Archaeology Research paper, on the evolution, origin of bipedality, Essay

Archaeology Research paper, on the evolution, origin of bipedality, and the different perspectives on it - Essay Example The evolution into bipedality because of climate change and the alterations which have occurred in various regions of the world all provide support which shows that environmental stimulation has also regulated the evolution of men. Environmental Stimuli in Hominids There are several theories which show that the environmental stimulation in an environment also affects the way in which ontogeny, organismal adaptation and spectation occur throughout time. Most of the adaptation which has been noted with evolution is from the ideal that there is a response to the needs of a specific species as well as the requirements to survive within a given region. While the adaptation is noted as a component of evolution, many have disregarded the environmental stimuli and the way in which this has altered the functions and evolutionary changes. The concept of neo-Darwinism is one of the main approaches to this. According to Darwin, all species would respond with evolution by competition within the s pecies and with the need to survive. In the neo-Darwinism thought process, there is a link to the understanding that the physical alterations in a species occur specifically because there is the need to adapt to various elements in the surroundings, such as the environment (Vrba, 1442). While there are several links to physical alterations and dimensions related to why evolution occurs, adaptation to the environment is one of the considerations which has evidence in relation to evolution. This is also known as allopatic speciation, which fragments and segments species into various populations. When looking at these populations, it can be seen that the original homo sapiens were fragmented into one sector of the world. The environmental tables within these regions then included adaptation to components such as food intake, temperature, vegetation cover, light intensity and the climatic and tectonic changes. When a species adapted from one region, also known as the stenobiomic region to a eurybiomic, or across biome region, changes would have to be made in regards to the various elements of the environment. Adaptation to the environment, such as different types of water, responses from the skin because of the light and changing behaviors from the climate then become a part of the natural adaptation process, specifically from the environmental stimulus which has occurred (Vrda, 1446). Evolution Into Bipedality While environmental stimuli shows a direct relationship to the anatomical features of hominids and the potential adaptations which are a part of the evolution. According to the adaptability hypothesis, the evolution of individuals is based on the need to endure environmental fluctuations, specifically as different species began to move into different regions of the world. This is combined with the theory of the turnover hypothesis, which states that the adaptability to different environments occurred over a longer period of time and evolved specifically as the environment began to change. The evidence of this occurs in the African Pliocene which shows fossils as evidence of older species of hominids that are now extinct. The body shape, looks of the species and the physical applications draw evidence to the climate alterations and the functions of the society, such as stone making, which no longer fit into the environment. The timing that leads to the specific evidence of the species relates directly to features that show

Journalling Personal Experiences Essay Example | Topics and Well Written Essays - 1750 words

Journalling Personal Experiences - Essay Example Yet, it’s is more fun for me to personally see the facial expression and body language of the person I am talking to. And hence suddenly not being able to see who I am talking to particularly when I am chatting with a group that I am not acquainted with can be quite perplexing. Yet, the whole endeavor is engaging and interesting especially when I am trying to keep the conversation going, choose carefully my statements, and sustain the interest of the person or group I am conversing with. In the chat room, these are more quite difficult to attain than in face-to-face interaction. Eventually, when I learned my way through the online environment, my opinion on this new approach of learning and teaching started to change. I guess†¦ I discerned many advantages and conveniences of online classes, especially if these are performed appropriately. So far all my online classes have been very successful because our professors used different means such as chat rooms, video conferenci ng, e-mail, etc. Even though the whole experience is far from being ‘real’, it really kept me motivated and involved. Entry # Time Task Behavior 2 12:00 pm- 1:00 pm Consulting a friend regarding whether to take an online course or a face-to-face class. If I had to choose between taking a course face-to-face and online, I would choose the latter. However if I discovered that the instructor did not know how to take advantage of or make the online learning setting efficient, if they are actually familiar with the online environment and know how to use it correctly, if they are then I would take a class online, otherwise, I would prefer face-to-face. Yet again I have to really be sure if the lecturer, professor, or instructor, whatever designation the person whose supervising the course has, has a proficient knowledge of the purpose, use, and importance of the online learning environment. It is an issue of convenience and practicality but also value and success of the learn ing experience. Thus I think I have to be prepared. I think I have to be dedicated to this endeavor because it is more demanding and challenging in a distinct manner. I think I have to be conscientious and professors should be always available online to address students’ concerns; if not, it is not successful†¦ and teachers cannot lead an online course and keep in touch with their students on a regular basis. It would be equivalent to not attending your classes. But I still believe that there should be face-to-face meetings as well, a substantial portion of the learning environment should be this way. It cannot be entirely online. That won’t work. I experienced taking an online course which does not meet face-to-face, even once. When I had things to clarify with the instructor, for instance, through the chat room, our streams of conversation were usually interrupted or, worst, lost in a barrage of questions, issues, and concerns popping out of the chat room all at the same time. Entry # Time Task Behavior 3 1:00 pm- 3:00 pm Meeting with a computer instructor to discuss about my problems with WebCT One of the things that take place in the online environment is the formation of peer groups, and I suppose I would not encourage any person from taking part in an online course that was merely random. I believe we have to develop that learning environment and have the help and advocacy of a peer to carry out a higher course online. I would suggest to all my pupils in

