The Bases of Geometry

The Bases of Geometry Geometry, From the Beginning ChaptersHow it All BeganEvolution of Geometric StudiesGeometry Studies TodayPractical Uses of GeometryIt sometimes crosses this writer’s mind to wonder about the first individual who looked at a rock and envisioned its possibilities â€" as a tool, a weapon; something that could be made into other useful things…How must one’s mind work to see something so ordinary, so commonplace and see within it endless potential uses?Likewise with recognising shapes, perhaps in oft-repeated patterns, and setting oneself to studying them.Admittedly, triangles, squares and parallelograms are not generally seen in nature; if any geometric shape could be said to be prevalent, it would be the circle or perhaps a sphere.Well, honeycombs and flies’ eyes are constantly-repeating hexagons…Still, doesn’t that thought make you wonder how quadrangles and polygons of all types came to be universally accepted as basic geometrical shapes?Today, your Superprof looks at geometry from its early days unti l now â€" a discipline so fundamental to our way of life that we cannot do without it. MyriamMaths Teacher 5.00 (13) £20/h1st lesson free!Discover all our tutors MarkMaths Teacher 5.00 (5) £200/h1st lesson free!Discover all our tutors Dr parikhMaths Teacher 5.00 (8) £40/h1st lesson free!Discover all our tutors KamalMaths Teacher 5.00 (9) £30/h1st lesson free!Discover all our tutors PetarMaths Teacher 5.00 (8) £40/h1st lesson free!Discover all our tutors GowsikaMaths Teacher 5.00 (5) £15/h1st lesson free!Discover all our tutors RubenMaths Teacher 5.00 (1) £15/h1st lesson free!Discover all our tutors ConorMaths Teacher 4.75 (4) £30/h1st lesson free!Discover all our tutorsHow it All Began Early geometers did not have tools such as this to solve their geometry problems Image by OpenClipart-Vectors from PixabayAlthough Euclid is widely considered the father of geometry, geometric studies were underway long before he consolidated observations into a treatise.In fact, about 2,500 years before Euclid was born, Ancient Mesopotamians were studying obtuse triangles. Babylonians had compiled substantial empirical data concerning angles, lengths, area and volume to build their fantastic cities and further their astronomy studies.Some of the principles they established are so elaborate that today’s geometers would have to draw on advanced calculus to arrive at the same conclusions those early mathematicians did.Concurrent to Babylonian studies, geometric advances were being made in India. By 800BC, Vedic teachings included what became known as the first statements of Pythagoras’ Theorem in their directions for building a suitable altar for worship.On the other side of the Fe rtile Crescent, Egyptians were forging ahead with their geometric studies as well. They had to have an understanding of geometry; how else would they have been able to construct the pyramids?Finally, Greek minds took matters in hand.Today, we credit Thales with the original mathematical deduction; unfortunately, none of his work survives. However, it is postulated that Pythagoras must have been a student of his because much of his work reflects his proposed teacher’s ideas.Did you know that, besides being mad for triangles of all types, Pythagoras was a world traveller? He made his way to Babylon and kept going until he arrived in Egypt.Some speculate that he was less a geometer than a compiler of already-existing information but what is clear is that he was the first to give deductive proof of what we know as the Pythagorean Theory.A century on, back in Greece, the great philosopher Plato was also a fan of geometry. Because he was so influential, mathematicians soon adopted his c redo: that geometry should employ no tools other than a compass and straightedge.Wouldn’t you know it? Some of the straightedge and compass problems were proven through the usage of the (mathematical) theory of fields to be impossible… but not until about 2,200 years later!Finally, we get to Euclid.Thought to be a student at Plato’s Academy, his 13-book (chapter) treatise titled Elements of Geometry presents certain ‘truths’ - ideas about geometry that are widely held to be correct.You can see for yourself; Euclid’s five axioms are:any two points can be joined by a straight lineany line segment can be extended indefinitely in a straight linea circle can be drawn with any centre and with any radiusall right angles are equaltwo parallel lines bisected by a transversal line form supplementary interior angles…this is known as the parallel postulateThese precepts, proven time and again, form the foundation of the discipline we know as geometry.Today, many of the concepts ex pressed by Euclid geometrically are now classified as algebra rather than purely as geometry, giving irrevocable proof that all maths are related.Have you mastered these basic geometry equations? The pyramids at Giza prove that Ancient Egyptians understood geometric forms Image by jarekgrafik from PixabayEvolution of Geometric StudiesThese classical Greek studies, which included geometry, had to somehow make their way into the wider world, specifically to Europe, where some of the greatest minds were at work.Much of the bounty of the Islamic Golden Age, the period between the 8th and 14th centuries appeared in the great royal courts of the day.Ptolemy’s Almagest, a mathematical/astronomical treatise to this day considered the most influential scientific