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Tuesday, August 25, 2020
Summarise the main development of a child from the age range 0-2, 3-5 years and 5-8 years Essay Example for Free
Sum up the primary improvement of a youngster from the age run 0-2, 3-5 years and 5-8 years Essay Advancement is the way toward increasing new aptitudes in all everyday issues. All kids are people in this way, in spite of the fact that they will all experience similar phases of advancement, they may not really experience these simultaneously. Consequently, the term ââ¬Ëaverage childââ¬â¢ is utilized when discussing the procedure of improvement, however we ought to consider each childââ¬â¢s advancement progress independently. The improvement of a kid is generally classified into five fundamental territories: Physical, Intellectual, Emotional, Social and Language. Physical Development. An infant will lie on his back with his head to the other side and his head will slack when he is pulled up to sit. He will have crude reflexes, for example, getting a handle on and sucking. By 3 months he will have the option to kick his legs, play with his own hands and lift his own head. At a half year, he will have the option to sit with help and pass a toy from one hand to the next. He will have made an enormous progress by 9 months and may sit without help, creep or mix and will start to utilize his file, center finger and thumb together to get little things. He will have started to walk independent by year and a half, can utilize a spoon and will endeavor to kick a ball. By 2 years, he will have the option to utilize a pencil to make straightforward structures, assemble a pinnacle of six blocks and begin to utilize his favored hand. Somewhere in the range of 3 and 5 years, he will have the ability to bounce from a low advance, pedal a tricycle and turn single pages in a book. His gross engine abilities improvement will imply that he will have the option to walk in reverse and advances along a line and point, toss and catch a huge ball. By 8 years of age he will have the option to bounce from statures and he will have improved his adjusting abilities enough to stroll along a divider or pillar and ride a bike without stabilizers. The improvement in his fine engine aptitudes will permit him to control a pencil in a little region and do itemized drawing. He will likewise have the control to tie and loosen his shoelaces and fabricate many-sided models. Scholarly (or psychological) advancement. Scholarly advancement is about how kids learn, think and create thoughts. Youngsters grow mentally at various rates and some in regions that others don't. During childbirth an infant will squint in response to brilliant light and cry as a reaction to his fundamental needs. By a half year he is effortlessly diverted by developments and questions and will make endeavors to connect forâ them. He will likewise place everything in his mouth. By a year he will perceive natural individuals at 6 meters and have the option to mimic everyone around him and the states of mind they express, for instance chuckling when somebody he is with is snickering. By 2 years of age he will appreciate nonexistent play and will regularly converse with himself. He will have the option to highlight and perceive the names of parts of the body. Between the ages of 3 and 5 years, his fine engine abilities will have sufficiently expanded to have the option to control a pencil satisfactorily and cut with scissors. He will have the option to draw a square and a scope of letters, some suddenly and paint with a huge paint brush. At 5 years old, the ideas of numeracy and proficiency will be inside his abilities and numerous youngsters will have the option to check and perceive straightforward words. Between the ages of 6 and 8 his capacity to compose will be creating, he will peruse straightforward books, anticipate next occasions and he will know his birthday. Enthusiastic Development From birth a child will have the option to react to their principle carer. He will look eagerly at his carer and by about a month and a half will begin to grin as a reaction to acknowledgment of that individual. At a half year he will give the primary indications of misery at the partition from his carer and dread of strangers.He will likewise effectively look for attention.Between 9 and a year, he will appreciate the organization of those individuals that he knows about. From 1 year old he will be additionally requesting and emphatic and hissy fits may begin. He recognizes himself as well as other people, however he is as yet egocentric and shows rage at being told ââ¬Ënoââ¬â¢. He is additionally beginning to create object perpetual quality, he no longer accepts that an article that has been covered up is entirely longer there. At 2 years old he will appreciate different childrenââ¬â¢s organization however will even now be hesitant to share his toys. He will, in any case, have the option to adapt to brief times of division from his carer, for instance while at nursery. At 3 years he is increasingly mindful of his own sentiments and ready to disclose to others how he is feeling Between 5 and 8 years he will appreciate co-usable play and get thinking and alternating. He will be progressively less on edge about partition and have a decent feeling of mindfulness. Social Development A child is brought into the world with the capacity to be agreeable. On the off chance that an infant gets troubled, he can regularly be appeased by the sight, contact or smell of his fundamental carer.Between the ages of 3 and a year he will have the option to associate with his condition, mirroring the states of mind showed by others. He will find how to play alone and engage himself for extensive periods. With his expanding versatility, he will turn out to be progressively certain and somewhere in the range of 2 and 5 years of age he will figure out how to make companions, despite the fact that on occasion he may depend on fits of rage when he doesn't get his own particular manner. By 8 years of age he will be genuinely free and certain with an expanding feeling of good and bad and he will have the option to shape firm fellowships with his friends. Language Development There are two particular phases of language improvement; pre-phonetic and semantic. The pre-semantic stage is from birth to a year, when he begins to state his first words.This is the period where an infant can just communicate by crying, when essential needs require consideration, cooing, in light of his carerââ¬â¢s talk and murmuring or laughing when playing. From around 9 months, he will start to ââ¬Ëbabbleââ¬â¢ sounds, for example, ââ¬Ëmamaââ¬â¢ or ââ¬Ëdadaââ¬â¢ and he will have the option to mirror straightforward creature clamors. The semantic stage from 1 year old will bring the beginnings of conspicuous words and the ââ¬Ëaverageââ¬â¢ youngster will have a jargon of around 50 words when he is 2. Somewhere in the range of 2 and 3 years he has a quickly extending jargon and can get baffled in the event that he can't communicate in words. By 5 years of age he will be a sure speaker and will perceive new words and solicit the importance from them. His jargon will be in the area of approximately 5000 words. By 8 years of age he will have the option to talk in various tenses and account for himself with certainty.