Terrorism Essay Essay Example for Free

Terrorism Essay Essay 2. Explain the differences between terrorism, state terrorism, and state-sponsored terrorism. From Merriam Webster: Terror- a state of intense fear; a cause of anxiety. Violent or destructive acts committed by groups in order to intimidate a population or Government into granting their demands. Terrorism- the systematic use of terror especially as a means of coercion. From Terrorism Today (The Past, the Players, the Future) The Homeland Security Act of 2002 defines terrorism as â€Å" any activity that involves an act that is dangerous to human life or potentially destructive of critical infrastructure or key resources; and is a violation of the criminal laws of the United States or any State or other subdivision of the United States and appears to be intended to intimidate or coerce a civilian population; to influence the policy of a government by intimidation or to affect the conduct of a government by mass destruction, assassination, or kidnapping. † From Merriam Webster: State- a politically organized body of people usually occupying a definite territory; especially: one that is sovereign. A government or politically organized society having a particular character. Sponsor- one who assumes responsibility for some other person or thing. A person or an organization that pays for or plans and carries out a project or activity. The difference between terrorism, state terrorism, and state-sponsored terrorism comes down to the persons involved in the act being committed. Much of the terrorism we see today on the news or in the papers are acts committed by terrorist groups linked by ideology and financed through the drug trade as well as ransom obtained from kidnappings. One example of this type of terrorism are the Somali pirates, these terrorists will hijack large container ships to small pleasure craft and hold those on board and any cargo for ransom. Money made from these deals is then used by the terrorists in their fight against  the Somali government or is funneled to other like-minded groups. Another form of terrorism we have seen here in the United States is what many call the â€Å"home grown† terrorist. These terrorists are usually born in the United States or came to the United States at a young age when their families left their home country. Course#: BCJ303 Unit 1 Many of the recent acts committed by this type of terrorist have been based on ideology and were carried out against civilian personnel. One of the most recent examples is the Boston Marathon attack, the two who carried out the attack had grown up in the United States and led seemingly â€Å"American† lives but had latched onto an ideology that views the United States as an enemy of Islam and that the targeting of innocent civilians is a legitimate tactic. Terrorism in the examples given is carried out by small disconnected groups that are mostly aligned by ideology. Although these groups are not supported by a larger organization or national government many governments with a similar ideology or nation with a large population of person who share a similar mind set to the terror group will many times fail to denounce the acts. This is where terrorism differs from state terrorism and state-sponsored terrorism as both of those types of terrorism are directly supported by the sta te. State terrorism is used by a nation state as way to control its citizenry and suppress any dissenting views or beliefs that are contrary to those of the government. Many of the governments that exercise this form of terror will sometimes start the process of suppression by creating new laws designed to protect the governing class and criminalize the opposition groups and others have completely thrown out their nations laws and implemented new laws based on strict adherence to a religious ideology or total government control in all aspects of the citizens lives. This was the case recently in Egypt, the elected government (Muslim Brotherhood) removed all secular and Christian officials from the government and in their place were seated members of the Muslim Brotherhood. Many of the top military leaders were also replaced with Brotherhood members. These changes and the removal of any opposition party led to many pro government groups to further oppress the ‘non-believers† through the shutting down of  businesses to the burning down of churches and the killings of Christian and secular citizens. Another tactic that has been used in Afr ica and Latin America by state terror regimes is the use of the police and or military as death squads. These squads are dispatched to eliminate anyone seen as opposition or supportive of the opposition. This type of terrorism is directed from the top of the government down to the group leaders. This is where state terrorism differs from state-sponsored terrorism, the state terror regime is open in its support of the terrorist tactics. The state-sponsored terror regimes do not direct the acts but do support them. State-sponsored terrorism is the support of a terror group by a nation state that provides supplies, training, equipment, and weapons. As well as safe haven for the group through the use of diplomatic protection. An example of state-sponsored terrorism is the Syrian government’s support of the terror group Hamas and their co-sponsoring of the terror organization Hezbollah with Iran. For their part Iran provides Hezbollah with military training, weapons and money, while Syria provides political support. Course#: BCJ303 Unit 1 Many of the state-sponsored terror organizations have a set area of operation not far from their sponsor state but this has changed recently as Hezbollah has been taking up shop in Latin America working alongside cartel and narco-terror groups. While all three types of terrorism are used to instill fear and bring about a change that is desired by the organization or state, the main difference between the three is the support (financing, training, political backing) that the group receives.

