fast runner

Sunday, 12 March 2017

MODEL FOR REFLECTIVE JOURNAL

INTRODUCTION

Reflective journals are note books or piece of paper that students use when writing about and reflecting their own thoughts. The act of reflecting on thoughts, ideas, feelings and their own thoughts, learning encourages the meta cognitive development skills by helping the students to self evaluate and sort what they from what they don’t know. The process of examining one’s own thoughts, feelings, is particularly helpful for students who are learning new concept or beginning to grapple with temples issues that go beyond right and wrong answers.

John Dewey (1938) believed that education should serve as a means of acquiring information, but also as a way to bring learning to our everyday actions and behaviors. Successful learners knew how to identify questions and problems as they reflect on what they already knew, what they aren’t and the neediness of knowing, and how they will proceed to increase their understanding. Less successful learners need to develop the habit of mind the underlying strategies of the learning process.

Reflective practices can be supported in classroom by creating opportunities that allow students to think about their learning their own lives and the world around them. The process often eliminates problems, misunderstandings and confusions and helps to determine new growth, independence and responsibility of learning. As learners continue to distinguish what they know from what they need to be evaluate that began to translate discoveries about what they made about their own learning into plans for improvement. A reflective journal is a personal record of students learning experience. It is a space where a learner can record and reflect upon their observations and response to situations, which can then be used to explore and analyze ways of thinking. Journals although generally written can also contain images, drawings and other types of reference materials.

A reflective journal is a means for learners to reflect on their learning and learning experiences in different ways. They are used to record the development of learner’s ideas and insights and or those of a group in a given context and can include concepts, ideas, and main points from experiences as a means to increase learners understanding, analyze learning process for self development.

REFLECTIONS ON COMMUNITY LIVING CAMP

PLANNING

As a part of the two year B.Ed curriculum, we decided to conduct a five day camp community living camp. For the better going of the camp different committees were selected and assigned duties for them. There was a clear planning and preparation before the camp.

EXECUTION

SITE 2017, our camp was carried on 23-27 January 2017 at Holiday Home Kumily. It was a good experience in all sense, which was enough to fulfill the set aims of developing special skills. We enjoyed the camp.

PRESENTATION

Overall the camp was a great success, without any gross pitfalls. The five days of the camp was very interesting and all have done their duties properly.

ACTION PLAN

We were tried to obey the rules of the camp and follow the five days as planned as earlier. If we planned the financial settings some more seriously, then we will be able to manage the financial problems to a great extent. All the faults that come to our conscious, will try to manage it in the next time.

NEW PERSPECTIVES

If we got another chance to take part in a camp we will try to follow all these planning and also try to manage the time in the absence of a guest .I think there is need to settle in a particular place for one day and take part in the activities of that community.

REFLECTIONS ON STUDY TOUR

PLANNING

As a part of the two year B.Ed curriculum, we need to take part in a three day tour. Our college planned to conduct a tour. The dates for the tour, expenditure, place etc were planned by discussing with the students and teachers. Different committees were arranged for the easy going of the tour. All the requirements for the tour were planned and prepared properly.

EXECUTION

We the students and teachers of UCTE Kumily went for a study tour, YATRA 2016,from 8-11 December 2016 .The tour was to one of the well known tourist place Mysore and kodagu. The travel, food and accommodation were arranged properly as planned earlier.

PRESENTATION

The study tour remains as an unforgettable moments. All the committees presented their duties clearly and neatly. The lessons we learned through this journey help as to lead many tours.

ACTION PLAN

All the sessions for the tour were a great success. Only one thing that I found as a suggestion is that when we select a place, must select a place which have to travel less and more to see.

NEW PERSPECTIVES

We were able to know more about these tourist places. More over enjoyment we learned the history behind these well known places. So for study tours we will try to choose a place having more to contribute to our knowledge.

REFLECTIONS ON EXTENSION ACTIVITIES

PLANNING

We were planned to make the society aware of some of the burning social issues. So as a part of the B.Ed curriculum, we planned two extension activities one to make people aware of the use of plastics and its harmful effects. For that we planned to play a flash mob and street play which highlights the theme of usage of plastic. The second one is to make the people aware of their body weight. Essential requirements for the program were made.

EXECUTION

As planned earlier, the first extension activity was carried out at Kumily bus stand by playing flash mob and street play on 1 December 2016. After the official meeting there was an awareness rally. The second activities were checking the weight and height of about 30 peoples and make them aware of their body weight.

PRESENTATION

The activities that we planned were conducted effectively in such a way that people get a clear idea about the social issues. We presented the flash mob and street play to make the people aware about the problems.

ACTION PLAN

It was the first time that we planned and prepared such a program. It having its own faults that need to be removed. If we got a chance to do such activities ,will try to do it better.

NEW PERSPECTIVES

Teachers have to work in the society. They need to be aware about the social issues and make people aware of the problems. So the teachers should be aware of all the social issues and make commitment.

