The Importance Of Music Education - 2171 Words

The Importance of Music Education Perhaps the largest distinction between humans and all other animals on earth is the ability to both create and appreciate fine art. The musical art form has existed for thousands of years, and has allowed different cultures to express themselves and connect with one another. The most primitive sounds were simply drum hits and clapping, but over time music has grown in sophistication. Now, complicated symphonies can be heard in halls all across the world, with a large variety of wind, brass and percussion instruments. This development of music over a large period of time reveals that music is fundamental to being human, that humans need music. Unfortunately, the U.S. education system is moving away from this very important human process. Now, officials see music as recreational and unnecessary. However, music education is a vital component of education because of its proven benefits to students. These benefits include not only higher academic perform ance as evidenced by higher test scores, but also specific improvements in job-skills. The idea that making music is a positive activity for students to engage in is not new. Many parents decide to put their children into the hands of private violin and piano teachers at ages as low as two years old. Up until the last couple decades, parents relied on intuition and experience to justify why music was beneficial for their children. Now, neuroimaging provides a more concrete basis for thisShow MoreRelatedThe Importance of Music in Education1426 Words   |  6 Pages2015 Final Paper The Importance of Music in Education Whether we choose to believe it or not, music is a very present thing in one’s day to day lifestyle. From turning on the radio in the morning, to listening to it while grocery shopping, putting in our headphones while we study, music is always there. Music is also extremely underrated, which is why so many public schools are constantly threatening to take away music programs all the time. But why is music education so vital in the growth ofRead MoreThe Importance Of Music Education790 Words   |  4 PagesTime Music education is a subject in school that should be essential for all students. If students continued to expand their music education, they would have higher test scores in subjects such as math and English. Having a school system where everyone is able to benefit from a school wide requirement of music education. Music education will help improve student test scores and improve students language development. Students who take music classes have higher test scores. Music education helpsRead MoreThe Importance of Music Education Essay951 Words   |  4 Pagestoday’s society? Some say that music education is a waste of valuable resources, takes time away from academic subjects, is noisy and distracting, when in reality this is false. Music is a valuable resource that every human being should enjoy. Although our economy has been failing lately, we should not let ourselves believe that the only way to be productive is in a field that makes us unhappy, like computers or science. In America’s recent economic downfall, music education is commonly one of the firstRead MoreEssay The Importance of Music Education1936 Words   |  8 Pagesinvigorating article, â€Å"Why Music Education? 2007† having so many atrocities pulling the world apart, music is a great way for bringing people together (9). Diagnosed with a severe case of autism and blindness at birth, Derek Paravacini is viewed as a music savant. He has the extraordinary ability to play a music piece after just hearing it. Derek has been engrossed by the piano since the age of two and has been performing around the world since the age of nine. From studying various music genres, at age 32Read MoreThe Importance of Music Education Essay885 Words   |  4 PagesImagine a world without music; it would be an extremely boring and quiet place to live. Music is found in every kind of culture and has been used for thousands of years as a means of expression. Music can deliver a message; it can be used as a vehicle for poetry; it can be appreciated for its aesthetic qualities, or it can serve as nothing more than entertainment. Recently, many studies have been conducted proving that music is vital to a childs education and development. However, many schoolRead MoreThe Importance and Effects of Music Education Essay examples1944 Words   |  8 Pages Music evaluated as a subjects that is many times