Saturday, August 22, 2020
Compare and contrast The Andy Griffith Show and I Love Lucy Essay
Investigate The Andy Griffith Show and I Love Lucy - Essay Example There are no violations for Andy to explain, and the greater part of his work includes intervening, philosophizing and quieting his cousin Deputy Barney. Then again, I love Lucy is the every day biography of a couple, Lucy and Ricky Ricardo. The two are hitched and draw out the logical inconsistency in intercultural relationships that were very unusual at the hour of this show. Lucy is an American lady while Ricky is a Cuban man. Lucy is a housewife and experiences numerous entertaining and unusual events throughout her life. She commits numerous errors and Ricky is constantly energized whenever this occurs as he gets an opportunity to address her. The couple carries on with a genuine wedded life that likewise includes thrilling minutes beside the interesting events that happen frequently. The couple lives in a basic home in a local that is loaded up with agreeable individuals as far as neighbors. The pace of the I Love Lucy show is quick and joyful, with neighbors moving from entryway to entryway without thumping. The earth they live in and the lives they live permit them to collaborate unreservedly and effortlessly. The pace of the show is vivacious through the melodic exhibitions by Ricky Ricardo. Lucy endeavors to join a portion of these moves in order to appreciate them with her significant other. This fairly brisk pace negates that of the Andy Griffith Show. This show is portrayed by a moderate pace that can be depicted as lethargic. This pace is on the grounds that the life of Andy isn't set apart by violations and ensuing examinations that make up the common existence of a Sheriff. He invests his energy ruminating and conversing with his cousin Barney. He additionally takes care of issues with neighbors and increases a ton of prominence in the area. The setting of the I Love Lucy show is during the 1950s. It delineates a decent domain in a highly contrasting show. This film is set in an American domain that despite everything thinks that its weird to have Americans hitched to non-Americans. Lucyââ¬â¢s spouse is a Cuban, and couple shows the chance
Monday, August 3, 2020
8 Celebrity Memoirs to Read this Fall
8 Celebrity Memoirs to Read this Fall Im a huge fan of celebrity memoirs. Whether Im reading about travels in France with Julia Child or if Im devouring the illustrious career of Doris Roberts, I just have an affinity for celebrity memoirs. I honestly think it has something to do with my love for celebrity gossip, but lets not get into that. Celebrities are often these untouchable people. We see the characters they portray on the big screen and then we see their real lives on social media. In either of these respects, I find myself wanting to deeply know these people. I want to be their friends and I want them to give me life advice that helped them succeed or fail at whatever theyre doing. So of course I want to read these memoirs and see the world through the celebritys eyes. What was it like growing up? How did you become the figure you are? What were the naysayers saying? With that, heres eight memoirs coming out in Fall 2018 that I hope you add to your reading lists. Whiskey in a Teacup: What Growing Up in the South Taught Me About Life, Love Baking Biscuits by Reese Witherspoon Reese Witherspoonâs grandmother Dorothea always said that a combination of beauty and strength made southern women âwhiskey in a teacup.â We may be delicate and ornamental on the outside, she said, but inside weâre strong and fiery. Reeseâs southern heritage informs her whole life, and she loves sharing the joys of southern living with practically everyone she meets. She takes the South wherever she goes with bluegrass, big holiday parties, and plenty of Dorotheaâs fried chicken. Itâs reflected in how she entertains, decorates her home, and makes holidays special for her kidsâ"not to mention how she talks, dances, and does her hair (in these pages, you will learn Reeseâs fail-proof, only slightly insane hot-roller technique). Reese loves sharing Dorotheaâs most delicious recipes as well as her favorite southern traditions, from midnight barn parties to backyard bridal showers, magical Christmas mornings to rollicking honky-tonks. Itâs easy to bring a little bit of Reeseâs world into your home, no matter where you live. After all, thereâs a southern side to every place in the world, right? This Will Only Hurt a Little by Busy Philipps A memoir by the beloved comedic actress known for her roles on Freaks and Geeks, Dawsons Creek, and Cougartown who has become the breakout star on Instagram storiesâ¦imagine I Love Lucy mixed with a modern lifestyle guru (The New Yorker). Busy Philippss autobiographical book offers the same unfiltered and candid storytelling that her Instagram followers have come to know and love, from growing up in Scottsdale, Arizona and her painful and painfully funny teen years, to her life as a working actress, mother, and famous best friend. Busy is the rare entertainer whose impressive arsenal of talents as an actress is equally matched by her storytelling ability, sense of humor, and sharp observations about life, love, and motherhood. Her conversational writing reminds us what we love about her on screens large and small. From film to television to Instagram, Busy delightfully showcases her wry humor and her willingness to bare it all. Ive been waiting my whole life to write this book. Im just so grateful someone asked. Otherwise, what was the point of any of it?? Cravings: Hungry for More by Chrissy Teigen Cravings: Hungry for More takes us further into Chrissyâs kitchenâ¦and life. Itâs a life of pancakes that remind you of blueberry pie, eating onion dip with your glam squad, banana bread that breaks the internet, and a little something called Pad Thai Carbonara. After two years of parenthood, falling in love with different flavors, and relearning the healing power of comfort food, this book is like Chrissyâs new edible diary: recipes for quick-as-a-snap meals; recipes for lighter, brighter, healthier-ish living; and recipes that, well, are gonna put you to bed, holding your belly. And it will have you hungry for more. Becoming by Michelle Obama In a life filled with meaning and accomplishment, Michelle Obama has emerged as one of the most iconic and compelling women of our era. As First Lady of the United States of Americaâ"the first African American to serve in that roleâ"she helped create the most welcoming and inclusive White House in history, while also establishing herself as a powerful advocate for women and girls in the U.S. and around the world, dramatically changing the ways that families pursue healthier and more active