REFLECTIONS ON SHORT FILM

PLANNING

As a part of the curriculum we were divided into 6 different groups and our group planned to prepare a short film related to a social issue. So we planned a story and prepared a script and also choose the location for the short film.

EXECUTION

As planned earlier, based on the script we proceed the shooting .The script that we prepared was very useful to us. It’s really a special experience for me .I was able to study the concepts regarding shooting, camera management, different shooting sessions etc were learned.

PRESENTATION

After finishing the shooting and editing we have presented our short film ROOPANTHARAM before the teachers. It reached beyond our expectations. It’s really a good work. We feel proud to the work.

ACTION PLAN

It was the first time that I am using the camera. Even though most of we were not aware of the use of shooting equipment we tried our best to make it perfect. Now I know the faults in it. If I get a chance to do another one I will make up all the faults that found in this.

NEW PERSPECTIVES

Socially related issues need to be bring before the society. Short films and documentaries related to the problems faced by the society will be highlighted in the next works.

REFLECTIONS ON SWOT ANALYSIS

PLANNING

It is essential for one to know the strengths and weaknesses of one’s own. As a teacher in order to know my strengths, weaknesses, threats and opportunities we planned to analyze the SWOT. For that I list out my strengths, weaknesses, threats and opportunities. Then I tried to analyze it.

EXECUTION

As a practical work I prepared my SWOT and analyze it. It helps me to reveal my positives and negatives , which helps me to improve myself. It is a good analyzing technique especially for teachers.

PRESENTATION

I presented my SWOT analysis before my guide and their I got some advices how to reduce the weaknesses and use my strength along with my opportunities for career development.

ACTION PLAN

I will try to find out more of my strengths, weaknesses, threats and opportunities. Also while preparing a SWOT analysis it is essential to club the items to get a clear idea about it.

NEW PERSPECTIVES

SWOT analysis enables me to know more about my strengths. It helps me for my professional development. It is a good tool especially for teachers.

REFLECTIONS ON EDUCATIONAL

JOURNAL REVIEW

PLANNING

Reviewing a journal article is not much easy matter. Certain systematic steps to be followed for reviewing an article. I planned and choose an educational journal “Journal on school educational technology.”By following the rules I read the journal thoroughly and selected 5 among them for review.

EXECUTION

The five articles from the journal- Journal on school educational technology have been read and review it. It helps me to improve my reading skills, to know how to write a research article and also to get more information about new technologies and inventions.

PRESENTATION

I presented my review before the guide and also I discussed the relevance of my journal with peers. This journal review is really informative.

ACTION PLAN

Before selecting a journal, we should bore in mind the journal selected must have an ISSN number and of high standard. Now I know how to review a journal article and I will improve my reading habits.

NEW PERSPECTIVES

Journal reviews make us think more about a particular problem. And also it help us to view others perspectives. Our reading skills can be improved.

REFLECTIONS ON PARTICIPATION IN

ARTS FEST

PLANNING

To exhibit the artistic talents of the students arts fest was conducted in our college. All the preparations for the arts fest were made in the right manner. Panels for the judgments, score sheets, scheduling of items, decoration of the stage etc were planned and arranged properly.

EXECUTION

As planned earlier, everything was executed properly. I have participated in two items Essay writing (Tamil) and Poem (Tamil) .All the programs shows its standard and also executed at the right time obeying all the rules.

PRESENTATION

I have participated in essay writing and poem. I presented it well and won first prize in both items that I have participated. Each and every one participated in at least one item. It is really a good experience to all and a good chance to present their talents.

ACTION PLAN

As a result of lack of time, there is limitations to take practices, that reflects mostly in group items. So sufficient practices is essential for all programs especially group items.

NEW PERSPECTIVES

Each and every one has their own abilities and talents. So arts day is a day to exhibit our talents before others. Arts day plays a major role in institutions.

REFLECTIONS ON PREPARATION & UPLOADING OF

JOURNAL ARTICLE IN THE BLOG

PLANNING

Technology plays a major role in the classroom teaching. As we have already created the blog, as a practical we planned to upload any of the work that we already prepared. And I selected my optional project as my article.

EXECUTION

I have uploaded the article presence of insecticide and pesticides in fruits and vegetables into my blog. Essential modifications for the article have made and uploaded in the article.

PRESENTATION

I have presented the article uploaded in the blog as a hard copy. Screen shot of the uploaded material also documented.

ACTION PLAN

A free blogging transform gives us the opportunity to reach out to our online learners. There is need to view or follow others blog to view their perspectives. It is a forum to share thoughts and opinions. So there is need for clear check on the articles that published in the blog.

NEW PERSPECTIVES

It helps us to learn more about the e-learning services and practices. It provides a forum for the sharing and viewing the thoughts of others.

REFLECTIONS ON PARTICIPATION IN SPORTS AND GAMES

PLANNING

Sports and games play an important role in educational institutions. As a teacher trainee it is essential to know how to conduct a sports meet or games rather than the participation. So we the student teachers planned well before conducting a sports meet. We made necessary arrangements in the ground. Different committees do their duties.

