Euclidean and Non-Euclidean Essay Example for Free

Euclidean and Non-Euclidean Essay The foundation of Euclidean geometry is the concept of a few undefined terms: points, lines, and planes. In essence, a point is an exact position or location on a surface. A point has no actual length or width. A line shows infinite distance and direction but absolutely no width. A line has at least two points lying on it. Euclid’s first postulate is that only one unique straight line can be drawn between any two points. Line segments are lines that have a set length and do not go on forever. Euclid’s second postulate is that a finite straight line, or line segment, can be extended continuously into a straight line. The last of Euclid’s undefined terms is a plane, a flat surface similar to a table top or floor. However, a plane’s area is infinite. It has never ending length and width but has no depth. Lines can intersect each other or they can be parallel. Intersecting lines can be perpendicular, meaning they cross at a right angle. Lines in a plane that do not intersect or touch at a point and have a constant, unchanging distance between each other are called parallel lines. Line segments can be used to create different polygons. As in Euclid’s third postulate, with any straight line segment, a circle can be drawn having the segment as radius and one endpoint as center. All the angles in a triangle add up to 180 degrees. An acute angle is less than 90 degrees. A right angle is 90 degrees; all right angles are equal, as stated in Euclid’s fourth postulate. An obtuse angle is greater than 90 degrees but less than 180 degrees. Lastly, 180 degrees makes up a straight line. Two triangles with the same angles are not necessarily congruent. Today we know the fifth postulate as the rule that through any point that is not on a line, there is only one line that is parallel to the line. One kind of Non-Euclidean Geometry is Riemannian, or elliptic, geometry. It is a geometry based on curved/spherical, surfaces invented by a German man named Bernhard Riemann. In 1889 he rediscovered the work of an Italian mathematician which stated certain problems in Euclidean Geometry. The earth is round and spherical so elliptic geometry is useful, and directly related to our everyday lives. Elliptical geometry is not limited to spheres and can be used applied on cylinders (Roberts). Euclid’s first postulate is false in elliptic geometry. Between two points there are many different lines that will connect them. The shortest distance between two points is called a minimal geodesic. Also, because it is based on curved surfaces, straight lines are impossible. This makes Euclid’s second postulate untrue as well. If you extend a line on a sphere or cylinder, most of the time the line will curve back around and form a circle. A line will always curve in elliptic geometry. In elliptic geometry all the angles in a triangle add up to greater than 180 degrees. Two triangles with the same angles are not just similar, they are actually congruent. In Elliptic there are no parallel lines (Elliptic geometry). Another kind of Non-Euclidean Geometry is Lobachevsky, or Hyperbolic, Geometry. It is also called Lobachevsky-Bolyai-Gauss (Weisstein). It is a geometry based on saddle-shaped space, similar to a Pringle. Hyperbolic geometry was invented by a Russian mathematician named Nicholas Lobachevsky. Lobachevsky also expanded on Euclid’s ideas. It’s very hard to see how this geometry is useful but it can be used in gradational fields, space travel, and astronomy (Roberts).

The Awakening - Personality Developments :: essays research papers

PERSONALITY DEVELOPMENT The idea that one can understand and comprehend the development of an individual is profound and abstruse, but very few people have actually had success dealing with such a topic. From obstacles such as proper test subjects to the whole stigma of taboo attached in trying to understand the human mind, researchers and psychologists have had success. One of the most notable successes is that of Sigmund Freud, the father of modern psychology, as we know it. Freud’s in depth pioneering journey into the minds of people, and how the mind itself develops with the passing of time and events. Other modern psychologists have elaborated on Freud, including the psychologists Erik Erikson and Karen Horney. Their thoughts on the personality development of people relate directly to Kate Chopin’s book, The Awakening. In this book, the theories discussed by Freud and his successors are shown explicitly and implicitly. Obviously, Sigmund Freud’s work in the field of personality development was by far the most prolific and controversial. The father of modern psychology, Freud broke all barriers to expose what he thought to be the real reasons for human behavior. His theories of personality development can best start with the discussion of the conscious and the unconscious mind. The conscious mind—along with the lesser preconscious mind—is that part of the mind that one has control, or knowledge of. Ironically, this is the least part of the mind that one has control over. The so called "subconscious" mind is the part of the mind that lurks beneath the surface, filled with instincts, emotions, and unfulfilled desires (Shaffer 26). The total human mind is divided into the famous three parts of the Id, the ego, and the superego. The Id can be correlated directly to the subconscious, since it contains one’s innermost thoughts, feelings, and desires, or as Freud w ould call them, "wishes". The Id represents one’s innermost and primitive desires, such as food and reproduction, and it constantly drives one’s actions. The total antithesis of the Id is the superego. The superego in the case of personality development, comes directly from parents. This superego is consisted of the conscience (punishments and warnings) and the ego ideal (positive rewards and role models). Thus the superego can be defined as what keeps the Id in check, which leads to the ego. The ego is the rationalizing factor, it is the result of the superego and the Id, canceling each other out.