Self Reflection | Learning And Performance

Self Reflection | Learning And Performance Self-reflection is the self-analysis of knowing oneself. This section describes the self-reflection of the researcher on own learning and performance. It facilitates the researcher to analyse his progress by considering the changes in his strengths and weaknesses. It analyses diverse learning styles theories put forward by various experts and examines the learning style of the researcher during the International Master in Business Administration course. It also describes about the various skills that were gained throughout this course. The various skills include communications skills, report writing skills, presentation skills, research skills and team player skills. Background of the researcher: The researcher completed his Bachelors degree in Information Technology from Madras University, India. IT skills were learned during this period. After completion of the degree, he worked in three companies before coming to Dublin Business School for International MBA. The first two companies that the researcher worked were IT based companies and therefore, the theoretical skills learned during the bachelors degree were transformed to practical skills during the term. The first six months in a job is the time when a new person in the job finds it difficult to get used to the job. The researcher went through this phase and the transformation was not easy. With the help of senior staff in the company, things went smooth. In the first company, the researcher got the opportunity to talk to customers all around the world through telephone, which enhanced his communication skills. He also got the opportunity train new people, which developed the presentation skills. In the second company, the researcher supported the customers through email and chat. This helped to develop the writing skills of the researcher. With more experience, the researcher was given the role of a team leader in the second company he worked. This enabled him to gain leadership skills. The third company that the researcher worked was his own family business. It was very different from the information technology companies that he worked before as this had real world experience. The researcher got a practical insight to the real problems faced by a company that did manufacturing and retailing of steel products. With the IT skills gained from previous years, he computerised the company using management information systems (MIS). This made all the process in that company faster. After gaining some experience, the researcher set plans to learn more about business and chose to get a masters degree in business administration. This is why he chose International MBA course in Dublin Business School, Irel and. Through the MBA International programme in Dublin Business School, the researcher was able to develop the research skills, time management skills, self-learning ability and other skills. There were group works involved in the first semester of the course when helped the researcher to improve team player skills, presentation skills and communication skills. In the second semester of the course, the assignments and examinations helped the researcher to gain self-learning and time management skills. Writing the dissertation proposal in the second semester gave an insight about doing the research. Research and writing skills were improved during this period. All the work had to be completed in certain amount of time, which developed the time management skills of the researcher. These skills have been utilised now, when the researcher is doing the dissertation. The reflections of this learning process can be related to Kolbs learning cycle because of the scope of learning something new is always there. Another method of learning has also been used for the review that was proposed by Honey and Mumford. Learning Reflection and Style: Kolbs learning reflection: According to Kolb (1984), learning is the process whereby knowledge is created through the transformation of experience. Knowledge results from the combination of grasping experience and transforming it. He described four stages in a learning cycle and viewed it as a circular process which involves the four stages which are Concrete experience Active Experimentation Abstract conceptualisation Reflective observation According to Kolbs model, the experience lays the foundation for observation and reflection, which are incorporated and condensed into concepts. These concepts are then tested to get a new experience. The cycle of activities such as experiencing, reflecting, thinking and acting occur in the learning process. There are four types of learning methods as shown in the figure below: Source: http://www.businessballs.com/kolblearningstyles.htm Diverger: This is the combination of concrete experimentation and reflective observation. They look at things from various perspectives but prefer to watch things than doing things. They also tend to gather information and use imagination to solve problems. Assimilator: This is a combination of abstract conceptualisation and active experimentation. These people can solve the problems and will use their learning to find solutions to practical issues. They are less focused on people and are focused on ideas and abstract concepts. Converger: This is a combination of abstract conceptualisation and active experimentation. They can solve problems and will use their learning to find solutions to practical issues. They prefer technical tasks and are less concerned with people and interpersonal aspects. Accommodator: This is the combination of concrete experimentation and active experimentation. They have the hands-on technique of solving problems. They rely on intuition rather than logic. They use others analysis and use a practical, experiential approach. During the International MBA course, the researcher used various learning styles in different situations. Assessing the researchers learning style according to the researcher has an accommodator style of learning. The researcher uses more trial and error method to solve the problems. This is a more practical approach to solve the problems even though it could be time consuming. The researcher feels that the proving things practically is