EXECUTION

As planned earlier the meet was carried out by obeying all its rules and regulations. Track officials were there for the meet. We got a good training regarding the conduction of sports meet or games. All the events were carried out as per the time scheduled.

PRESENTATION

The sports or games day was a great success in all ways. All the events were presented in a right manner following all the rules and regulations. All the sessions from the opening ceremony to closing ceremony was of good standard.

ACTION PLAN

All the irregularities or faults that we assessed were to be removed for the next time .After the event we had an evaluation session to find out the positives and negatives .It will help to improve the next one.

NEW PERSPECTIVES

We got a good chance to conduct a marvelous sports meet. New ideas were observed in the meet. Thorough knowledge about the events is needed for the success of the meet.

REFLECTIONS ON ORGANISING

A CULTURAL EVENT

PLANNING

Inorder to know more about the cultural events, its importance and conduction we planned and organize cultural events. In the midst of our camp, we celebrated Republic day. After the formal function we planned to organize cultural programs. All the groups prepared for the cultural program.

EXECUTION

As planned earlier, all the students prepared varieties of programs and all they were planned and executed in a different way.

PRESENTATION

All the groups presented the cultural programs in a successful manner. Each group has variety themes to be presented. It’s really colorful to our eyes.

ACTION PLAN

There were certain defects in the programs that we organized. Lack of practice is one of the problems. So this can be maintained by taking sufficient practices.

NEW PERSPECTIVES

Through the cultural events we were able to think about the Indian culture. It generates love towards our nation and as a teacher for future it is necessary to know how to organize functions.

REFLECTIONS ON FILM REVIEW

PLANNING

As a part of the practical it is necessary to view a film and review it. So we were planned to show two films which are of great importance in educational field. So two films Pasanga 2 and Wall-E were shown for reviewing.

EXECUTION

As planned earlier two films, a Tamil film named Pasanga 2, an educational film and Wall-E a scientific film were shown. All the students enjoyed the film and tried to find out the relevance of it.

PRESENTATION

After the show, we were able to find out the relevance of it and choose one of the films for review. Based on the steps, I write the review of the educational film, Pasanga 2 and presented it before the guide.

ACTION PLAN

Both the films were shown on the same day. I think it’s better to show it in two days. If we know the steps before watching it will be easy to review it.

NEW PERSPECTIVES

As a student teacher, it is essential to watch a film which having more educational importance. Reviewing improves our ability to critize films.

REFLECTIONS ON PORTFOLIO

PLANNING

A student portfolio is a compilation of academic work and other forms of educational evidence assembled for the purpose of evaluating course work, quality, learning progress etc. We planned to prepare a portfolio to evaluate ourselves which includes works of all the four semesters.

EXECUTION

As planned earlier, each students prepare their own portfolio, it is a personal evidence that helps to know one’s own learning standards and to reflect on their academic goals and progress as learners.

PRESENTATION

After completing all the works, I have prepared my portfolio by adding essential evidences and presented it.

ACTION PLAN

I think it is essential to do some more modifications and perfections in the port folio. And it is helpful for the teachers and learners to monitor and evaluate learning progress.

NEW PERSPECTIVES

It is better , if we make portfolio in such a way that which can encourage students to take more ownership and responsibility over the learning process.

Thursday, 9 March 2017

AS A MATHEMATICS TEACHER

MY REFLECTIONS AS A MATHEMATICS TEACHER

My school internship programme is done at GHSS Amaravathy . I cleared 50 lessons and 5 innovative lessons in Mathematics . In the school Smt. Indiradevi P was my mentor and she gave the class 8 A for my teaching practice. She was very helpful during the internship periods . I took the chapters equal triangles, equations, polygons, identity and money math. I got 40 students in my class and the experience was good. I started the classes by the chapter polygons for gaining the attention of students through interesting mathematical areas that related with daily life situations. I fully prepared before all the classes and used all the available learning materials.

Qualities developed me through school internship are collaboration, confidence, honesty , duty boundness, respect, commitment to teaching and learning, emotional maturity, responsibility, fairness, belief that all students can learn.

Collaboration – I worked with 4 of my peers in GHSS Amaravathy. During this period we worked together and helped each other. We got some duties in school and we done it by collaborative manner. We discussed about our classes , duties and also talked about how to improve our classes. We also worked collaboratively with the teachers of GHSS Amaravathy and they gave necessary tips and supports for the successful practice.

Confidence – school internship programme helped me to acquire the quality of confidence, and the awareness of the necessary of being confident. As a teacher confidence is a necessary quality to face problems arising during classroom teaching and in school. A confident teacher can make enthusiastic generation. School internship also gives me the confidence to speak in front of students and people.

Respect – during those days of school internship I learned to show respect to others, it includes my colleagues, school head, parents and also students. Everyone has their own peculiarities and differences. Respecting these differences is helpful for maintaining a healthy classroom environment. Without respecting the individual differences of students we can’t teach in the correct manner.