text of all time, was given to King William I, the second king of Sicily, as a gift.This work and others written by Euclid were translated, permitting further development of Euclidean geometry as well as algebraic geometry. The end result was explosive new theorems and concepts.By this time, the Italian Renaissance was well underway; artists became unlikely beneficiaries of advances in geometric studies; their paintings gain ed depth and dimension from the geometrical method of perspective.Think about Leonardo da Vinci’s most famous work, Vitruvian Man: the exactly-proportioned human form perfectly contained within a circle which itself is ‘squared’ - again, we return to the compass-and-straightedge challenge!Still, information moved slowly; not every Renaissance artist or scholar gained exposure to the latest ideas regarding shapes and equations.Mathematician and philosopher René Descartes levelled the playing field by introducing geometry with coordinates and equations â€" what is now known as analytic geometry.The second big shift in geometric studies of the day was projective geometry â€" how points align with no measurement involved.French mathematician Poncelet blew the field of projective geometry wide open but it wasn’t until Isaac Newton and Gottfried Leibniz, working independently, established calculus as a method of solving geometry’s intractable problems.Do you need a geometry tut or to help you understand calculus as it relates to geometry?Geometry Studies TodayNot everything Euclid postulated was gospel; the parallel postulate proved impossible to prove, which gave rise to a type of geometry that proves the impossibility of that postulate; it was dubbed non-Euclidean geometry.Other theories and discoveries soon followed. One, by Bernard Riemann, applied calculus to smooth surfaces, founding a different branch of non-Euclidean geometry and provided the groundwork for the world’s most famous equation: e=mc2.From there, we’re treated to further developments in algebraic geometry, which led to finite geometry, which, in turn, permitted development in coding theory and cryptography.Topology, the study of the properties of a geometric object, looks at larger aspects of shapes such as their connectedness and boundaries rather than elemental qualities such as length and equality of angle measurements.Today, with computer applications governing so many aspects o f human life, new fields of geometry have taken the lead. Some deal with geometric algorithms (computational geometry) while others concern themselves with individual geometric data sets (digital geometry).Make use of these online geometry resources to further your studies in geometry Everything from drones to satellites operate on a coordinate plane Image by S. Hermann F. Richter from PixabayPractical Uses of GeometryIt seems almost a shame that the field of geometry is so advanced; long gone are the days of Euclid and Descartes â€" after all, nobody is going to rename the Cartesian coordinates system after a current-day geometer.Meanwhile, students in primary and secondary school scratch their heads over why they have to learn the Pythagorean Theorem when there are so many tools at our disposal to measure, calculate and quantify everything.Such a view is painfully short-sighted.You may not ever build a house or a piece of furniture yourself but you surely must appreciate that whoever is involved in the building process, from the architect to the machinist running the lathe that spins the wood to make the chair or table leg, must know geometry â€" otherwise, houses would crumble and no chair would be safe to bear any weight.Everything, from the volume of the gla ss you drink your morning juice out of to the tyres on your car employ geometric principles in their making and in their usage.What if you simply don’t care about straight lines and geometric shapes?If you can’t see a future for yourself in some murky lab, doing calculations all day long, indeed if you’ve reasoned that coding and computer programming is where the money and prestige are at… guess what? You will have to know geometry!If you aspire to become the next great game designer, you should know that everything from vector graphics to the polygons that form the game’s terrain is geometric.What about sat-nav, GPS and even your new flatscreen television? All of them make use of geometry to calculate everything from positioning to pixels to provide you with the optimal experience based on your position.Maybe you’re currently stymied at having to calculate the circumference of a circle or the area and volume of a pyramid now but, the more you learn about geometry and it s functions in the world around you, surely, the more you will warm to this area of study â€" maybe even make it your life’s work!Geometry truly is so much more than obtuse angles taught by obtuse professors…To get you properly started, we've compiled basic Euclidean geometry formulas in this handy table.Basic Formulas of Euclidean GeometryShapePerimeterAreaTrianglea+b+c Pythagorean Theorem: a2+b2=c2Area= (1/2)*b*h b=base; h=height Heron's Formula: Area = sqrt [ s(s - a)(s - b)(s - c) ] , where s = (a + b + c)/2.Square4aa2Other Quadrangles2L + 2WRectangle: l*w Parallelogram: b*h Trapezoid: (1 / 2)(a + b) * hOther Polygonsx(number of sides)Pentagon: (5 / 2) × s × a Hexagon: 1/2(P)(a) Octagon: 2 x (1 + v2) x b2 a = apothem b = baseCirclescircumference: 2*pi*rpi*r 2Now digest this complete guide to geometry.