Family Systems and Healthy Development Essay

In today’s world, families are dynamic and interdependent systems. The developmental processes of the children in the family are deeply affected by how the family system operates. However, a family’s structure does not determine whether it is a healthy family system or not. Today, families consist of single parents, stepparents, divorced parents, remarried parents, grandparents, aunts and uncles. They are all able to contribute to a healthy functioning family system by meeting each family member’s needs and encouraging positive communication (Jamiolkowski, 2008). Unhealthy family systems have negative and possibly long-term effects on a child, both physically and emotionally. An unhealthy family system affects brain development and social development. Moreover, parents hold a particularly important part in their child’s spiritual development. When a family system lacks spiritual modeling, the children do not develop a spiritual relationship and lack religi ous meaning in their family life (Roehlkepartain, King, Wagener, Benson, 2006). Healthy Family Systems A healthy family system is a family unit in which each members has their needs met. These needs include safety, security, survival, love and belonging, as well as self-esteem and developmental skills. In a healthy family structure, the family members share a love for one another, respect each other and follow a set of rules that protect and maintain the welfare and development of each family member (Jamiolkowski, 2008). A happy and healthy family system has open communication between family members. Opinions and ideas are encouraged. Since children in a healthy family system are encouraged to communicate their wants and needs, they are confident enough to speak up in family matters. This helps develop a positive and confident self-identity. The children in the family are taught a core group of values to establish right from wrong, as well as personal boundaries. Rules, which must be applied, are enforced fairly and consistently, but are flexible. A healthy family system makes a child feel  cared for, validated and valued. Supportive parenting is a term used to describe parents whose authoritative parenting style is firm, with clear and consistent limits, but with warmth, proactive teaching, interest and involvement in their child’s peer activities, as well as calm discussions while disciplining. Authoritative parents tend to be firm and set clear and consistent limits. Although strict, they are loving and supportive, and communicate to the child the rationale for their punishment, along with an explanation for why they should behave a certain way. This encourages independence in the child (Feldman, 2014). Research has shown that healthy friendships in which close ties emerge are developed when parents provide a warm and supportive home environment (Feldman, 2014). Children emulate positive social interactions and roles, which they learn from the adults in their lives who they model after. Children living in healthy family systems develop a strong and positive relationship with their parents or caregiver and will encourage positive relationships with others. Unhealthy Family Systems The parenting style in the home will result in differences in the children’s behavior. For example, an authoritarian parent is controlling, punitive and strict. Their rules are not flexible and do not tolerate expressions of disagreement. These children tend to be withdrawn with little sociability. Girls are usually especially dependant on the parents, while boys tend to be unusually hostile. On the other hand, permissive parenting provides a relaxed and inconsistent method of discipline. They place little to no limits or control on how their children behave, and require little of their children. These children also tend to be dependent and moody, low in social skills and self-control (Feldman, 2014). It can sometimes be difficult to discern whether a family system is healthy or not. Even healthy family members can become understandably upset by circumstances and don’t always deal with stressful situations well. However, an unhealthy family system is usually created by one or more members. Parents who were raised in unhealthy family systems may carry over the same traits to their own families. Also, other factors that can cause an unhealthy family system is a parent or main caregiver with a serious problem such as mental illness, alcohol abuse or drug addiction. This causes communication in the family to  be strained and distorted. Opinions and ideas are discouraged and usually ignored. Usually children deal with mixed messages and conflicting ideas, making it harder for them to discern between appropriate and inappropriate behavior. They develop poor personal boundaries and have a hard time participating in loving relationships (Jamiolkowski, 2008). Effects of an Unhealthy System Children in unhealthy family systems usually suffer from one or more forms of abuse. This can range from physical abuse to psychological abuse or neglect. At least five children are killed each day by their parent or caregiver, and about 3 million children are abused or neglected each year in the United States (Feldman, 20124). Abuse, at any level causes long-term and permanent effects on the development of a child. Physically abused children are more likely to be resistant to control and do not adapt well to new situations. They suffer from more headaches and stomach aches than the average child. They also experience frequent bed-wetting, suffer from high anxiety and may show developmental delays. Psychological abuse is associated with low self-esteem, lying, underachievement in school, and misbehavior. They can easily become depressed and are at high risk for suicide. Victims of physical and psychological abuse suffer from so many consequences because their brain goes through permanent changes due to the abuse. Childhood abuse can lead to a reduction in the size of the amygdala and hippocampus. Antisocial behaviors are caused by the overstimulation of the limbic system through the feeling of stress, fear or terror (Feldman, 2014). It is likely that the child’s parents will influence their religious and spiritual development. This is done through verbal communication, induction and indoctrination of beliefs with the help of disciplinary tactics as well as rewards (Roehlkepartain, King, Wagener, Benson, 2006). Therefore, parents have the important task of guiding their children through their spiritual development. However, if the parent makes their child’s spiritual experience a negative one, it may make the child rebel. This can occur when the parents show fanaticism towards a certain belief or religion (Jamiolkowski, 2008). Parents should apply spiritual modeling, in which children model their parents’ spiritual behavior. This can include engaging in activities that promote religious and spiritual development and  performing religiously motivated charity for others. These kinds of family routines and traditions help form the religious meaning in family life (Roehlkepartain, King, Wagener, & Benson, 2006). Conclusion Maintaining a healthy family system is key for raising a confident, loving and emotionally balanced child. A healthy family system provides a positive and safe home environment which promotes communication and respect between parents and children. Supportive parents uphold rules in a consistent, yet flexible manner while explaining to the child the reasoning and lesson behind the consequence. In an unhealthy family system, children sometimes endure physical and psychological abuse, as well as neglect. This affects brain development, as well as emotional and social development. Children from unhealthy family systems are usually dependent on the parents, have withdrawn personalities or are aggressive. They are unable to create personal and lasting relationships outside of the home, including those at a spiritual level. If the parents do not show positive religious and spiritual role modeling at home, the child will likely not take an interest in it as well. References Feldman, R. S. (2014). Development across the life span (7th ed.). Upper Saddle River, NJ: Pearson. Jamiolkowski, R.M. (2008). Coping in a Dysfunctional Family. New York: Rosen Pub. Group Roehlkepartain, King, Wagener, & Benson (2006). The handbook of spiritual development in childhood and adolescence. Thousand Oaks: SAGE Publication.