Honesty – I learned to be honest to my colleagues and to my students. Honesty is a unavoidable quality for teachers. If we working in a organization we must need honesty. This honesty strengthen our collaboration and ensure the smooth working of the organization.

Commitment to learning – A teacher must acquire more knowledge about his own discipline and also in other discipline to provide more and updated knowledge to students. School internship teaches me to the commitment for learning. Teachers can’t avoid learning. Teacher must acquire knowledge and a teacher with master in certain discipline can lead a class smoothly.

Responsibility – I learned to be responsible. As a teacher my first duty is to know my subject matter and the second one is be responsible to give necessary knowledge to the students about subject matter. School is a organization and their must be more activities curricular or extracurricular, if we get any charge for the conduct of a programme we must be responsible for that duty and give full commitment to its perfect functioning. During internship I got charges in mathematics club activities, school sports meet, and Independence day celebrations, I worked with the teachers with full of my effort and responsibility.

Fairness – I learned to be fair to my students and colleagues. If I am fair others will interested to me otherwise they never gives importance to my words or actions.

Belief that every students can learn – Every students has their own differences. The learning strategy of each student is also different. Identifying the best method for each student is helpful for a teacher. Mathematics is a difficult subject for most of the students it is because how they approach the subject. If we change the mode of interaction between mathematics and learners it will helps the learners to create a positive mentality.

Many learners face difficulty in understanding the concept of mathematics. Many students face difficulty in mathematical problem solving and difficulty in acquiring mathematics related skills. It is because of the way they approach the subject. Traditional classroom situations are not sufficient for a better mathematics learning. Implementation of technologies in mathematics classroom will help the teacher and students. ICT enabled classes for mathematics is helpful for the understanding of students. It helps to deliver knowledge in a different manner. Ensuring pupil participation in learning process is very important , activity oriented and interesting teaching methods to be applied. Innovative methods can also be introduced for mathematics learning. My experience as a mathematics teacher was some challenging and interested. I took extra study times for effective mathematics learning. This school internship gives the idea of how difficult the mathematics learning and how can be overcome it.

Thursday, 23 February 2017

STRATEGIES TO DEVELOP SELF CONCEPT AND SELF ESTEEM ON LEARNERS

INTRODUCTION

Self is a reference by an individual to the same individual person. This reference is necessarily subjective and it follows that self is a reference by a subject to the same subject. The philosophy of self seeks to describe essential qualities that constitute a person’s uniqueness or essential being. There have been various approaches to defining these qualities . The self can be considered that being which is the source of consciousness ,the agent responsible for an individual’s thoughts and actions , or the substantial nature of a person which endures and unifies consciousness over time.

One’s self concept is a collection of beliefs about oneself that includes elements such as academic performance , gender roles , sexuality and racial identity . Generally self concept embodies the answer to “ Who am I ? ”. Self concept is distinguishable from self awareness , which refers to the extend to which self knowledge is defined , consistent, and currently applicable to one’s attitude and disposition . Self concept is also differs from self esteem : self concept is a cognitive or descriptive components of one’s self, while self esteem is evaluative and opinionated . Self concept is made up of one’s self schemas , and interacts with self esteem , self knowledge , and the social self to form the self as whole.

Self esteem refers to generate feelings of self worth or self value. Self esteem is not identical to self concept though the two are often confused . Self esteem , refers to one’s evaluation of one’s own qualities.

STRATEGIES TO DEVELOP A HEALTHY SELF CONCEPT

One’s self concept is how the view themselves . How they view their self determine how they will experience life . If you see yourselves in a positive and healthy light , your life experiences will be free of challenges and adversity , just that you will have a healthier approach to dealing with them . In order to possess a positive or healthy self concept you must

· Know yourself

· Love yourself

· Be true to yourself

Healthy self concept constituted by

Ø The ability to know yourself ; to be able to assess your strengths , weaknesses, talent and potential.

Ø The ability to be honest with yourself and be true to who you are and what you value.

Ø The ability to take responsibility for your choices and actions.

Ø The ability to love and accept yourself as you are, knowing that you can improve and develop any aspects of yourself that you choose.

Developing a healthy self concept takes deliberate planning and concentrated effort. It takes acknowledging your intrinsic value as a human being, and then working to acquire the skills needed to confront the many challenges and adversities we encounter in life.

STRATEGIES TO DEVELOP A POSITIVE SELF ESTEEM

Crises of self esteem are a part of the human experience when you feel troubled by low self esteem , can follow the suggestions given below ,

v Free yourself from “should’s”

Live your life on the basis of what is possible for you and what feels right to you instead of what you or others think you “should do .” “ Should’s” distract us from identifying and fulfilling our own needs , abilities, interests and personal goals.

v Respect your own needs

Recognize and take care of your own needs and wants first. Identify what really fulfills you not immediate gratifications. Respecting your deeper needs will increase your sense of worth and well being.

v Set achieve goals

Establish goals on the basis of what you can realistically achieve, and then work step by step to develop your potential.