overlooked. If a school seems to have financial trouble, then music and art programs are the first to get cut. Essentially, students do not need them to succeed and they are just hobbies. This is the mindset that many school boards have towards music education. I have had the pleasure of being involved in music from a young age. My schools did not offer music programs, but my parents saw an opportunity in music education so they decided to lookRead MoreEssay on The Importance of Music Education in the School Curriculum2336 Words   |  10 PagesMusic is all around us, yet many of us do not understand it. A simple man with an office job that you pick randomly off the street could most likely tell you the basic rules of American Football, and yet that same man could have never played football in his life before. If you asked that same guy the basics of the music he is listening to, I bet you would get a blank stare back. My argument relates directly to schools so many people can reason football is not technically taught in school, but whatRead MoreHigh School And The Neural And Scholastic Benefits Essay1626 Words   |  7 PagesGerald Ford said, â€Å"Music education opens doors that help children pass from school into the world around t hem a world of work, culture, intellectual activity, and human involvement. The future of our nation depends on providing our children with a complete education that includes music.† Music can do so much for the youth of the nation because it encourages group cooperation, independent study, and a way to relax. It has often been debated whether the benefits of music in school are significantRead MoreLiterature Review on Music Education Essay1000 Words   |  4 PagesLiterature Review This complex problem of music education has been studied for many years. Some disciplines go off of one another to conduct studies and analyze one’s results. Music educators tend to study how music education came to be. They are huge advocators for music education because of the benefits that come with the programs. Psychologists have studies done around the world to see what the affects of having knowledge in the subject of music are. With so many studies done, there are so manyRead MoreSchools Should Provide Better Funding For Such Programs1734 Words   |  7 Pagesschool years. Do you remember going to music classes? Learning how to pluck out simple songs on the piano, a xylophone, or a recorder; or learning how to sing out a catchy tune? Did you have as much fun as I remember having? This fun is about to come to an end for the coming generations. Public schools are beginning to cut music programs from their budgets altogether, so our children may never know the sweet sol ace of scratching out a simple song. Generally, music programs-- as well as fine arts as a

Essay about Diagnosed With Depression - 2054 Words

Everyone you know and everyone you see gets sad. It is a common feeling for any human being and completely natural for people to have high and low moods. But at what point does sad become â€Å"too sad?† There does come a point when being sad for a long period of time or being too sad can actually affect your health, and can become dangerous. â€Å"Almost everyone suffers from occasional depression with symptoms like sadness, pessimism, and low energy. It is only when depression lasts 2 weeks or more that it becomes a clinical disorder at which point it is called major depression.†(What is Depression?). This paper will explain everything about depression: what exactly it is, how to recognize it and realize the symptoms, treatments, affects, and even†¦show more content†¦It is evident why these three neurotransmitters are so important and how an imbalance can throw off the function of the brain. Depression can become something very serious so it is important to at least be aware of the symptoms and the difference between being sad and actually being depressed. As previously noted, being qualified as depressed means having symptoms for over two weeks. These symptoms include: â€Å"a depressed mood during most of the day, particularly in the morning, fatigue or loss of energy almost every day, feelings of worthlessness or guilt, impaired concentration or indecisiveness, insomnia or hypersomnia, markedly diminished interest or pleasure in almost all activities, recurring thoughts of death or suicide, a sense of restlessness or being slowed down, significant weight loss or gain.