lives, and standing with her husband as he led America through some of its most harrowing moments. Along the way, she showed us a few dance moves, crushed Carpool Karaoke, and raised two down-to-earth daughters under an unforgiving media glare. In her memoir, a work of deep reflection and mesmerizing storytelling, Michelle Obama invites readers into her world, chronicling the experiences that have shaped herâ"from her childhood on the South Side of Chicago to her years as an executive balancing the demands of motherhood and work, to her time spent at the worldâs most famous address. With unerring honesty and lively wit, she describes her triumphs and her disappointments, both public and private, telling her full story as she has lived itâ"in her own words and on her own terms. Warm, wise, and revelatory, Becoming is the deeply personal reckoning of a woman of soul and substance who has steadily defied expectationsâ"and whose story inspires us to do the same. I Might Regret This: Essays, Drawings, Vulnerabilities, and Other Stuff by Abbi Jacobson When Abbi Jacobson announced to friends and acquaintances that she planned to drive across the country alone, she was met with lots of questions and opinions: Why wasnt she going with friends? Wouldnt it be incredibly lonely? The North route is better! Was it safe for a woman? The Southern route is the way to go! You should bring mace! And a common oneâ¦why? But Abbi had always found comfort in solitude, and needed space to step back and hit the reset button. As she spent time in each city and town on her way to Los Angeles, she mulled over the big questionsâ"What do I really want? What is the worst possible scenario in which I could run into my ex? How has the decision to wear my shirts tucked in been pivotal in my adulthood? In this collection of anecdotes, observations and reflectionsâ"all told in the sharp, wildly funny, and relatable voice that has endeared Abbi to critics and fans alikeâ"readers will feel like theyre in the passenger seat on a fun and, ultimately, inspiring journey. With some original illustrations by the author. My Squirrel Days by Ellie Kemper There comes a time in every sitcom actressâs life when she is faced with the prospect of writing a book. When Ellie Kemperâs number was up, she was ready. Contagiously cheerful, predictably wholesome, and mostly inspiring except for one essay about her husbandâs feet, My Squirrel Days is a funny, free-wheeling tour of Ellieâs lifeâ"from growing up in suburban St. Louis with a vivid imagination and a crush on David Letterman to moving to Los Angeles and accidentally falling on Doris Kearns Goodwin. But those are not the only famous names dropped in this synopsis. Ellie will also share stories of inadvertently insulting Ricky Gervais at the Emmy Awards, telling Tina Fey that she has âgreat hairâ"really strong and thick,â and offering a maxi pad to Steve Carell. She will take you back to her childhood as a nature lover determined to commune with squirrels, to her college career as a bench-warming field hockey player with no assigned position, and to her young professional days writing radio commercials for McDonaldâs but never getting paid. Ellie will guide you along her journey through adulthood, from unorganized bride to impatient wife to anxious mother whoâ"as recently observed by a sassy hairstylistâ"âdresses like a mom.â Well, sassy hairstylist, Ellie Kemper is a mom. And she has been dressing like it since she was four. Ellie has written for GQ, Esquire, The New York Times, McSweeneyâs, and The Onion. Her voice is the perfect antidote to the chaos of modern life. In short, she will tell you nothing you need to know about making it in show business, and everything you need to know about discreetly changing a diaper at a Cibo Express. American Like Me: Reflections on Life Between Cultures by America Ferrera America Ferrera has always felt wholly American, and yet, her identity is inextricably linked to her parentsâ homeland and Honduran culture. Speaking Spanish at home, having Saturday-morning-salsa-dance-parties in the kitchen, and eating tamales alongside apple pie at Christmas never seemed at odds with her American identity. Still, she yearned to see that identity reflected in the larger American narrative. Now, in American Like Me, America invites thirty-one of her friends, peers, and heroes to share their stories about life between cultures. We know them as actors, comedians, athletes, politicians, artists, and writers. However, they are also immigrants, children or grandchildren of immigrants, indigenous people, or people who otherwise grew up with deep and personal connections to more than one culture. Each of them struggled to establish a sense of self, find belonging, and feel seen. And they call themselves American enthusiastically, reluctantly, or not at all. Ranging from the heartfelt to the hilarious, their stories shine a light on a quintessentially American experience and will appeal to anyone with a complicated relationship to family, culture, and growing up. In Pieces by Sally Field One of the most celebrated, beloved, and enduring actors of our time, Sally Field has an infectious charm that has captivated the nation for more than five decades, beginning with her first TV role at the age of seventeen. From Gidgets sweet-faced girl next door to the dazzling complexity of Sybil to the Academy Award-worthy ferocity and depth of Norma Rae and Mary Todd Lincoln, Field has stunned audiences time and time again with her artistic range and emotional acuity. Yet there is one character who always remained hidden: the shy and anxious little girl within. With raw honesty and the fresh, pitch-perfect prose of a natural-born writer, and with all the humility and authenticity her fans have come to expect, Field brings readers behind-the-scenes for not only the highs and lows of her star-studded early career in Hollywood, but deep into the truth of her lifelong relationshipsâ"including her complicated love for her own mother. Powerful and unforgettable, In Pieces is an inspiring and important account of life as a woman in the second half of the twentieth century. What memoirs are you excited about? Sign up for True Story to receive nonfiction news, new releases, and must-read forthcoming titles. 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Saturday, May 23, 2020
Use Of Information Systems On The Life Of Data - 910 Words