The New Teenage Parent Essay - 1902 Words

The New Teenage Parent I originally wrote this essay as an assignment for Monique DuFours class about how we classify different groups of people. I think that the part of the student population that are parents (especially single parents) are often forgotten by the University as a whole. I say this because there are very few, if any, programs that recognize and cater to the needs of parents/students that may need a little extra help, with time or financially. As I revised this essay, I tried to think of ways that I could speak to a larger audience and raise general awareness on this issue. A young man is at a party. He reaches in his pocket for some money, but he smiles to himself and pulls out a pacifier. Hes a young single†¦show more content†¦The following statistics come from a book about adolescent sexuality written by Maris A. Vinovskis, a University of Michigan social historian. He points out that the concern about teenage pregnancy and parenthood is about a generation too late. The peak for adolescent pregnancy was in 1957, when 97 out of every 1,000 girls between the ages of 15 and 19 had babies, as compared to 52 out of every 1,000 girls in 1983. Recently, the concern has grown because it seems that the ages of girls becoming pregnant are getting lower and lower. The initial study included girls between the ages of 15 and 19. Now, girls are getting pregnant as young as nine years old. Most single parents, according to national statistics, are black, women, and live in poverty for most of their lives. Also, according to a recent article in U.S. News and World Report by Rose McClain, the cycle continues. The children that are born to teenagers usually have children at a young age as well. However, when we look at national statistics, does it take into account the differences in culture and resources between people who live in the suburbs versus people who live in urban areas? There are people that really believe that there is no truth to the urban dilemma that is portrayed through the media and there is no excuse for children to grow up in poverty. Poverty, the lack of education, the crime--it is all very real. For many people who live in the United States,Show MoreRelatedSimilar to quantitative research, the concern of money is also mentioned as a stress factor,1500 Words   |  6 Pageshowever, majority of teenage parents designate stigma as the most influential contributor. The media plays a huge role in linking and presenting stigmatization of teenage parenthood as a social issue. According to Scherer (2009), stigma creates experiences and feelings of despair, guilt, and disgrace due to what is falsified in the media hence, the unwillingness of seeking or accepti ng help needed. 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Whereas some are convinced that it promotes teenage pregnancy through the fame some of the young couples haveRead MoreTeenage Pregnancy And Teen Pregnancy871 Words   |  4 Pagesshows like â€Å"16 and Pregnant† and â€Å"Teen Mom† promote or discourage teenage pregnancy, most of us will readily agree that it in fact does promote teenage pregnancy. Where this agreement usually ends, however, is on the question of how does this promote teenage pregnancy. Whereas some are convinced that it promotes teenage pregnancy through the fame some of the young couples have achieved, others maintain that it in fact discourages teenage pregnancy by showing the struggles and realities of having a childRead MoreTeenage Pregnancy : Society s Biggest Problem1503 Words   |  7 Pages Teenage Pregnancy Teenage Pregnancy is society s biggest problem, there are so many ways to prevent it, also many advices from people and many decisions a teen parent must make in life. It is today s biggest issue because it affects teen parent s future in many results. The three most important things that it affects is education, financial problems, and being a teenage parent. Those three important things are key to each other in order to succeed in life. Teenage Parents are most likelyRead MoreA New Zealand Health Issue : Teen Pregnancies1404 Words   |  6 PagesAnalyse a New Zealand health issue: Teen Pregnancies A health issue is something that affects the well-being of groups or populations in a way that causes (public) concern. In this report I will be discussing why teenage pregnancy is a health issue in New Zealand and how it links to all the determinants of health which are influenced from teen pregnancy and parenthood. I am going to be discussing three determinants of health, these being; cultural, economic and social determinants of health. I