† (WebMD). If any five of these nine symptoms are present at the same time for at least a two week period, it is evident that depression is the diagnosis and needs to be tended to immediately. It sometimes can be hard to decipher the difference between just feeling sad or a little bit off track and feeling depressed but the symptoms for depression are far more severe and noticeable. As a person it is important to know these symptoms because it is just as important to be able to notice the symptoms are occurring, whether it be in yourself or somebody you know. There are ways to notice if depression is occurring and they all coincide with the symptoms.Show MoreRelatedThe Most Common Diagnosed Depression Disorders1387 Words   |  6 PagesIt’s normal to feel down in the dumps every so often but, if it affects daily life activities you may have depression. Depression is when a person is excessively sad, anxious, or apathetic for a certain amount of time. There are other symptoms to classify depression but the main ones would be a consent feeling of sadness and the thought of suicide or death. When depression is consumed by a person it may be difficult to revert them without the assistance of treatments such as: Anti-depressants, PsychotherapyRead MoreThe Severity Of Depre ssion Epidemic1485 Words   |  6 Pagesnoticeable increase in the number people who have been diagnosed with depression According to the Center for Disease Control and Prevention one in ten Americans twelve and over are currently on antidepressants. This fact is especially true for females whose use was double of what men used. This increase in diagnosis and use of antidepressant many believe that depression is becoming an epidemic. Rottenberg mentions in his article the severity of depression epidemic according to the World Health OrganizationRead MoreEssay on Grief and Mourning1283 Words   |  6 Pagesself-medicate. Several literatures have indicated that individuals diagnosed with schizophrenia are susceptible to experiencing depression and suicidal thoughts. When it comes to be newly diagnosed with schizophrenia, clinicians need to proactive when working with these individuals. Helping them come to accept the diagnosis, to discuss and work through their emotions, and to develop a safety plan that will be helpful if clients experience depression or thoughts of suicide. In this paper, the topic of discussionRead MoreDepression : The Most Common Form Of Mental Illness1202 Words   |  5 PagesDepression, a serious epidemic in the nation, is a sickness that makes one feel sad or upset throughout the course of their daily lives. This illness called depression affects many people’s lives, does it not? This is here to analyze and explore how depression is one of many serious epidemics in society, why it’s important to know about, how it affects people, and what ways there are to help them. Depression, the most common form of mental illness known has taken over a quarter of the AmericanRead MoreHow Diabetes Does Not Cause Depression962 Words   |  4 Pagesexperienced depression, I want to know if there is a correlation between the two. Diabetes does not cause depression; although, I do believe there is a correlation between them. Diabetes can be a very tiring diseases. It can wear you out every day. Diabetes is something you can not walk away from -- it is there every day of your life. Same goes for depression. No matter what you do, it is always around. I believe that these two things go hand in hand. Being diabetes does not cause depression, but itRead MoreOutline and Evaluate Issues Surrounding the Classification and Diagnosis of Depression1051 Words   |  5 PagesClassification and Diagnosis of Depression Scheff’s Labelling Theory is a process which involves labelling people with mental disorders when they produce behaviour that does not fit with socially constructed norms and labelling those who reflect stereotyped or stigmatized behaviour of the ‘mentally ill’. A disadvantage of labelling an individual with depression is that labelling can accentuate and prolong the issue. In addition by labelling someone with depression who in fact is not depressed mayRead MoreSymptoms And Treatment Of Depression1015 Words   |  5 Pagesfocus on is a mood disorder called depression, or major depressive disorder. Depression is the most common mood disorder, and one of the most common mental illnesses. Depression is a mood disorder clinical depression affects how you feel, think and behave and can lead to a variety of emotional and physical problems. You may have trouble doing normal day-to-day activities, and depression may