Use of Information Systems in the Life of Data Is there a way to differentiate between whether we know something presented in an Information System, whether we believe it, or simply have a piece of information. And further, is an information system a valid tool for moving our thinking up the hierarchy. Actions and decision are what matter most when you are traversing the DIKW hierarchy. There are many actions that can be taken, and decisions that can be made by information systems. In fact some might argue that certain decisions can only effectively be made with the assistance of technology. Humans have gone thousands of years without information systems and have derived knowledge out of practice and experience. The invention (discovery?) of Information Systems has only accelerated the speed and effectiveness of knowledge creation, transfer, and management. Decision Support Systems are prominent information systems used to aid in decision making within an organization. These systems take a variety of input and aid management in an organization in deciding between certain decisions. When there are conflicting results provided by both a decision support system and a human, you must make the decision as to which one is providing more credible results. HERE IS SOME MORE INFORMATION ABOUT THAT The tools we use today to aid in this conversion of data are extremely vast. Carvalho and Ferreira grouped these types of systems into 10 categories: Intranet-based systems,Show MoreRelatedAbstract:. With The Development Of The Business, The Competitive1605 Words à |à 7 Pageshave advantage of the competitive. Customer relationship management system as a new technology was used in the company. this essay is talk about the different part and the function of the customer relationship management system, introduce the product of customer relationship management system and also talk about the practical application about the customer relationship management system. Key word Customer relationship management system. company Review the Theories Customer relationship management:Read Morecgmt 400 week 3 individual securing and protecting information1490 Words à |à 6 PagesProtecting Information Michael Anthony Horton University of Phoenix August 18, 2014 Instructor: Dr. Stephen Jones Securing and Protecting Information The specific purpose of this paper is to describe the authentication process and to describe how this and other information security considerations will affect the design and development process for new information systems. The authentication process is a necessity for safeguarding systems against variousRead MoreDatabase Management and Information Retrieval1367 Words à |à 5 PagesDifferentiate between database management system and information retrieval system by focusing on their functionalities. Answer A database management system (DBMS) is the main software tools of the database management approach because it controls the creation, maintenance and use of the databases of an organization and its end users. Information retrieval is a system that to provide the relevant information based on the user needed. This process can be find through the passwords or keywords or queryRead MoreInformation Lifecycle Management1111 Words à |à 4 PagesInformation Lifecycle Management How do you think information lifecycle management will affect coordination and conflicts between operations managers and information technology managers? It has become progressively more documented that information is the most important strategic resource that any organization has to deal with. Key to the compilation, analysis, production and allocation of information within an organization is the quality of IT services provided to the business. It is necessaryRead MoreWhat Is The Physical Security Of A Data Center?1307 Words à |à 6 Pagesparticularly how their data can be accessed quickly from almost anywhere and leveraged when needed. However, it can be easy to overlook the fact that the centers that safeguard cloud-stored data are not located somewhere ââ¬Å"up there,â⬠but are in fact very real physical spaces (Chris, 2015). Many organizations focus almost exclusively on virtual security and nearly forget about the building or room that houses their data and whether it is properly secured. To be fully secure, a data center one must considerRead Moreinformation system1104 Words à |à 5 PagesDistinguish data from information and describe the characteristics used to evaluate the value of data? Data versus Information 1 ,Data 2, information 3,knowledge. 1, Data raw facts, such as an employee s name and number of hours worked in a week, inventory part numbers, or sales orders .several types of data can be used to represent these facts Data Represented by alphanumeric data numbers, letters, and other characters image data graphic images or pictures audio data soundRead Moreââ¬Å"Blue Eyesâ⬠Technology1538 Words à |à 7 Pagesroom and switch on your computer, and then it tells you ââ¬Å"Hey friend, good morning you seem to be a bad mood today. And then it opens your mail box and shows you some of the mails and tries to cheer you. It seems to be a fiction, but it will be the life lead by ââ¬Å"BLUE EYESâ⬠in the very near future. à à à The basic idea behind this technology is to give the computer the human power. We all have some perceptual abilities. That is we can understand each others feelings. For example we canRead MoreInformation Systems For An Emergency Department Or Med / Surg Unit1459 Words à |à 6 PagesPeople Resources For any Information system to function correctly people are needed. IS specialist develop and operate information systems for end users to use and manage. System analysts design Information systems based on the requirements of the end users to create the desired functionality of the system. The cooperation between end users and system designers is key in developing a well-balanced and thorough information system. End Users The development of information systems requires cooperationRead MoreThe Right to Privacy1152 Words à |à 5 Pagesthese concerns remain, but many others have joined them. Advances in information and communications technology have increased our ability to collect, store and transmit data about individuals. While these advances could be considered useful, some see them as a situation where anyone can watch and record the actions of every individual, and where the individual has lost control over information about herself and thus over her very life. As a reaction to these concerns, new regulations have been formulatedRead MoreImportance Of Information Technology And The Healthcare Industry1452 Words à |à 6 PagesIMPORTANCE OF INFORMATION TECHNOLOGY IN HEALTHCARE. Jude Alumuku, SEIS 605-07 Alum0001@stthomas.edu I. Introduction. II. Background Information A. What is Information Technology B. Information technology and the healthcare industry. C. Facts about Information technology and its application in Healthcare 1.0 Strategic Analysis ââ¬â Industry. 1.1 Strategic Analysis ââ¬â Competition III. Healthcare Information Technology Adoption, Quality and Costs IV. Problems With health Information technology V.