better than talking the about the theoretical side of it. This enables the researcher to adapt to changes quickly to changing circumstances and allows making concrete decisions. Honey and Mumford Learning Style: Source: adapted from http://www.learningandteaching.info/learning/experience.htm) Honey and Mumford (2000), mentions that, the term learning style is used as a description of the attitudes and behaviours that determine an individuals preferred way of learning. According to them, there differnt of learning styles and categorise individuals into four types as shown in the figure above. Activists Reflectors Theorists Pragmatists Activists: They completely involve themselves into a new experience without any previous experience. They have the attitude of trying everything once. They act first and worry about the consequence later. (Honey and Mumford, 2000) Reflectors: They are very cautious and thoughtful people who like to consider all possible angles and implications before making a move. They like to stand back and evaluate the previous experiences before they commit something. (Honey and Mumford, 2000) Theorists: If it is logical, then its good is the main philosophy that is associated with theorists. They integrate observations into complex but logically sound theories. They think about solving a problem in logical, step-by-step manner. (Honey and Mumford, 2000) Pragmatists: They always positively search out for new ideas and take the first opportunity to experiment with its applications. They are always keen to see if the theory will work out practically. They are always associated with people taking practical decisions and solving problems. (Honey and Mumford, 2000) (Honey and Mumford, 2000, pp 11, 12) The researcher has more pragmatist style of learning. This is useful for the researcher in making quick decisions. The researcher likes to experiment a lot and get bored with long time activities. This is why for this research; the researcher tries to practically prove the things that have been mentioned in the theory. The MBA International program has helped the researcher to experiment the new ideas practically. Key Skills Learned from MBA International: The international MBA programme provided by the Dublin Business School helped the researcher to develop numerous amounts of skills through rigorous academic activities. Various activities included assignments, presentations, group work, exams and finally the dissertation. The skills that have been developed through the program can be divided into two. The first one is academic skills and the second one is personal skills. Academic Skills: The key academic skills that were learned were Research skills, Presentation skills, and Team player skills. Research Skills: Research and investigation skills are very important in terms of academic studies. It is the way one carry out the research about a particular subject. In this case, the researcher carried out different studies especially when doing the dissertation. Researcher understood about the different methods to be followed when doing a research. It was not as an easy task as the researcher had to consult the books, journals and magazines in order to find out the relevant information on the topic. Researcher also understood the importance of critical analysis, what different authors say about the same topic. Presentation Skills: The researcher developed this skill during the class time. The researcher had to give presentations for most of the modules which he did during the semester. Even though, there was trouble in the beginning because of the stage fear, things improved after some time. This gave him the real confidence to stand in front of a group of people without any fear. This would be very useful in future in a professional field. Team player skills: A few modules like International business management and integrated marketing communications had group work involved. This meant that the work would be equally divided among the team members and each had to do their own part. There were team members who would not cooperate for meetings or discussions. However, the researcher found his own ways to overcome this and ensured that the teamwork was done in the end. This would be helpful in future in a professional field as all the work these days are team based. Personal Skills: The key personal skills that were learned were communication skills, time management skills. Communication Skills: A cultural shock is customary for someone who has crossed the globe to study in a foreign country, which was the same for the researcher. The researcher found the communication slightly difficult in the beginning but later improved. The interaction with the international students in the class improved the communication skills of the researcher. The interaction with the lecturers and other staff in the college helped improve the communication skill by a great deal. Time management skills: Time management skills are very important for a person. During the MBA course and through the dissertation, the researcher had to set goals to be achieved in a specific time frame. The researcher had to meet the deadlines for various assignments, which he did successfully. This helped to improve time management skills by a great deal. Future application of the learning skills: The International MBA course has helped the researcher in developing many skills that lacking before. The hard skills of finance, marketing and operations and the soft skills such as communication, leadership and teamwork will be useful for the future. The research skills that were developed during the research will certainly help in the future to choose appropriate techniques and methods. With the help of presentation skills, the researcher will be able to convince people easily. The team player skills will enable him to work as part of a team without any problems. The improved communication skills will with an international exposure will give him the benefit when meeting other people. The time management will skills will help him to do things on time. The MBA program as a whole has contributed a fair deal in improving academic and behavioural competencies. The skills acquired throughout the MBA course will definitely help the researcher in career advancement.