make you feel as if life isn’t worth living. ( Mayo Clinic Staff). Depression is more than what it seems to beRead MoreDepression in Teens1459 Words   |  6 Pagesone, if not multiple, mental illness. Some of these individuals have been diagnosed as a result of symptoms they exhibit, while others struggle in silence. For those that have received help, life slowly looks brighter for them, while loved ones work to help in any way possible. One of the serious mental illnesses that teens struggle with is depression. There are various aspects as to why an adolescent may develop depression including social, academic, or family problems, as well as stress or pastRead MoreDepression: Real or Imaginary?1471 Words   |  6 Pagesand The Dead Poet Society, depression is a common problem in our society. Many of us have known someone who has suffered from depression. Depression is a condition that affects everyone – not just the person diagnosed with it. It is imperative that depression be recognized and treated at an early stage , before it becomes an endangering factor in a person’s life. Depression is defined as extreme sorrow lasting at least two weeks. There are many symptoms of depression, as well as varying degreesRead MoreExperiencing Depression Throughout Life Essay936 Words   |  4 PagesDoes the average person experience depression throughout their life? Introduction In psychology, depression is a mental illness in which a person experiences deep, unshakable sadness and diminished interest in nearly all activities, it involves disturbances in emotion(Encarta). Depression is among the most common mental illnesses. About 8 percent of adults in the United States experience serious depression through out their lives (Encarta). Women are about three times more likely

Lpg in India Liberlization Privatization Globalization Essay Example For Students

Lpg in India Liberlization Privatization Globalization Essay Appendix I LPG and its Impact on India Liberalization, Privatization and Globalization (LPG) have become dominant forces shaping societies and economies the world over. These three processes are interrelated. Globalized economies are likely to be more privatized and liberalized economies. Rapid growth and poverty reduction in China, India, and other countries that were poor 20 years ago, has been a positive aspect of Liberalization Privatization and Globalization (LPG). India opened up the economy in the early nineties following a major crisis that led by a foreign exchange crunch that dragged the economy close to defaulting on loans. The response was a slew of Domestic and external sector policy measures partly prompted by the immediate needs and partly by the demand of the multilateral organizations. The new policy regime radically pushed forward in favor of a more open and market oriented economy. One of the major consequences of globalization, privatization and liberalization is the acceleration in Foreign Direct Investment flows. While Foreign Direct Investment has been increasing for sometime among the developed triad countries, in recent years it has spread to other parts of the world, especially to the giant emerging economies. The privatization and liberalization policies pursued by these emerging economies have created new opportunities for Foreign Direct Investment. International investors now face difficult problems such as choosing countries, evaluating risk-return relationships and assessing profitability in private and public sectors. Financial Services Sector has gained momentum since LPG and has shown major growth in the following aspects: 1) Disinvestment, PPP: In order to make the process of globalization smooth, privatization and liberalization policies are moving along as well. Under the privatization scheme, most of the public sector undertakings have been/ are being sold to private sector. Hence, PPP (Public Private Partnership), BOT (Build, Operate and Transfer) models are new areas developed for financial services. 