What To Do When Rejected From Your Dream School

What To Do When Rejected From Your Dream School A lot of weight is put on a high school seniors shoulders to get into the best college they can. Not only that, but the pressure is on to get into that dream school he or she has been after. Most students have a particular school in mind that theyve decided would be absolutely perfect for them. It may be the culture, it may be a certain program, or it may be a combination of a lot of factors but regardless of the specific reasons, it is nice to feel so confident about this next phase of your life. The only problem is, there is no guarantee of attending that school until that large envelope of acceptance arrives in the mail. Students are rightfully encouraged to not put all of their eggs in one basket and make sure to apply to at least a handful of schools, even if they already have their decision made in their heads. More importantly, having a back-up school for which you know you can get into is crucial so you are not left with zero options come decision-making time. We certainly dont like to think about it, but it has to be acknowledged what if you dont get into your dream school? You may have scored exactly as needed on the SAT and acquired enough leadership positions in high school to meet this schools requirements, but admissions decisions are not always that simple and you just cannot predict these things. The outcome may be one you dont like or dont expect, and it is important that you prepare for that possibility. Just because you felt you this school would be perfect for you doesnt necessarily mean the admissions officers will feel youre perfect for it. If you are applying to medical school, you may also want to check out these tips on what to do if you get rejected from medical school. If you do find yourself in this unfortunate situation, dont throw in the towel! A fulfilling college experience can still be in your future. There a few steps you can follow to ensure you handle things in a healthy and proactive way so you can still enjoy those years ahead of you. #1. Accept it: It may sound a little harsh and obvious, but you really wont be able to move on unless you do it. Getting over the fact that you wont be spending your exciting college years at your first choice institution is a tough thing to face, especially if youve built up the dream in your mind over the past few years. But an important thing to realize is that not everyone attends the college they thought they were going to. Some people end up going to a different school even if they were accepted into their dream one. Why? Because people grow and change their minds, and that includes high school students. Just because you thought something was right for you once doesnt mean it still is or always will be. Dont be afraid of something different. Comprehend the fact that another school can offer you the things you want. It may not be the place you pictured in your head for so long, but it could make you very happy if you let it. A closed mind is one of the quickest ways to avoid a h appy college experience. Dont stand in your own way. Here are some great tips on how to handle rejection in college admissionsthat you may want to take a look at as well. #2. Congratulate yourself for the schools that did accept you: Unless you really did put all of your eggs in one basket, you should have a few other schools that are inviting you to be a part of their campuses. Take a moment to let that soak in and be proud of yourself for the accomplishment. It is always a great feeling to know you gained acceptance, so dont let it slide by just because you werent accepted by your number one pick. You can take comfort in the fact that you have still been given the opportunity to attend other universities, and now you are the one in control. Be happy you have other options and take the reins as the decision-maker of which path you will go on now. #3. Start over and research: Theoretically, you have already researched these schools because you decided to apply to them in the first place. But since you were planning on attending the one that didnt accept you, you probably didnt give the details on these remaining schools as much thought as necessary. Now is the time to have a little fun and take a deeper look into each of these universities elements, knowing that the hard part is over and all you have to do is pick what you like best. However, it is important that you do not directly compare them to your dream school. As has already been established, accepting the rejection from that dream school is critical so you do not have it in the front of your mind as you evaluate these other colleges. If you do have it in the front of your mind, none of these schools are going to look appealing to you and the fun and excitement will be gone. Look at each of these institutions with a clear head and youre bound to naturally find and learn about things they offer that genuinely intrigue you. Before you know it, youll be leaning toward one of them with the confidence that you do have an exciting experience ahead of you. Here is some great information you may also want to take a look at on why top colleges have lowered acceptance rates. In a nutshell acceptance, moving on, recognizing what you do have, and making an informed decision is what lies ahead of you. Its a bummer not getting into your top choice school, but dont let that stop you from having the experience you deserve!