Monday, May 11, 2020
Definition and Examples of Subordinate Clauses
Inà English grammar, a subordinate clause is aà group of words that has both a subject and a verb but (unlike an independent clause) cannot stand alone as a sentence. Also known as a dependent clause. Contrast this with a main clause and coordinate clause. Subordinate clauses are usually attached to main clauses or embedded in matrix clauses. Pronunciation: Suh-BOR-din-it Exercises Exercise inà identifying adverb clausesPractice identifying independent and dependent clauses Examples and Observations Whenever you find yourself on the side of the majority, it is time to pause and reflect.(Mark Twain)That spring, when I had a great deal of potential and no money at all, I took a job as a janitor.(James Alan McPherson, Gold Coast, 1969)Memory is deceptive because it is colored by todays events.(Albert Einstein)Bailey and I did arithmetic at a mature level because of our work in the store, and we read well because in Stamps there wasnt anything else to do.(Maya Angelou,à I Know Why the Caged Bird Sings, 1969)If you cant leave in a taxi you can leave in a huff. If thats too soon, you can leave in a minute and a huff.(Groucho Marx, Duck Soup)If a free society cannot help the many who are poor, it cannot save the few who are rich.(John F. Kennedy)When you lose your laugh, you lose your footing.(Ken Kesey)Every book is a childrens book if the kid can read.(Mitch Hedberg) Grammatical Juniors Subordinate clauses are grammatical juniors, dependent on the main clause for complete sense. They are not subordinate in any other way; they need not be stylistically inferior, and indeed may be more informative than the main clause they depend on, as in this example: If you go on with a diet that consists exclusively of cottage cheese, dry toast, and Brazil nuts, I shall worry. The main clause is I shall worry: it is, I think, rather feeble in view of what precedes it, a sad anticlimax to what was promising to be a fairly arresting sentence. But although that previous clause is much more interesting in every other way, it remains grammatically subordinate: it could not stand on its own.(Richard Palmer, Write in Style: A Guide to Good English, 2nd ed. Routledge, 2002) Types of Subordinating Conjunctions Finite clauses are introduced by a subordinator, which serves to indicate the dependent status of the clause together with its circumstantial meaning. Formally, subordinating conjunctions can be grouped as follows: simple conjunctions: when, whenever, where, wherever, because, if, unless, until, while, as, althoughconjunctive groups: as if, as though, even if, even though, even when, soon after, no soonercomplex conjunctions:: there are three subclasses: (i) derived from verbs . . .: provided (that), granted (that), considering (that), seeing (that), suppose (that), supposing (that), so (that)(ii) containing a noun: in case, in the event that, to the extent that, in spite of the fact that, the day, the way(iii) adverbial: so/as long as, as soon as, so/as far as, much as, now (that) Angela Downing,à English Grammar: A University Course. Routledge, 2006) Subordinate Clauses in Poetry When I heard the learnââ¬â¢d astronomer;When the proofs, the figures, were ranged in columns before me;When I was shown the charts and the diagrams, to add, divide, and measure them;When I, sitting, heard the astronomer, where he lectured with much applause in the lecture-room,How soon, unaccountable, I became tired and sick;Till rising and gliding out, I wanderââ¬â¢d off by myself,In the mystical moist night-air, and from time to time,Lookââ¬â¢d up in perfect silence at the stars.(Walt Whitman, When I Heard the Learnââ¬â¢d Astronomer. Leaves of Grass)
Wednesday, May 6, 2020
Vampire Academy Chapter 1 Free Essays
string(50) " I could see the silhouettes of trees and bushes\." ONE I FELT HER FEAR BEFORE I heard her screams. Her nightmare pulsed into me, shaking me out of my own dream, which had had something to do with a beach and some hot guy rubbing suntan oil on me. Images ââ¬â hers, not mine ââ¬â tumbled through my mind: fire and blood, the smell of smoke, the twisted metal of a car. We will write a custom essay sample on Vampire Academy Chapter 1 or any similar topic only for you Order Now The pictures wrapped around me, suffocating me, until some rational part of my brain reminded me that this wasnââ¬â¢t my dream. I woke up, strands of long, dark hair sticking to my forehead. Lissa lay in her bed, thrashing and screaming. I bolted out of mine, quickly crossing the few feet that separated us. ââ¬Å"Liss,â⬠I said, shaking her. ââ¬Å"Liss, wake up.â⬠Her screams dropped off, replaced by soft whimpers. ââ¬Å"Andre,â⬠she moaned. ââ¬Å"Oh God.â⬠I helped her sit up. ââ¬Å"Liss, you arenââ¬â¢t there anymore. Wake up.â⬠After a few moments, her eyes fluttered open, and in the dim lighting, I could see a flicker of consciousness start to take over. Her frantic breathing slowed, and she leaned into me, resting her head against my shoulder. I put an arm around her and ran a hand over her hair. ââ¬Å"Itââ¬â¢s okay,â⬠I told her gently. ââ¬Å"Everythingââ¬â¢s okay.