The Most Dangerous Game versus The Child by Tiger Essay -- essays rese

The conflict of good and evil presents itself in â€Å"The Most Dangerous Game† and â€Å"The Child by Tiger† in two completely different ways. One story being commercial fiction and the other being literary fiction, there are many ways of viewing variables such as good versus evil, realistic versus unrealistic stories and moral significance. The stories have different voices and are meant for different audiences, but in viewing the overall moral importance of both fictional works, the story with a greater moral significance is â€Å"The Child by Tiger†. The plot in â€Å"The Most Dangerous Game† is simple, obvious and unrealistic. There is a â€Å"good guy† trying to escape from the â€Å"bad guy† who lives on Ship-Trap Island. Rainsford clumsily tumbles off of his yacht into the â€Å"blood-warm waters† (59), starting the game. His belief that animals are unable to feel and understand fear makes him the perfect, unsuspecting prey in the irony of the story. The miraculous return of Rainsford to slaughter Zaroff is the most straightforward example to the unrealistic manner of this piece. In â€Å"The Child by Tiger† there is greater artistic unity in the series of events. Dick, a handyman to the Sheppertons, is a role model to the boys in the story and they look up to him because he is fun to be around and he teaches them good morals. The resignment of the cook and Dick’s pent-up feelings he keeps inside spark something in him to kill people. During Dick’s rampage, he kills not only white men but black men, too. He is not racist like the white people are—any person standing in his way gets shot. His act of murder is artistic and swift, he kills people with one, clean blow and moves on expressionless. This artistic massacre expresses some excellent charac... ...st person. The narrator is looking back on this story and remembering things from a child’s point of view. The reader only sees the narrator’s opinion in the story, but that allows the reader to have his own opinions as well, questioning the literary work constantly. This makes the story more complex and permits the reader to wonder what is going on inside each of the characters’ heads. In considering each piece of literary work, â€Å"The Child by Tiger† is the more intricate story of the two, and thus the most morally important. â€Å"The Child by Tiger† makes the reader look deeper into the story, questioning it constantly, enquiring what each symbol means and the importance of it in the story. Interrogations like that lead the reader to get a better insight to life by questioning it rather than accepting it page-by-page as one does in â€Å"The Most Dangerous Game†.