v Talk to yourself positively

Stop listening to your “cruel inner critic” , when you notice that you are doubting or judging yourself, replace such thoughts with self accepting thoughts.

v Test your reality

Separate your emotional reactions , your fears and bad feelings from the reality of your current situation.

v Experience success

Seek out and put yourself in situations in which the probability of success is high.

v Take chance

New experiences are learning experiences which can build self confidence . Feel good about trying something new , making progress and increasing your competence.

v Solve problems

Don’t avoid problems , face them , and identify ways to solve them or cope with them . If you run away from problems you can solve, you threaten your self confidence.

v Make decisions

Practice making and implementing positive decisions flexibly but firmly and trust yourself to deal with the consequences.

v Develop your skills

Know what you can do and can’t do . Assess the skills you need; learn and practice those.

v Emphasize your strengths

Focus on what you can do rather than what you can not . Accept current limitations and live comfortably within them .

We are not born with any certain level of self esteem or confidence . What we believe and feel about ourselves is instead developed early in life as we are presented with numerous messages from family, friends, media, and culture that begin to shape the way we view ourselves and the world around us. We may have been criticized , ignored, or we may have been lucky and experienced success, and received praise and respect. Either way, we must learn to be comfortable with whom we are and the best we have within us in order to have any self worth.

CONCLUSION

If we can accept that we change our beliefs , values, moods and attitudes then we can change ourselves. Two psychological terms that are very commonly used interchangeably are self concept and self esteem. They are reflective process . They can be influenced not only by observing one’s own self and behavior objectively but also by observing the reactions that other people have to you and your behavior , or imagining what other people might think of you . In addition self confidence , self concept and self esteem can be developed through comparing oneself to those around you, and that is a big reason that self esteem is raised or lowered.

REFERENCES

http:// en.m.wikipedia.org/wiki/self

http:// en.m.wikipedia.org/wiki/self-concept

youhaveacalling.com/personal-success/6-strategies-to-build-exceptional-self-esteem

www.cbr.ns.ca/sstudies/links/learn/1914.html

www.doorway-to-self-esteem.com

Wednesday, 15 February 2017

FIBONACCI NUMBER AND GOLDEN RATIO IN NATURE

FIBONACCI NUMBER AND GOLDEN RATIO IN NATURE

ABSTRACT

In mathematics , the Fibonacci numbers or Fibonacci sequence are the numbers in the following integer sequence.1,1,2,3,5,8,13,21,34,55,89,144,…….. Or (often in modern usage) 0,1,1,2,3,5,8,13, 21,34,55,89,144,…….. In mathematical terms ,the sequence F_n of Fibonacci numbers is defined by the recurrence relation $F_n = F_{n-1} + F_{n-2},\!\,$ with seed values $F_1 = 1,\; F_2 = 1$ Or $F_0 = 0,\; F_1 = 1.$ Fibonacci number is visible in petals of flowers and seed arrangement. We can see Golden ratio in animals ,plants ,fruits, galaxy and in human body also.

INTRODUCTION

Fibonacci an Italian mathematician described the Fibonacci number in 1902 AD , although it had been described by Indian mathematicians earlier . The Fibonacci numbers are a sequence of numbers . You start with zero and one . Then the next number is the sum of the previous two . Zero plus one is one , the next number ,one and one are two , the next number . one and two are three , two and three are five , three and five are eight , and so on. Leonardo Fibonacci (circa 1175-1240),who discovered the sequence named after him and its properties, was an Italian mathematician who helped introduce the Hindu-Arabic numerals(0,1,2,3, etc.) into Western Europe. He is also better known as the originator of the special sequence of numbers , now called the Fibonacci Sequence or Fibonacci Numbers . Fibonacci was born in Pisa , Italy and he sometimes known as Leonardo of Pisa . In his youth he travelled in the Middle East , where he learned the Hindu – Arabic numeral system. The original problem the Fibonacci investigated (in the year 1202) was about how fast rabbit could breed in ideal circumstances.

NAMES FOR ALL FIBONACCI NUMBERS

The inveterate Fibonacci addicts tends to attribute a certain individuality to each Fibonacci number . Mention 13 and he thinks F₇;55 and F₁₀ flashes through his mind. But regardless of this psychological quirk , it is convenient to give the Fibonacci numbers identification tags and since they are infinitely numerous , these tags takes the form of subscripts attached to the letter F . Thus 0 is denoted by F₀; the first 1 in the series is F₁; the second 1 is F₂; 2 is F₃; 3 is F₄; 5 is F₅; etc. The following table for F_nshows a few of the Fibonacci numbers and then provides additional landmarks so that it will be convenient for each Fibonacci explorer to make up his own table.

N	F_n	N	F_n
0	0	11	89
1	1	12	144
2	1	13	233
3	2	14	377
4	3	20	6765
5	5	30	832040
6	8	40	102334155
7	13	50	12586269025
8	21	60	1548008755920
9	34	70	190392490709135
10	55	80	23416728348467685

SUMMATION PROBLEM

The first question we might ask is ; what is the sum of the first n terms of the series ? A simple procedure for answering this question is to make up a table in which we list the Fibonacci numbers in one column and their sum up to a point in another.