The 2 Soft Skills You Need for Business School

The 2 Soft Skills You Need for Business School Two soft skills? Only two? Yes, there are countless skills, both hard and soft, that you need for business school. Areas like mathematics, data analysis, spreadsheet construction, and statistics interpretation fall on the hard side. The soft side includes stress management, self-awareness, communication, and collaboration. But which soft skillsare most important? In addition to actually listening to the people around you, the two soft skill areas you must develop for any MBA program fall under two main categories: being a strong colleague and being a strong leader. Learning to master this pair of skills will help you immensely as you navigate the competitive world of business schooland business! [RELATED: 5 Tips to Ease the Transition from Business School to the Business World] Being a strong colleague First, you need to develop friendships with your fellow classmates, particularly those in your study groups, assigned or otherwise. In the long term, you are building connections for the future; but for the short term, making new friends can make school more fun, especially when your group is spending hours together performing research, studying for an exam, or completing a project. Working with people who share an accord and solidarity can help create a more enjoyable MBA experience for all those involved. Second, it is also wise to cultivate positive relationships with members of your business schools faculty and administration. These individuals often have years of real world management experience, so you can learn from their perspectives as people who have truly been there. Furthermore, not everyone makes the effort to talk with their professors outside class, so you may stand out in your instructors mind if they have to make a tough administrative decision. For instance, its harder for someone to keep you out of a full class or give you a failing grade if they have had multiple endearing conversations with you. Finally, convert recruiters and alumni at your target companies from acquaintances to buddies. Dont merely learn a recruiters name, rank, and serial numberfind out about their company culture, what they like about their job, what they dont like about their job, and what they are looking for in a future team member. Ask what they like to do outside of work; discover what you have in common. Knowing you have advocates at the places you would like to work helps you feel more confident as you submit your applications to those companies. Being a strong leader When trying to persuade other individuals to share your point of view, it helps if these people already view you as a strong colleague. Lets start with your fellow classmates, particularly those in your study groups. MBA programs abound with students who have strong personalities. Therefore, it is crucial to master the art of leading others and managing conflict. As in your future career, influencing team dynamics involves working across culturesdifferent departments, ages, companies, viewpoints, and countries. You will need to exert great patience to effectively regulate these situations, and business school provides a valuable setting in which to practice these skills. Onto your business schools faculty and administration. As mentioned above, issues like getting into the classes you want and petitioning for a higher grade are easier to steer in your favor when you have a positive rapport with the people in charge. Additionally, when you want to connect with certain mentors in your field, asking professors who have personal links to these people may be the way to go. Those who can influence others with aplomb will likely have more success in these endeavors. Finally, in your career, you must be able to convince recruiters and alumni at target companies to hire you for positions, sometimes over your equally qualified peers. You are selling yourself both as a potential asset to the company and as a harmonious team member. If an alum or a recruiter selects you, then they may be interacting with you every day. To swing these professionals your way, present yourself as the only solution to their problems, stated or implied. After all, this is one of the main reasons you are attending business school, so make your influence count. [RELATED:Top Questions to Ask Alumni When Exploring Business Schools] As you can see, being both a good colleague and a good leader are inextricably linked. These are not just two of the most important soft skills you need for business school, but they are also two imperative talents to develop as you move from the classroom into your future career. In addition to learning how to gather, analyze, and present facts and figures as an MBA graduate and colleague, you will also need to know how to persuade your peers on how to act on that information, as you later hopefully move into management. Let your time in business school serve as an environment for you to expand both your emotional intelligence and management expertise.