The Age of European Exploration Essay -- European Europe History

The Age of European Exploration The age of exploration was filled with courageous voyagers and conquistadores from all over Europe, much like today, there was much competition for land rights. The main disputes were between Spain and Portugal. And these are the representatives from not only these two countries, but surrounding ones as well. Christopher Columbus was a sea captain from Genoa. He first tried to convince Portugal, then Spain to sponsor a voyage to Asia across the Atlantic. Columbus thought that the voyage would take two months, others said four months, but he left with enough food and supplies for only two months. He landed in the West Indes (Bahamas, Haiti, Cuba) when the two months of supplies ran out. Their voyage began on August 3, 1492, from Palos, Spain and ended on October 12 when land was sighted at the Americas. Amerigo Vespucci, an Italian that represented the Medici Bank in Spain, chartered the coastline of Central America and described this as the "Mundus Novus", meaning "New World". In 1507, a German carto...

Math Ia

Math IA Math Internal Assessment EF International Academy NY Student Name: Joo Hwan Kim Teacher: Ms. Gueye Date: March 16th 2012 Contents Introduction Part A Part B Conclusion Introduction The aim of this IA is to find out the pattern of the equations with complex numbers by using our knowledge. I used de Moivre’s theorem and binomial expansion, to find out the specific pattern and make conjecture about it. I basically used property of binominal theory with the relationship between the length of the line segments and the roots. Part ATo obtain the solutions to the equation ) | | Moivre’s theorem, (| | equation, we will get: , I used de Moivre’s theorem. According to de . So if we apply this theorem in to the (| | ) ( (| | ) ) | | ( ) If we rewrite the equation with the found value of , it shows (| | ( ( ( ( ) )) )) Let k be 0, 1, and 2. When k is 0, ( ) ( ) v v Now I know that if I apply this equation with the roots of ( ) ( ) we can find the answers on the unit circle. I plotted these values in to the graphing software, GeoGebra and then I got a graph as below:Figure 1 The roots of z-1=0 I chose a root of and I tried to find out the length of two segments from the point Z. I divided each triangle in to two same right angle triangles. By knowing that the radius of the unit circle is 1, with the knowledge of the length from D or Z to their mid-point C is length of the segment segment ) v , I found out . So I multiplied this answer by 2. And I got the v . I used same method to find out the length of the . (v v Figure 2 The graph of the equation z^3-1=0 after finding out line segment Thus we can write that the three roots of , and we can also factorize the equation by long division.Since I know that one of the roots is 1, I can divide the whole equation by (z-1). And then I got . So if we factorize the equation as: ( )( ) As question asks I repeat the work above for the equations . Using De Moivre’s theorem, can be rewritten as: ( ) Sup pose So the roots of the equation are . As we can see the graph below, I drew a graph of the roots and connected two other from a point A. The question wants me to find out the length of the line segments which I connected from a single roots to two other roots, . Since are isosceles right-angle triangles with two sides of 1.With the basic knowledge of right triangle with two I found out that the length of the v v Figure 3 Graph of z^4-1=0 before finding out the line segment Figure 4 Graph of z^4-1=0 after finding out the line segments Again I am finding out the roots of ( ( ( Suppose that the k is equal to 0,1,2,3 and 4. ) ) ) ( ( ( ( I plotted those roots of the equation ) ) ) ) ( ( ( ( ) ) ) ) ( ( ( ( ) ) ) ) in to GeoGebra and on an