2) Dismantling of The Industrial Licensing Regime: At present, only six industries are under compulsory licensing mainly on accounting of environmental safety and strategic considerations. Liberal policies require more prudent and cautious approach by the industry and hence provides more areas of servicing such as due diligence, social cost benefit analysis. ) Liberal FDI Policies: The Government has put in place a liberal and transparent foreign investment regime where most activities are opened to foreign investment on automatic route without any limit on the extent of foreign ownership. Some of the recent initiatives taken to further liberalize the FDI regime, inter alias, include opening up of sectors such as Insurance. This has given gro wth to consulting opportunities in the new and growing sectors and also intermediation services such as foreign transaction services have grown significantly. ) Non Resident Indians’ Investments: The general policy and facilities for foreign direct investment as available to foreign investors/ Companies are fully applicable to NRIs as well. In addition, Government has extended some concessions specially for NRIs and overseas corporate bodies having more than 60% stake by NRIs. This has lead to growth in fund management and wealth management services for NRIs. 5) Banking: Private sector banking has grown substantially and we have seen many new generation modern banks in India. ) Strategic Consulting: Wide-ranging financial sector reforms in the banking, capital markets, and insurance sectors, including the deregulation of interest rates, strong regulation and supervisory systems, and the introduction of foreign/private sector competition have triggered the requirement of strat egic consulting. 7) Foreign Exchange: Forex inflow has grown significantly and forex intermediation, management and hedging services are rising. MCS-SX has seen new derivatives in foreign currencies. ) Commodity Markets: Commodity transactions are more liberal and have introduced new products such as futures, options in Indian market. Commodity procurement and trade has also witnessed paradigm shift in the processes. ITC’s e-chaupal and Warna-wired village are bright examples for this. For over a century the United States has been the largest economy in the world but major developments have taken place in the world economy since then, leading to the shift of focus from the US and the rich countries of Europe to the two Asian giants- India and China. .ufcf4b3341ec845827b24cbb2609b6544 , .ufcf4b3341ec845827b24cbb2609b6544 .postImageUrl , .ufcf4b3341ec845827b24cbb2609b6544 .centered-text-area { min-height: 80px; position: relative; } .ufcf4b3341ec845827b24cbb2609b6544 , .ufcf4b3341ec845827b24cbb2609b6544:hover , .ufcf4b3341ec845827b24cbb2609b6544:visited , .ufcf4b3341ec845827b24cbb2609b6544:active { border:0!important; } .ufcf4b3341ec845827b24cbb2609b6544 .clearfix:after { content: ""; display: table; clear: both; } .ufcf4b3341ec845827b24cbb2609b6544 { display: block; transition: background-color 250ms; webkit-transition: background-color 250ms; width: 100%; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #95A5A6; } .ufcf4b3341ec845827b24cbb2609b6544:active , .ufcf4b3341ec845827b24cbb2609b6544:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .ufcf4b3341ec845827b24cbb2609b6544 .centered-text-area { width: 100%; position: relative ; } .ufcf4b3341ec845827b24cbb2609b6544 .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .ufcf4b3341ec845827b24cbb2609b6544 .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .ufcf4b3341ec845827b24cbb2609b6544 .ctaButton { background-color: #7F8C8D!important; color: #2980B9; border: none; border-radius: 3px; box-shadow: none; font-size: 14px; font-weight: bold; line-height: 26px; moz-border-radius: 3px; text-align: center; text-decoration: none; text-shadow: none; width: 80px; min-height: 80px; background: url(https://artscolumbia.org/wp-content/plugins/intelly-related-posts/assets/images/simple-arrow.png)no-repeat; position: absolute; right: 0; top: 0; } .ufcf4b3341ec845827b24cbb2609b6544:hover .ctaButton { background-color: #34495E!important; } .ufcf4b3341ec845827b24cbb2609b6544 .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .ufcf4b3341ec845827b24cbb2609b6544 .ufcf4b3341ec845827b24cbb2609b6544-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .ufcf4b3341ec845827b24cbb2609b6544:after { content: ""; display: block; clear: both; } READ: How to do your laundry EssayEconomics experts and various studies conducted across the globe envisage India and China to rule the world in the 21st century. India, which is now the fourth largest economy in terms of purchasing power parity, may overtake Japan and become third major economic power within 10 years. Questions: 1) After LPG what growth has taken place in the financial services sector in India? (Oct. 08)

Number Stairs Essay Example