How to Get Real-World Experience in Your College Major

How to Get Real-World Experience in Your College Major While pursuing your college degree, you will take many classes that will help you explore your intended field. The knowledge gained from these major-focused courses can be very beneficial; however, gaining real-world experience in your college major can be the extra boost you need when entering the job search. Unfortunately, many students neglect to get real-world experience during their schooling, only to realize its importance once its too late. You can get real-world experience in your college major by taking on internships, career-related jobs, and relevant extracurriculars while in school. Having examples from classes can be helpful, but showing potential employers you have more direct experience can increase your chances of standing out. But what steps can you take to get this real-world experience? Read on: Gain real-world experience from internships There are many reasons you could choose to pursue an internship in college. Some colleges or majors require that you complete a minimum number of hours in an internship role before graduation, while others leave it up to the student to decide. Regardless, holding an intern position at some point throughout your college career is a great way to apply what youve learned about your major in the real-world. [RELATED:4 Career Skills for Students to Develop] Internships in your field give you the opportunity to have multiple professional experiences throughout your education. Typically, internships range from three to five months and may occur during one of the semesters of school. For example, a potential employer may have an opening for a fall or summer internship, which would typically last the duration of that session. Depending on the internship and company, these can sometimes be paid positions and potentially turn into a real job opportunity! Neither is guaranteed, but regardless, gaining the experience and networking opportunities may come in handy down the road. Utilize your college major in a campus job or organization Another great way to gain experience in your major is to take on a part-time job in your field (or in a related field). This could be the university newspaper if you are interested in graphic design, advertising, or journalism, for instance. Or, you could consider the admissions department if you are interested in hospitality, public speaking, or anything else that involves heavily interacting with people. Often, there are many roles right on campus for students to take on as well, including: Writing, math, or science center tutor Teaching assistant Lab assistant/technician Assistant in the IT department You can also join various college extracurriculars that may support your intended field. Holding leadership positions (and even simply being involved) in campus groups and organizations can broaden your knowledge of your area of study. Jobs or volunteer opportunities off campus in your community are another great way to showcase your major-related skills. Consult with your academic advisor who may be able to help you locate these opportunities. Gain real-world experience through networking Both internships and jobs in your intended field give you the opportunity to begin networking with individuals in the career you hope to go into. Oftentimes underrated, taking advantage of any networking opportunities available to you can be a great way to get your name out there. Many universities host job fairs and other networking events that allow students to meet professionals in their desired field. This is where everything ties together: by having gained real-world experience in your major, you will have something to showcase when talking to these individuals that will give you the confidence to network. At the end of the day, gaining real-world experience in your college major can do nothing but benefit you. It doesnt hurt to help yourself feel as confident and prepared as possible for what the real world will bring! Any topics you want to know more about? Let us know! The Varsity Tutors Blog editors love hearing your feedback and opinions. Feel free to email us at blog@varsitytutors.com.