Argand Diagram. And as shown below I found out the length of the line segments Figure 5 Graph of z^5-1=0 before finding out the line segments Figure 6 Graph of z^5-1=0 after finding out the line segmentsSo if I rewrite the lengths of line segments fo r each different equations and , they are: , ( ) ( ) , | | | | | ( ( ( ( )| )| ( ) )| ( ) )| ( )| With my values of distance of the line segments between the chosen root and others, I made a conjecture that says ( | ( | | ( [ ]) |) ( | ( |) ) † I tried to prove this conjecture. But as shown below, it is impossible to prove due to unknown amount of multiple of the sin properties ( ) Then I tried to prove it by binominal expansion, which is totally different way. I drew a graph of an equation (shown below) and connected between a root to all the other roots.Figure 7 The graph of z^n-1=0, with its roots connected As shown above, the graph has certain amount of roots, and they are connected to a root as told in the problems. And the lengths of those line segments are able to be written as ( So I rewrote the equation ( And with the knowledge of ( )( )( )( ) ( ) )( ) in the form of )( )( ) ( ) And since the angles , And I will have ( ) And then, with the binominal expansion, I folde d it out, and got ( ( ( ( ) ( ) ) )( )( )( ) ( ) ) ( ) And I can find out that ( ) ( ( ( )( ) )( ) )( ( ) ( ) ) And I know that ( ) , so with this knowledge, I rewrote ( ( )( ) )( ( )( ( ) ) And all those ( to zero. So it finally has )and ( ) refer ( ( ( ( ( ) ( )( )( )( ) ) ) ( ( ) ) ) ) And there are two condition where n can be even number or odd number, And according to this condition the value of n ( { ) | | | | So the total product of the length of the line segment equal to the power of the equation Proved. And I factorized When I factorized ( ( ( )( )( , I got the answers like: )( ) ) ) And I also tried to test my conjecture with some more values of For ( ) Suppose ( ) ( ) ( ( ) ) Figure 8 The graph of z^6-1=0 with line segments The product of lengths of the line segments are v vFor ( Suppose ) Figure 9 The graph of z^7-1=0 with its line segments Part B I am going to find the solutions of this equation for each Moivre’s theorem to obtain solutions to the equation . And I will use de . And I also drew diagrams for each roots of the equation s. I used Geo Gebra to represent each roots of the equation on the Argand Diagram. So, when ( ) ( ( ) ) ( ( ( ) ) ) ( ( ) ) ( ) ( ) v v ( ) ( ) Figure 10 The graph of roots of equation z^3=i As shown above, the equation has three distinct roots. And the distance of arc between each neighboring roots are same with others.Roots of this equation increase by are three roots on the unit circle. , so we can find that there When ( ( ( ) ) ) Suppose ( ) ( ( ( ) ) ) Figure 11 The graph of roots of equation z^4=i When n=5, ( ( ) ) Suppose ( ( ) ( ( ( ) ) ) ) ( ) Figure 12 The graph of roots of the equation z^5=i Basically all the roots we found are on the lane of the unit-circle, because we use the complex ( ) number whose modulus is 1. ] . So if I generalize the equation of , I would get: ( ( So for the equation like equation is Generalize the equations of , ) ) that satisfy this ( ). And I can should be (0+1i)= i.And t he value of into , where n=3,4 and 5. rad. So we can change the equation ( ) ( ( ( ) ) ) With the knowledge of in the right triangle of a b So With the knowledge v It is possible state that This generalization is proved naturally as we found out that the angle of the roots is . When But when | under the condition of | | | has a generalization of the generalization would change as Conclusion I found out some patterns about two different equation: some conjectures that led me to find out and prove it. For of all length of the line segments connected form a root to others. . There were n is equal to the product