N	F_n	Sum
1	1	1
2	1	2
3	2	4
4	3	7
5	5	12
6	8	20
7	13	33
8	21	54

What does the sum look like ? It is not a Fibonacci number , but if we add 1 to the sum , it is a Fibonacci number two steps ahead . Thus we could write

1+2+3+…+34+55(F₁₀) = 143 = 144-1 = F₁₂-1,

where we have indicated the names of the key Fibonacci numbers in parenthesis. It is convenient at this point to introduce the summation notation . The above can be written and concisely :

_k=F₁₂-1

It appears that the sum of any number of consecutive Fibonacci numbers starting with F₁is found by taking the Fibonacci number two steps beyond the last one in the sum and subtracting 1 .

Let us go back then to sum of the first ten Fibonacci numbers , we have seen that this sum is F₁₂-1. Now suppose that we add 89 or (F₁₁) to both sides of the equation . Then on the left hand side we have the sum of the first eleven Fibonacci numbers and on the right we have,

144-1+89=F₁₂-1+F₁₁=233-1=F₁₃-1 .

Thus , proceeding from the sum of the first ten Fibonacci numbers, we have shown that the same type of relation must hold. Is it not evident that we could now go on from eleven to twelve ; then from twelve to thirteen ; etc.,so that the relation must hold in general ?

This is the type of reasoning that is used in the general proof by mathematical induction . We suppose that the sum of the first n Fibonacci numbers in F_n+2-1. In symbols:

_n=F_n+2-1

We add F_n+1to both sides and obtain

_k=F_n+2-1 + F_n+1= F_n+3-1

By reason of the fundamental property of Fibonacci series that the sum of any two consecutive Fibonacci number is the next Fibonacci number , we have now shown that if the summation hold for n , it holds also for n+1 . All that remain to be done is to go back to the beginning of the series and draw a complete conclusion. Let us suppose , as can readily be done that the formula for the sum of the first n terms of the Fibonacci sequence hold for n≤7. Since the formula hold for seven , it hold for eight, since it is hold for eight, it hold for nine; etc. Thus the formula is true for all integral positive values of n.

We have seen from this example that there are two parts to our mathematical exploration. In the second we prove that the formula is true in general.

GOLDEN RATIO

If we take the ratio of two successive numbers in Fibonacci´s series ,(1,1,2,3,5,8,…) and we divide each by the number before it , we will find the following series of numbers :

1/1=1 2/1=2 3/2=1.5

5/3=1.666… 8/5=1.6 13/8=1.625 21/13=1.61538…

It is easier to see what is happening if we plot the ratios on a graph

The ratio seems to be setting down to a particular value , which we call the golden ratio or the golden numbers . It has a value of approximately 1.618034, although we shall find even more accurate value.

The golden ratio 1.618034 is also called the golden section or the golden mean or just the golden number . It is often represented by a Greek letter Phi Ø . The closely related value which we write as phi with a small “p” is just the decimal part of phi ,namely 0.618034.

FIBONACCI RECTANGLE

We can make picture showing the Fibonacci numbers 1,1,2,3,5,8,13,… if we start with two smaller squares of size one next to each other . On top of these draw a square of size two.

We can now draw a new square – touching both a unit square and the latest square of side 2 – so having sides 3 units long ; and then touching both the 2-square and the 3-square (which has sides of 5 units).We can continue adding squares around the picture , each new square have a side which is as long as the sum of the latest two square’s sides. This set of rectangles whose sides are two successive Fibonacci numbers in length and which are composed of squares with sides which are Fibonacci numbers , we will call the Fibonacci rectangles.

FIBONACCI SPIRAL

The Fibonacci spiral : an approximation of the golden spiral created by drawing circular arcs connecting the opposite corners of squares in the Fibonacci tiling, this one uses squares of sizes 1,1,2,3,5,8,13,21, and 34 .

Here is a spiral drawn in the squares , a quarter of a circle in each square. The spiral is not a true mathematical spiral( since it is made up of fragments which are parts of circles and does not go on getting smaller and smaller) but it is a good approximation to a kind of spiral that does appear often in nature. Such spirals are seen in the shape of shells of snails and sea shells and, as we later , in arrangement of seeds on flowering plants too. The spiral-in-the-squares makes a line from the centre of the spiral increase by a factor of the golden number in each squares . So points on the spiral are 1.618 times as far from the centre after a quarter-turn. In a whole turn the points on a radius out from the centre are 1.618⁴=6.854 times further out than when the curve last crossed the same radial line.

GOLDEN SPIRAL

The Golden Spiral is a type of logarithmic spiral that is made up of a numbers of Fibonacci relationships , or more specifically , a number of Golden ratios , for example , if we take a specific arc and divide it by its diameter , that will also give as the Golden Ratio 1.618 . We can take , for example , arc WY and divide it by its diameter of WY . That produces the multiple 1.618 . Certain arcs are also related by the ratio of 1.618 . If we take the arc XY and divide that by are WX , we get 1.618 . If we take radius 1 (r₁) , compare it with the next radius of an arc that’s at a 90⁰angle with r₁,which is r_2
,and divide r₂ by r₁ , we also get 1.618.