Number Stairs Essay Part 1: To investigate the relationship between the stair total and the position of the stair shape on the grid, for other 3-step stairs. The number in the bottom left corner of the stair shape labels the position of the stair shape. The aim of this part of the investigation is to find a formula to work out the s-total (stair total) by knowing the s-number (stair number).45353625262725 + 26 + 27 + 35 + 36 + 45 = 194s-number = 25s-total = 1942111121231 + 2 + 3 + 11 + 12 + 21 = 50s-number = 1s-total = 502212132342 + 3 + 4 + 12 + 13 + 22 = 56s-number = 2s-total = 562313143453 + 4 + 5 + 13 + 14 + 23 = 62s-number = 3s-total = 622414154564 + 5 + 6 + 14 + 15 + 24 = 68s-number = 4s-total = 68Another observation here is that in each column of the stair shape, the difference between these rows of numbers in the same column, is 10. (Apart from the last column, which only consists of 1 number.) The difference between these numbers is 10 because in the grid, each row contains 10 numbers.Table of Results:s-numbers-total150+ 6256+ 632+ 646825194To go from one term to the next, simply add 6 each time. However, this does not show the relationship between the s-number and the s-total. This sequence (adding/subtracting a number each time), is known as an arithmetic sequence. A formula to find out the relationship between the s-number and the s-total is: first term + common difference x ( n 1 ). The first term here is 50, and the common difference is 6.50 + 6(n 1)= 50 + 6n 6= 6n + 442515165675 + 6 + 7 + 15 + 16 + 25 = 74(6 x 5) + 44 = 74s-number = 5s-total = 742616176786 + 7 + 8 + 16 + 17 + 26 = 80(6 x 6) + 44 = 80s-number = 6s-total = 8046363726272826 + 27 + 28 + 36 + 37 + 46 = 200(6 x 26) + 44 = 200s-number = 26s-total = 200After testing the formula to see if it works, a proof must be presented to show that it works for any s-number (with a few exceptions see Conclusion). If the s-number is represented as n:nAs mentioned in the aim, the bottom left corner square is the s-num ber (or in this example, known as nnn + 1n + 2Because the numbers in the grid increases by 1 each time, I can say that the two numbers, in the same row, increases by 1, thus the diagram; n + 1 and n + 2.n+20n+10nn + 1n + 2As mentioned previously, the numbers in the same column have a difference of 10. Thus, n + 10 and n + 20 as shown in the diagram. I can then show: (v)n+20n+10nn + 1n + 2If I add all these values (inside the squares) together:n + (n + 1) + (n + 2) + (n + 10) + (n + 11) + (n + 20)= 6n + 44*Proof 1: Note that there are 6 ns in this equation, because there are 6 squares.Thus, I have proven that my formula 6n + 44 works for every stair shape in that grid size. I can carry this investigation further by investigating the relationship between the stair totals on other number grids.Part 2: To further investigate the relationship between the stair totals and other step stairs on other number grids. I have decided to investigate the relationship between the stair totals on ot her number grids when the s-number stays constant because it will be easier to observe the relationship between the s-grid (stair number grid) and the s-total.7451231 + 2 + 3 + 4 + 5 + 7 = 22s-grid = 3s-total = 229561231 + 2 + 3 + 5 + 6 + 9 = 26s-grid = 4s-total = 2611671231 + 2 + 3 + 6 + 7 + 11 = 30s-grid = 5s-total = 3013781231 + 2 + 3 + 7 + 8 + 13 = 34s-grid = 6s-total = 34Table of Results:s-grids-total322+ 4436+ 4530+46341050In the table, it shows that the s-total increases by 4 each time as the s-grid increases by 1. (When g = grid size,) this is because:n+2gn + gn+g+1nn + 1n + 2; Previously, I noticed that the difference between each row in the same column is the grid size.n + (n + 1) + (n + 2) + (n + g) + (n + g + 1) + (n + 2g)= 6n + 4g + (4)**Note: 6n + 4g because there are 4gs in the formula (as shown above).Now that I have found out the relationship between the s-number, s-grid, and the s-total, I can carry this investigation further by investigating the relationship betw een the other step stairs, s-number, s-grid, and s-totals.I will investigate the relationship between the s-number, s-total, s-grid and s-shape (stair shape). The s-shape will be investigated by enlargement; 1 square increase in length, and 1 square increase in width.nThe s-number remains at the bottom left corner of the stair shape. Instead of 6 squares, there are 10. Based on my previous observations, I can predict the relationship between this s-shape, the s-number, s-grid, and the s-total as: 10n + 10g + 10.I can check my prediction:n+3gn+2gn+2g+1n+gn+g+1n+g+2nn+1n+2n+3n+(n+1)+(n+2)+(n+3)+(n+g)+(n+g+1)+(n+g+2)+(n+2g)+(n+2g+1)+(n+3g)= 10n + 10g + 10I shall investigate the next stair shape, which