â⬠ââ¬Å"I had that dream.â⬠ââ¬Å"Yeah. I know.â⬠We sat like that for several minutes, not saying anything else. When I felt her emotions calm down, I leaned over to the nightstand between our beds and turned on the lamp. It glowed dimly, but neither of us really needed much to see by. Attracted by the light, our housemateââ¬â¢s cat, Oscar, leapt up onto the sill of the open window. He gave me a wide berth ââ¬â animals donââ¬â¢t like dhampirs, for whatever reason ââ¬â but jumped onto the bed and rubbed his head against Lissa, purring softly. Animals didnââ¬â¢t have a problem with Moroi, and they all loved Lissa in particular. Smiling, she scratched his chin, and I felt her calm further. ââ¬Å"When did we last do a feeding?â⬠I asked, studying her face. Her fair skin was paler than usual. Dark circles hung under her eyes, and there was an air of frailty about her. School had been hectic this week, and I couldnââ¬â¢t remember the last time Iââ¬â¢d given her blood. ââ¬Å"Itââ¬â¢s been like?à more than two days, hasnââ¬â¢t it? Three? Why didnââ¬â¢t you say anything?â⬠She shrugged and wouldnââ¬â¢t meet my eyes. ââ¬Å"You were busy. I didnââ¬â¢t want to ââ¬â ââ¬Å" ââ¬Å"Screw that,â⬠I said, shifting into a better position. No wonder she seemed so weak. Oscar, not wanting me any closer, leapt down and returned to the window, where he could watch at a safe distance. ââ¬Å"Come on. Letââ¬â¢s do this.â⬠ââ¬Å"Rose ââ¬â ââ¬Å" ââ¬Å"Come on. Itââ¬â¢ll make you feel better.â⬠I tilted my head and tossed my hair back, baring my neck. I saw her hesitate, but the sight of my neck and what it offered proved too powerful. A hungry expression crossed her face, and her lips parted slightly, exposing the fangs she normally kept hidden while living among humans. Those fangs contrasted oddly with the rest of her features. With her pretty face and pale blond hair, she looked more like an angel than a vampire. As her teeth neared my bare skin, I felt my heart race with a mix of fear and anticipation. I always hated feeling the latter, but it was nothing I could help, a weakness I couldnââ¬â¢t shake. Her fangs bit into me, hard, and I cried out at the brief flare of pain. Then it faded, replaced by a wonderful, golden joy that spread through my body. It was better than any of the times Iââ¬â¢d been drunk or high. Better than sex ââ¬â or so I imagined, since Iââ¬â¢d never done it. It was a blanket of pure, refined pleasure, wrapping me up and promising everything would be right in the world. On and on it went. The chemicals in her saliva triggered an endorphin rush, and I lost track of the world, lost track of who I was. Then, regretfully, it was over. It had taken less than a minute. She pulled back, wiping her hand across her lips as she studied me. ââ¬Å"You okay?â⬠ââ¬Å"I?à yeah.â⬠I lay back on the bed, dizzy from the blood loss. ââ¬Å"I just need to sleep it off. Iââ¬â¢m fine.â⬠Her pale, jade-green eyes watched me with concern. She stood up. ââ¬Å"Iââ¬â¢m going to get you something to eat.â⬠My protests came awkwardly to my lips, and she left before I could get out a sentence. The buzz from her bite had lessened as soon as she broke the connection, but some of it still lingered in my veins, and I felt a goofy smile cross my lips. Turning my head, I glanced up at Oscar, still sitting in the window. ââ¬Å"You donââ¬â¢t know what youââ¬â¢re missing,â⬠I told him. His attention was on something outside. Hunkering down into a crouch, he puffed out his jet-black fur. His tail started twitching. My smile faded, and I forced myself to sit up. The world spun, and I waited for it to right itself before trying to stand. When I managed it, the dizziness set in again and this time refused to leave. Still, I felt okay enough to stumble to the window and peer out with Oscar. He eyed me warily, scooted over a little, and then returned to whatever had held his attention. A warm breeze ââ¬â unseasonably warm for a Portland fall ââ¬â played with my hair as I leaned out. The street was dark and relatively quiet. It was three in the morning, just about the only time a college campus settled down, at least somewhat. The house in which weââ¬â¢d rented a room for the past eight months sat on a residential street with old, mismatched houses. Across the road, a streetlight flickered, nearly ready to burn out. It still cast enough light for me to make out the shapes of cars and buildings. In our own yard, I could see the silhouettes of trees and bushes. You read "Vampire Academy Chapter 1" in category "Essay examples" And a man watching me. I jerked back in surprise. A figure stood by a tree in the yard, about thirty feet away, where he could easily see through the window. He was close enough that I probably could have thrown something and hit him. He was certainly close enough that he could have seen what Lissa and I had just done. The shadows covered him so well that even with my heightened sight, I couldnââ¬â¢t make out any of his features, save for his height. He was tall. Really