FIBONACCI NUMBER AND GOLDEN RATIO IN NATURE

NAUTILUS SHELL

The shell of the chambered nautilus has Golden proportions . It is a logarithmic spiral. The shell has grown by a factor of the golden ratio.

BODY PROPORTION OF DOLPHIN

The eyes , fins and tail of dolphin fall at golden section along body. Other fishes also exhibit golden ratio in their body.

STAR FISH

A star fish has five arms ( 5 is the fifth Fibonacci number ). If a regular pentagon is drawn and diagonals are added , a five sided star or pentagon is formed . Where the sides of the pentagon are one unit in length , the ratio between the diagonals and the sides is Phi , or the Golden ratio . This five-point symmetry with Golden proportion is found in starfish.

SPIRAL GALAXIES

Spiral galaxies also follow the familiar Fibonacci pattern . The Milky Way has several spiral arms , each of them a logarithmic spiral of about 12 degrees . As an interesting aside , spiral galaxies appear to defy Newtonian physics . As early as 1925 , astronomers realized that , since the angular speed of rotation of the galactic disk varies with distance from the centre , the radial arms should become curved as galaxies rotate . Subsequently , after a few rotations , spiral arms should start to wind around the galaxy . But they don’t – hence the so called winding problem . The stars on the outside , it would seem , move at a velocity higher than expected – a unique traits of the cosmos that helps preserve its shape .

PLANTS AND FIBONACCI

Since the time of Johannes Kepler, natural scientists have been fascinated and intrigued by the observation that the phylla (elements such as leaves, florets, stickers or branch) on many plants are arranged in such a manner that each phyllo lies on three families of spirals. Moreover the numbers of arms in each of the spiral families are in almost 95% of al cases sequential triads in the regular Fibonacci sequence, 1,1,2,3,5,8,…further the surface of these plants are tiled in polygonal shapes.

PETALS ARRANGEMENT IN PLANTS

The number of petals in a flower consistently follows the Fibonacci sequence. Famous examples include the lily, which has three petals, buttercups, which have five (pictured at left), the chicory's 21, the daisy's 34, and so on. Phi appears in petals on account of the ideal packing arrangement as selected by Darwinian processes; each petal is placed at 0.618034 per turn (out of a 360° circle) allowing for the best possible exposure to sunlight and other factors.

Probably most of us have never taken the time to examine very carefully the number or arrangement of petals on a flower. If we were to do so, several things would become apparent. First, we would find that the number of petals on a flower is often one of the Fibonacci numbers.

Scale patterns of pinecones

The seed pods on a pinecone are arranged in a spiral pattern. Each cone consists of a pair of spirals, each one spiraling upwards in opposing directions. The number of steps will almost always match a pair of consecutive Fibonacci numbers. For example, a 3-5 cone is a cone which meets at the back after three steps along the left spiral, and five steps along the right.

The seed-bearing scales of a pinecone are really modified leaves, crowded together and in contact with a short stem. Here we do not find phyllotaxis as it occurs with true leaves and suchlike. However, we can detect two prominent arrangements of ascending spirals growing outward from the point where it is attached to the branch.

Pineapple scales

Seed heads

The head of a flower is also subject to Fibonaccian processes. Typically, seeds are produced at the center, and then migrate towards the outside to fill all the space. Sunflowers provide a great example of these spiraling patterns.

In some cases, the seed heads are so tightly packed that total number can get quite high — as many as 144 or more. And when counting these spirals, the total tends to match a Fibonacci number. Interestingly, a highly irrational number is required to optimize filling (namely one that will not be well represented by a fraction). Phi fits the bill rather nicely.

HUMAN BODY AND GOLDEN RATIO

Man is structured divine proportion

All cultures and spiritual traditions have always sought to discover the canon of human perfection. We are heirs of many visions and concepts relating to the harmony of human being. Sages have found but, above all, this model of perfection in beauty and harmony of mind, those that allow man to become truly 'measure of all things "after the famous phrase of Greek Protagoras.' And God created man his own image, says Genesis, first book of Moses. Univer ¬ sal man in which this utterance, the Christian doctrine of Christ, Adam Kadmon of the Kabbalistic tradition, is even seen as a person divine macrocosm manifest, therefore, all the qualities and heavenly Father. Good, truth and beauty are divine being fully awakened to

In turn, the soul of every man hiding in the potential of this face divine, whose lead in acquiring the full revelation neasemuitei Frumuseti spiritual. Thus, man carries in his treasure deep perfection, order, harmony, proportion and symmetry of the divine. It was still looking and outward signs, body of these beauties, tangible evidence of the omnipresence of the Divine Proportion, as an expression of Great Power Cosmic Tripura Sundari.

