the other person, this set-up is basically like racing on a drag strip, just without lights and tech and safety people around. There is a person that acts like the lighting tree, who stands in the middle, and is called the â€Å"flagger.† This person puts his/her arms up, ... ...he track. That is why my opinion stands that they should re-open the Brotherhood Raceway, so racers can go and be safe while doing what they do. Street racing is a dangerous sport, but it’s a life and love that people have and are not willing to give up. I believe that as long as racers do what they can to keep street racing, that it should be legal. It all racers do their part in trying to keep it safe and not dangerous, then I think the government or city or whoever, should give street racers respect and allow them a place to have fun and do what they do best. Works Cited Atwood, Kathy. â€Å"Red Flag For The Racing Crowd.† Hearld Net. 2 January 2002. 13   Ã‚  Ã‚  Ã‚  Ã‚  April 2002 . Brown, John, Adam Jensen, Pat Silla, David Wong. â€Å"Streetracing: On The Inside.† 14 April   Ã‚  Ã‚  Ã‚  Ã‚  2002   Ã‚  Ã‚  Ã‚  Ã‚  . Fontana, Aaron M. â€Å"The Fast and the Furious.† Entertainment Today. 10 April   Ã‚  Ã‚  Ã‚  Ã‚  2002 .

Allowing Gays To Adopt

In most cases, the legality of adoption is based very strongly upon the principle of consent. Consent refers to the agreement by the child’s parents or the child’s guardian (the person or the agency under whose custody the child is) to accede the child for adoption and to expel the rights and duties with regard to the child. The process of consenting requires that the birth parents of the child notify a judge or court officials in writing.Alternatively, a part from the biological parents, other people issuing their consent can be the agency in charge of the child, the guardians, the court of law, or a close relative or the next friend who has already attained the legal age. In some states such as the Virgin Islands and the District of Columbia for instance, the child should issue consent when or when above 14. Sometimes this may be abnegated if the child is mentally ill. The execution of the consent normally takes 13 days while cases with the fastest ratification speed may take 12-24 hours.Heretofore, the next stage may differ since rules are state-specific. In most states, the written consent is notarized to the concerned public, while in other states; the consenting parents are taken for counseling as touching the matter. A provision for the revocation of the consent is normally very limited but in most cases, the adoption process is irrevocable. States in which there are absolutely no provision for the revocation include; Mississippi, Samoa and the Nebraska.The limited provision come in when the parents or guardians were defrauded, coerced or were under duress when issuing their consent. Some states also issue a time frame within which any case of disgruntlement can be aired by the parents. Conversely if the application to revoke the consent has been found to be in the interest of the child or if both the biological parents and the adoptive parents have reached this consensus, it will be the duty of the court of law to consider the petition.The 14th amendment of the American constitution, a post civil war judicial reconstruction, was originally intended to bolster the 13th amendment which in turn had brought slavery to a grinding halt. This amendment was to promote the rights of the former slaves. When it was proposed in the June 13, 1866, it spelt out equal protection of all by the law, birthing the â€Å"Separate but equal† doctrine. This amendment placed all persons on the same pedestal since all became under one law. It is upon this concept of equality that the marginalized groups began to come out for equal recognition.Privacy rights such as abortion, homosexuality became subject to debates. Currently perhaps the most heated form of debate is the one touching on the prospects of gay adoption (Ricketts, 1991). The laws for the best interest of the child assume that for any normal child to develop well, this should happen under the jurisdiction of the two parents. It is on this backdrop that in the best interest of the child, the law has come up with regulations which are geared towards the child’s protection for instance, in case of a divorce.By default, the law stipulates that upon divorce, both parents should have equal access and responsibility to and over the child. This can only be negated upon a parent being found to be harmful to the child. As far as the issue of the best interest of the child in relation to gay parenting is concerned, the law is not yet unified and therefore varies from one state to another. For instance gay parenting is prohibited in Florida but reconstructions are underway to recognize it in Alabama, Georgia, Ohio and Tennessee.The pro-gay parenting legal practitioners argue that it is better for a child to have a two parent family than a one parent one, and that it will be furthering the interest of the child since a two parent family can easily fend for the child’s needs than if the child had one or no parent at all. A case these lawyers have bro ught to the fore is the fact that there are presently (Clifford, Hertz, Doskow, Curry 2007)119,000 needy children in the US alone waiting to be adopted. Furthermore, they posit that children have more serious concerns than their parent’s sexual orientation.Discrimination against children raised by gay parents is not so far fetched compared to the discrimination encountered by gay parents. In America, this is not much of a problem compared to Australia where the parents are discriminated against in areas touching on taxation, social security, and workers’ compensation. The only case of discrimination against children with gay parents witnessed in