tall. He stood there for just a moment, barely discernible, and then stepped back, disappearing into the shadows cast by the trees on the far side of the yard. I was pretty sure I saw someone else move nearby and join him before the blackness swallowed them both. Whoever these figures were, Oscar didnââ¬â¢t like them. Not counting me, he usually got along with most people, growing upset only when someone posed an immediate danger. The guy outside hadnââ¬â¢t done anything threatening to Oscar, but the cat had sensed something, something that put him on edge. Something similar to what he always sensed in me. Icy fear raced through me, almost ââ¬â but not quite ââ¬â eradicating the lovely bliss of Lissaââ¬â¢s bite. Backing up from the window, I jerked on a pair of jeans that I found on the floor, nearly falling over in the process. Once they were on, I grabbed my coat and Lissaââ¬â¢s, along with our wallets. Shoving my feet into the first shoes I saw, I headed out the door. Downstairs, I found her in the cramped kitchen, rummaging through the refrigerator. One of our housemates, Jeremy, sat at the table, hand on his forehead as he stared sadly at a calculus book. Lissa regarded me with surprise. ââ¬Å"You shouldnââ¬â¢t be up.â⬠ââ¬Å"We have to go. Now.â⬠Her eyes widened, and then a moment later, understanding clicked in. ââ¬Å"Are you?à really? Are you sure?â⬠I nodded. I couldnââ¬â¢t explain how I knew for sure. I just did. Jeremy watched us curiously. ââ¬Å"Whatââ¬â¢s wrong?â⬠An idea came to mind. ââ¬Å"Liss, get his car keys.â⬠He looked back and forth between us. ââ¬Å"What are you ââ¬â ââ¬Å" Lissa unhesitatingly walked over to him. Her fear poured into me through our psychic bond, but there was something else too: her complete faith that I would take care of everything, that we would be safe. Like always, I hoped I was worthy of that kind of trust. She smiled broadly and gazed directly into his eyes. For a moment, Jeremy just stared, still confused, and then I saw the thrall seize him. His eyes glazed over, and he regarded her adoringly. ââ¬Å"We need to borrow your car,â⬠she said in a gentle voice. ââ¬Å"Where are your keys?â⬠He smiled, and I shivered. I had a high resistance to compulsion, but I could still feel its effects when it was directed at another person. That, and Iââ¬â¢d been taught my entire life that using it was wrong. Reaching into his pocket, Jeremy handed over a set of keys hanging on a large red key chain. ââ¬Å"Thank you,â⬠said Lissa. ââ¬Å"And where is it parked?â⬠ââ¬Å"Down the street,â⬠he said dreamily. ââ¬Å"At the corner. By Brown.â⬠Four blocks away. ââ¬Å"Thank you,â⬠she repeated, backing up. ââ¬Å"As soon as we leave, I want you to go back to studying. Forget you ever saw us tonight.â⬠He nodded obligingly. I got the impression he would have walked off a cliff for her right then if sheââ¬â¢d asked. All humans were susceptible to compulsion, but Jeremy appeared weaker than most. That came in handy right now. ââ¬Å"Come on,â⬠I told her. ââ¬Å"Weââ¬â¢ve got to move.â⬠We stepped outside, heading toward the corner heââ¬â¢d named. I was still dizzy from the bite and kept stumbling, unable to move as quickly as I wanted. Lissa had to catch hold of me a few times to stop me from falling. All the time, that anxiety rushed into me from her mind. I tried my best to ignore it; I had my own fears to deal with. ââ¬Å"Rose?à what are we going to do if they catch us?â⬠she whispered. ââ¬Å"They wonââ¬â¢t,â⬠I said fiercely. ââ¬Å"I wonââ¬â¢t let them.â⬠ââ¬Å"But if theyââ¬â¢ve found us ââ¬â ââ¬Å" ââ¬Å"They found us before. They didnââ¬â¢t catch us then. Weââ¬â¢ll just drive over to the train station and go to L.A. Theyââ¬â¢ll lose the trail.â⬠I made it sound simple. I always did, even though there was nothing simple about being on the run from the people weââ¬â¢d grown up with. Weââ¬â¢d been doing it for two years, hiding wherever we could and just trying to finish high school. Our senior year had just started, and living on a college campus had seemed safe. We were so close to freedom. She said nothing more, and I felt her faith in me surge up once more. This was the way it had always been between us. I was the one who took action, who made sure things happened ââ¬â sometimes recklessly so. She was the more reasonable one, the one who thought things out and researched them extensively before acting. Both styles had their uses, but at the moment, recklessness was called for. We didnââ¬â¢t have time to hesitate. Lissa and I had been best friends ever since kindergarten, when our teacher had paired us together for writing lessons. Forcing five-year-olds to spell Vasilisa Dragomir and Rosemarie Hathaway was beyond cruel, and weââ¬â¢d ââ¬â or rather, Iââ¬â¢d ââ¬â responded appropriately. Iââ¬â¢d chucked my book at our teacher and called her a fascist bastard. I hadnââ¬â¢t known what those words meant, but Iââ¬â¢d known how to hit a moving target. Lissa and I had been inseparable ever since. ââ¬Å"Do you hear that?