Not by chance, hermetistul Agrippa von Netteseheim (1486-1535) said, 'Man, work and complete choice that God created it, have a more harmonious body than all other creatures and in him all the numbers ingemaneaza all measures, all weights, movements, elements […] are touched by this sublime work perfectiuneaf …] There is not even a single component of the human that does not have in the world of divine ideas, mail or: a celestial sign, a star , an idea-force, a name of God. Human body shape is an expression of completeness. "

Ancient eel known symbol of the number of Gold in the human body is the navel, a microcosm reflecting Omphalosului, called the new and old,, Navel of the Earth”.

Only after the Renaissance, when oral transmission was about to die, this knowledge began to be revealed in a required wider insa'din increasingly poor their metaphysical core. History has preserved the names of some of connoisseurs ancient secret: Pythagoras, Plato, Vitruvius, etc.. Canonical figures of Leonardo da Vinci and Albrecht Dürer were but those who have submitted today to the ancient idea of body perfection.

They reveal us that, semniflcativ, navel divides the human body maltimea Gold Report (a fact noted by all curiosii statistical and a range satisfying). Meanwhile, the pelvic area, connections with the Earth element, lower extremity octave symbolic 1-2, divided maltimea half. Observe the symbolic connotations: Earth corresponds to four, square, but his two, dejos end of the octave, the primary division matrix. It is known that, at birth, the navel is placed at half height, and then to move, with maturation, to the point of division as harmonic, is given by the ratio of gold. This evokes the idea of moving from state primary duality in a relationship, the proportion of Divine Unity, as the assimilation experience of life, in order to proclaim then:

The Human Body is based on patterns of 5, which is the basis for Phi as well

Another interesting relationship of golden section to the design of the human body is that there are:

· 5 appendages to the torso, in the arms, leg and head.

· 5 appendages on each of these, in the fingers and toes

· 5 openings on the face.

· 5 sense organs for sight, sound, touch, taste and smell.

The golden section in turn, is also based on 5, as the number phi, or 1.6180339…, is computed using 5’s, as follows:

5 ^ .5 * .5 + .5 = Phi

In this mathematical construction “5 ^ .5” means “5 raised to the 1/2 power,” which is the square root of 5, which is then multiplied by .5 and to which .5 is then added.

HUMAN FINGERS AND HAND

We have

· 2 hands each of which has…

· 5 fingers each of which has…

· 3 parts , separated by…

· 2 knuckles.

· If we measure the length of the bones in finger it looks as the ratio of the longest bone in a finger to the middle bone with ratio is phi.

· The ratio between the forearm and the hand is in the Golden ratio .

It was found statistically between the lengths of phalanges hand close and Fibonacci's series, even if in practice the relationship is not always rise to the Golden Number, the principle of growth identical to itself and preserves the shape is very well ogliiidit decreasing length of the phalanges or skeletal segments.

FACES

Faces , both human and nonhuman , abound with examples of the Golden ratio. The mouth and nose are each positioned at Golden sections of the distance between the eyes and the bottom of the chin . Similar proportions can been seen from the side , and even the eye and ear itself ( which follows along spiral ).

It’s worth nothing that every person’s body is different , but that averages across populations tends towards phi. It has also been said that the more closely our proportions adhere to phi , the more attractive those though traits are perceived . As an example , the most “beautiful” smiles are those in which central incisors are 1.618 wider than the lateral incisors , which are 1.618 wider than canines , and so on . It’s quite possible that , from an evo-psych perspective , that we are primed to like physical forms that adhere to the Golden ratio – a potential indicator of reproductive fitness and health .

DNA MOLECULES

Even the microscopic realm is not immune to Fibonacci . The DNA molecule measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral . These numbers , 34 and 21 , are numbers in the Fibonacci series , and their ratio 1.6190476 closely approximates phi , 1.6180339.

Research has shown that if you look at the height of the DNA molecule relative to its length , it is in the proportion of .618 : 1 if we look at the components of the DNA molecule , there is a major groove in the left section and a minor groove in the right section . The major groove is equal to .618 of the entire length of the DNA molecule , and the minor groove is equal to .382 of the entire length .

UTERUS

According to Jasper Veguts , a gynecologist at the university hospital Leuven in Belgium , doctors can tell whether a uterus looks normal and healthy based on its relative dimensions that approximate the Golden ratio .

BIBLIOGRAPHY

· http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3578919/

· http://www.nauticcus.org/exhibits/fibonacci_forecourt

· http://goldenratio.wikidot.com/human-body

· http://www.goldennumber.net/human-body/

· http://www.goldennumber.net/human-hand-foot/

· http://www.divinetemplatecreations.com/sacred_geometry/fibonacci.html

· https://en.wikipedia.org/wiki/Patterns_in_nature

· http://math.arizona.edu/~anewell/publications/Plants_and_Fibonacci.pdf

· http://fcbs.org/articles/fibonacci.htm

· http://www.popmath.org.uk/rpamaths/rpampages/sunflower.html

· http://www.goldennumber.net/spirals/