Australia is limited to the peer groups and is always manifested in schools and in the neighborhood.This is because the Article 2 of the Convention of the Rights of the Child which was ratified in the 1990 sternly warns against child discrimination of any kind (Ricketts, 1991). Although some maintain that there is no strong bas is for the prohibition of the adoption by gay parenting, yet children rights and welfare agencies cite the child bearing studies on the other hand to maintain that children raised in heterosexual marriages thrive best emotionally, physically and mentally.They maintain that spates of violence are 2-3 times higher in homosexual marriages when compared to the heterosexual ones. In addition to this, they posit that homosexual marriages are always susceptible to dissolution with the normal gay marriage lasting 2-3 years and that homosexual activities are often marked with substance dependence, mental illnesses, suicidal tendencies and a shortened lifespan in comparison to heterosexual marriages.The proponents of same sex marriage and the adoption by the same sex parents have countered that these dysfunctions accrued by this group are as a result of the US socio-economic pressure, to which the opponents of adoption by the gay parents rebutted that the same pressure rests on the normative/ conservative form of marriage without yielding such results (Lerner and Nagai 2001). They further deliberate that children adopted or reared under the same sex marriage are highly vulnerable to sexual confusion, homo sexual behavior and premature sex.Nevertheless, it must be kept in mind that numerous strides have been made to entrench gay adoption and this has also produced gradual acceptance of the practice. A testimony to this is Florida which since 1977 had proscribed gay adoption but as per now efforts are in the offing to abrogate this law due to the push by the American Civil Liberties Union (ACLU) on the Supreme Court. In the same vein, the 1997 ACLU fact sheet, â€Å"the gay parenting statistics† to confirm this discloses that approximately, 6-14 million children are living under gay parenting.This could still be an understatement since most gays and lesbians are always reserved about disclosing the structure of their families due to fear of losing children (Mc Gurry , 2003). These changing prospects can be attributed to the fact that the emphasis on traditional form of marriage is gradually waning, and the subsequent overturning of state laws to assimilate gay marriages is in force. A case in point is when the then president Bill Clinton, signed the Defense On Marriage Act (DOMA), thus giving way to same sex marriage in Hawaii (Rimmerman, Wald, Wilcox, 2000).Gay adoption is also growing because of the fast rate with which gay parenting is spreading. Gay parenting, apart from the normal procedure of adoption occurs when one partner pulls out of a heterosexual marriage while still maintaining the custody of a child and moves into a gay marriage or, through lesbians opting for an artificial insemination upon siring a child enters into an agreement with gay partners for adoption. The co-parent adoption occurs when one gay who has an adopted child with him moves in with a partner who automatically assumes the role of a co- parent.This practice is co mmon in Washington, District of Columbia, Vermont, California, Minnesota, Alaska, and Oregon (Tonnerson, Andenaes and Wintemute, 2001). As touching on the stability of the children, the children grow up healthy and well adjusted compared to those who have one or no parent at all. This scores highly with the concept of the best interest of a child since the child’s financial and material needs are met. Conversely, the children under gay adoption turn out successfully just as the ones under heterosexual care.The American Psychological Association (AMA), out of its research maintained categorically that there was no evidence that children brought under gay adoption and parenting were susceptible to maladjustment or that they turned out less intelligent or suffered low self esteem; neither was there a connection between homosexuality and pedophilia or direct influence in the child’s sexual orientation in future. On the contrary, the AMA observed that 90% of child sexual ab uses were carried out by heterosexual men (Baker, 2005).To further dispel the misgivings on gay adoption, both the parents who want to adapt a child undergo a screening procedure which is a meticulous exercise meant to filter out those who have less prospects of making good parents. The fact that many potential gay parents navigate successfully these enchanted waters is a testimony of the type of parents they would make. Bibliography. Baker P. Public Discourses of Gay men. Rutledge: United States, 2005. Clifford D. Hertz F. Doskow E. Curry H. A Legal Guide for Lesbian and Gay Couples. Nolo: United States, 2007. Lerner R. Negai A.No Basis: What studies don’t tell us about parenting. Marriage Law Projects /Ethics and Public Policy Center: United States, 2001. Mc Garry J. K. Fatherhood for Gay Men: Emotional and Practical Guide to becoming a gay dad. Haworth Press: United States, 2003. Ricketts W. Lesbians and Gay men as foster parents. Wendel/ Ricketts: United States, 1991. Rim merman A. C. Wald D. K. Wilcox C. The Politics of Gay Rights University of Chicago: United States, 2000. Tonnerson M. Andenaes R. Wintemute M. Legal Recognition of Same Sex Partnership: A Study of National and European Law. Hart Publishing

Woolworths Research Project - Free Essay Example

Sample details Pages: 1 Words: 0 Downloads: 3 Date added: 2017/06/26 Category Public Relations Essay Type Analytical essay Did you like this example? Don’t waste time! Our writers will create an original "Woolworths Research Project" essay for you Create order