â⬠she asked suddenly. It took me a few seconds to pick up what her sharper senses already had. Footsteps, moving fast. I grimaced. We had two more blocks to go. ââ¬Å"Weââ¬â¢ve got to run for it,â⬠I said, catching hold of her arm. ââ¬Å"But you canââ¬â¢t ââ¬â ââ¬Å" ââ¬Å"Run.â⬠It took every ounce of my willpower not to pass out on the sidewalk. My body didnââ¬â¢t want to run after losing blood or while still metabolizing the effects of her saliva. But I ordered my muscles to stop their bitching and clung to Lissa as our feet pounded against the concrete. Normally I could have outrun her without any extra effort ââ¬â particularly since she was barefoot ââ¬â but tonight, she was all that held me upright. The pursuing footsteps grew louder, closer. Black stars danced before my eyes. Ahead of us, I could make out Jeremyââ¬â¢s green Honda. Oh God, if we could just make it ââ¬â Ten feet from the car, a man stepped directly into our path. We came to a screeching halt, and I jerked Lissa back by her arm. It was him, the guy Iââ¬â¢d seen across the street watching me. He was older than us, maybe mid-twenties, and as tall as Iââ¬â¢d figured, probably six-six or six-seven. And under different circumstances ââ¬â say, when he wasnââ¬â¢t holding up our desperate escape ââ¬â I would have thought he was hot. Shoulder-length brown hair, tied back in a short ponytail. Dark brown eyes. A long brown coat-a duster, I thought it was called. But his hotness was irrelevant now. He was only an obstacle keeping Lissa and me away from the car and our freedom. The footsteps behind us slowed, and I knew our pursuers had caught up. Off to the sides, I detected more movement, more people closing in. God. Theyââ¬â¢d sent almost a dozen guardians to retrieve us. I couldnââ¬â¢t believe it. The queen herself didnââ¬â¢t travel with that many. Panicked and not entirely in control of my higher reasoning, I acted out of instinct. I pressed up to Lissa, keeping her behind me and away from the man who appeared to be the leader. ââ¬Å"Leave her alone,â⬠I growled. ââ¬Å"Donââ¬â¢t touch her.â⬠His face was unreadable, but he held out his hands in what was apparently supposed to be some sort of calming gesture, like I was a rabid animal he was planning to sedate. ââ¬Å"Iââ¬â¢m not going to ââ¬â ââ¬Å" He took a step forward. Too close. I attacked him, leaping out in an offensive maneuver I hadnââ¬â¢t used in two years, not since Lissa and I had run away. The move was stupid, another reaction born of instinct and fear. And it was hopeless. He was a skilled guardian, not a novice who hadnââ¬â¢t finished his training. He also wasnââ¬â¢t weak and on the verge of passing out. And man, was he fast. Iââ¬â¢d forgotten how fast guardians could be, how they could move and strike like cobras. He knocked me off as though brushing away a fly, and his hands slammed into me and sent me backwards. I donââ¬â¢t think he meant to strike that hard ââ¬â probably just intended to keep me away ââ¬â but my lack of coordination interfered with my ability to respond. Unable to catch my footing, I started to fall, heading straight toward the sidewalk at a twisted angle, hip-first. It was going to hurt. A lot. Only it didnââ¬â¢t. Just as quickly as heââ¬â¢d blocked me, the man reached out and caught my arm, keeping me upright. When Iââ¬â¢d steadied myself, I noticed he was staring at me ââ¬â or, more precisely, at my neck. Still disoriented, I didnââ¬â¢t get it right away. Then, slowly, my free hand reached up to the side of my throat and lightly touched the wound Lissa had made earlier. When I pulled my fingers back, I saw slick, dark blood on my skin. Embarrassed, I shook my hair so that it fell forward around my face. My hair was thick and long and completely covered my neck. Iââ¬â¢d grown it out for precisely this reason. The guyââ¬â¢s dark eyes lingered on the now-covered bite a moment longer and then met mine. I returned his look defiantly and quickly jerked out of his hold. He let me go, though I knew he could have restrained me all night if heââ¬â¢d wanted. Fighting the nauseating dizziness, I backed toward Lissa again, bracing myself for another attack. Suddenly, her hand caught hold of mine. ââ¬Å"Rose,â⬠she said quietly. ââ¬Å"Donââ¬â¢t.â⬠Her words had no effect on me at first, but calming thoughts gradually began to settle in my mind, coming across through the bond. It wasnââ¬â¢t exactly compulsion ââ¬â she wouldnââ¬â¢t use that on me ââ¬â but it was effectual, as was the fact that we were hopelessly outnumbered and outclassed. Even I knew struggling would be pointless. The tension left my body, and I sagged in defeat. Sensing my resignation, the man stepped forward, turning his attention to Lissa. His face was calm. He swept her a bow and managed to look graceful doing it, which surprised me considering his height. ââ¬Å"My name is Dimitri Belikov,â⬠he said. I could hear a faint Russian accent. ââ¬Å"Iââ¬â¢ve come to take you back to St. Vladimirââ¬â¢s Academy, Princess.â⬠How to cite Vampire Academy Chapter 1, Essay examples
Thursday, April 30, 2020
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.
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