will have a height of 5 squares, and a width of 5 squares, a total of 15 squares.n+4gn+3gn+3g+1n+2gn+2g+1n+2g+2n+gn+g+1n+g+2n+g+3nn+1n+2n+3n+4n+(n+1)+(n+2)+(n+3)+(n+4)+(n+g+)+(n+g+1)+(n+g+2)+(n+g+3)+(n+2g)+(n+2g+a)+(n+2g+2)+(n+3g)+(n+3g+1)+(n+4g)= 15n + 20g + 20Observation: I have noticed that the number of squares in each stair shape has a link with triangle numbers. For example: a triangle number sequence is as follows:When the stair shape size was 3, it has 6 squares. When the stair shape size was 4, it has 10 squares, and when the stair shape size was 5, it has 15 squares. Just like the diagram on the previous page, the pattern for the stair shape size is the same pattern as triangle numbers. This is because the stair shape is a triangle:s-sizeno. of squares23+ 336+ 4410+ 5515+ 6621I can predict the number of squares they are for any s-size, following the triangle number sequence.The formula for the triangle number sequence is:(Where s is the s-size.)I should test this formula to check if it works. I shall try it on an s-size of 7.7+ 6+ 5+ 4+ 3+ 2+ 1Number of squares in this diagram: 28Since I have successfully tested out that the relationship between the s-size and the number of squares in that s-size is the same as triangle number sequence; thus the formula to work out the s-total when the s-number, s-grid, and s-size is known, can be currently worked out as:s-total = (Note: X is the unknown)In this case, I have used the Xs twice, only because they are of equal value. By putting the s-size value and the formula in a table, I could see why I used the Xs twice in the formula.s-sizeformula36n + 4g + 4410n + 10g + 10515n + 20g + 20The co-efficient has the same value as the constant.I then needed to find to how to find out the co-efficient and the constant. Because there doesnt seem to have a constant difference between the co-efficient, I shall use the method changing differences to find the formula for the co-efficient. There is a formula to find the changing difference known as the Gregory Newton Formula.Firstly, I would need to find the value of the co-efficient when the s-size is 0. Obviously, if the s-size is 0, the s-total will be 0, as there are no squares to add up its value. To show how I worked out the difference in order to use th e Gregory Newton Formula, I made a table of differences:s-sizeX1st Difference2nd Difference3rd Difference4th Difference00+ 010+ 1+ 1+ 121+ 2+ 0+ 3+ 134+ 3+ 0+ 6+ 1410+ 4+ 10520After producing the table of differences, I was able to carry out the Gregory Newton Formula and found out how to find X:However, I must test this formula to see if it works. I shall test it out on an s-size of 6.n+5gn+4gn+4g+1n+3gn+3g+1n+3g+2n+2gn+2g+1n+2g+2n+2g+3n+gn+g+1n+g+2n+g+3n+g+4nn+1n+2n+3n+4n+5n+(n+1)+(n+2)+(n+3)+(n+4)+(n+5)+(n+g)+(n+g+1)+(n+g+2)+(n+g+3)+(n+g+4)+(n+2g)+(n+2g+1)+(n+2g+2)+(n+2g+3)+(n+3g)+(n+3g+1)+(n+3g+2)+(n+4g)+(n+4g+1)+(n+5g)= 21n + 35g + 35It appears that this section of the formula works. Now the new current formula is:s-total =Important: However, this formula has its limitations. For example, the step stair may be placed on a certain area that causes the step stair to be off the grid. This means that the formula cannot calculate the s-total as there are no numbers off the grid. Per haps another limitation can be found if it cannot calculate negative numbers.I shall test it out on an s-size of 7, s-grid of 8, and the s-number is 20.6860615253544445464736373839402829303132332021222324252620 + 21 + 22 + 23 + 24 + 25 + 26 + 28 + 29 + 30 + 31 + 32 + 33 + 36 + 37 + 38 + 39 + 40 + 44 + 45 + 46 + 47 + 52 + 53 + 54 + 60 + 61 + 68= 1064Now to test the formula out on negative numbers:1314151617187891011121234560-1-2-3-4-5-6-7-8-9-10-11-12-13-14-15-16-17(-12)+(-13)+(-14)+(-6)+(-7)+(0)= -52It appears that negative numbers do not work with this formula, thus the formula is limited to positive integers and that the stair shape must not have any part of it exceeding the grid. However, the formula works excluding the limitations. In conclusion, the relationship between the s-number, s-grid, s-size, and s-total is:s-total =(With certain restrictions as mentioned above)However, this formula can be simplified because as previously mentioned, the Xs were in 2 parts of the formula, thus it can be simplified. The first part of the equation where the formula for triangle number lies, can also be simplified to:An extention of this investigation, could be to investigate the relationship between negative numbers, or transformation of the stair shape.