What is it Like to Attend Duke University

What is it Like to Attend Duke University The tutors behind Varsity Tutors are not just here to teach theyre sharing their college experiences as well. Margaret is a Washington D.C. tutor specializing in Writing tutoring, AP Psychology tutoring, all levels of Spanish tutoring, and more. She is a graduate of Duke University holding a Bachelors degree in Psychology. Check out her review of her alma mater: VT: Describe the campus setting and transportation options.How urban or safe is the campus?Are there buses or do you need a car/bike? Margaret: For my undergraduate, we had an interesting situation. There wasnt that much public transportation at the time in Durham, North Carolina. I think that might have changed in the last decade. However, we always had a free bus service not only for the campus, but between our school and The University of North Carolina at Chapel Hill called the Robertson bus. It was a way to go to not only different library resources if we needed them, but to a different, more typical college town. Durhams not exactly the safest place as its very urban and not a place to walk alone at night, to be honest. Chapel Hill, by contrast, was the typical college hamlet and it was a fun place to be able to get to as a change of pace. VT: How available are the professors, academic advisers, and teaching assistants? Margaret: I really had a great relationship with my professors as I got to my upper level classes. They were great mentors as I worked on applying for graduate school and on my senior theses. That said, as a freshman, I had pretty terrible teaching assistants for General Chemistry who were barely able to speak English. It made the class almost impossible to pass and I resented it. VT: How would you describe the dorm life rooms, dining options, location, socialization opportunities with other students? Margaret: I always laugh about the dorm life. There was this show from the late 90s called Dawsons Creek that filmed its final two seasons sometimes on Dukes campus to show where Katie Holmes character went to college. Her dorm room was massive. I knew kids my freshman year whose living space was literally converted from an old janitors closetfor two people. Despite the price tag, you dont go to Duke for spacious on-campus accommodations! VT: Which majors/programs are best represented and supported?What did you study and why? Did the university do a good job supporting your particular area of study? Margaret: I know back in 2002, that the big thing to start majoring in was in Investment Banking. I know that since the bank crashes in 2008, thats probably not the hot ticket major it was before. Of course, Dukes extremely proud of its pre-med program and takes about 10% of its actual medical school classes from its undergraduate program, which is fairly unheard of. Also, theyre very supportive of their pre-law students and make sure they have the best resumes possible before applying to programs. I was a Psychology major and we had a great wealth of access to lab research and paper writing opportunities. I always felt supported there. Similarly, as one of the few people involved heavily in their primate/lemur studies program, I had very enthusiastic mentors who were happy I was continuing their work. VT: How easy or difficult was it for you to meet people and make friends as a freshman? Does Greek life play a significant role in the campus social life? Margaret: Its possible to make friends without Greek life. In fact, Duke wont let anyone rush a fraternity or sorority until the second semester so bonds can be established before then. That said, I made great sorority friends when I did rush and join but I also had great friends whose weddings Ive attended since then that I met the first week in my freshmen-only dorm! VT: How helpful is the Career Centerand other student support services?Do many reputable companies recruit on campus? Margaret: I honestly dont know. I never used it because I was in a science track and relied on my mentors to help me apply to graduate schools. VT: How are the various study areas such aslibraries, the student union, and dorm lounges? Are they over-crowded, easily available, spacious? Margaret: Again, this is sort of a sign of having been out of college for so long. When I was there, the main library was Perkins and hadnt been renovated since the 1970s. However, by the time I was a senior, most of the library stock had moved to a beautiful, new spacious library called Bostock. I lived in Durham again for two years from 2011-2013 for other reasons and sometimes went into Bostock for books and research. Its not overcrowded, has comfortable sitting areas, and tons of available computers. So, Dukes come a long way from when I was using their stacks. VT: Describe the surrounding town. What kinds of outside establishments / things to do are there that make it fun, boring, or somewhere in between?To what extent do students go to the downtown area of the city versus staying near campus? Margaret: Its Durham, North Carolina. Theres just not that much to do. I like the South Point Mall off campus. I also liked going to Chapel Hill. Again, take the free bus over there on weekends. Its your best bet! VT: How big or small is the student body? Were you generally pleased or displeased with the typical class sizes? Margaret: It was about 6,000 undergraduates back then with about 1,600 per class. The typical intro class sizes for things like General Chemistry are huge, but mostly, the classes are around 20 people. Its very intimate past the general requirements. VT: Describe one memorable experience with a professor and/or class. Perhaps one you loved the most or one youregretthe most. Margaret: I dont have one memory specifically as much as a whole year. I really enjoyed every minute of working on my senior thesis for lemur studies with my mentor, Dr. Digby. She had been my favorite teacher in the primate department and she was invaluable in helping me get grants and learn the art of being a good scientist and building up my own study from the ground up. Check out Margarets tutoring profile. The views expressed in this article do not necessarily represent the views of Varsity Tutors.

How to Talk about Transport in English - Intermediate Level English

How to Talk about Transport in English - Intermediate Level English Transport and the ways we use it in our daily lives captures the attention of all of us. I thought that today I would talk about transport in English and set out some of the means of transport we use in English vocabulary across Europe and the UK. This will help you to improve your English. Talk about Transport in English Transport to work is often a choice of Private or Public  transport. Private transport is what we provide ourselves (e.g a car) or by a private operator who wishes to make a profit. Public transport is the means of transport which is provided by governments and is not necessarily provided for profit.Vehicle  is a general noun used to describe any motorised method of travel and transport. This can include a car, bus, lorry and truck. The choice of vehicle depends normally on where we live. Governments usually provide many different choices in capital cities  and bigger towns  but there is normally less choice in rural  or country areas.Some examples of private transport are:cars saloon cars, sports cars and 4 x 4buses double decker, single decker, mini buses and trolley buses.For those who wish to skip the traffic then there are  motor bikes (motor cycles) and mopeds (scooters) are becoming increasingly popular.Taxis remain popular for those in the larger cities such as London and N ew York. You can find taxis waiting for passengers at a taxi rank. We now also have the new taxi option referred to as Uber Taxi’s.  Public transport comes in the following forms:buses double decker buses such as the traditional red buses seen on the streets of London and regular single decker busestrolley bus   buses with overhead power lineselectric bus this is a bus powered by electricity and they are getting very common in many cities in Europetram is a vehicle powered by electricity, it travels on 2 rails that are laid in a public roadcoach this is a bus that runs between towns and citiesTrains also come in many guises (forms) diesel, electric, underground and over ground). Trains travel on two tracks made of metal.Underground trains have different names depending on the city/country that we live in. In America they are referred to as subways, in London as simply the underground or the tube and other cities as metro. You wait for a train on a platform.If you prefer a fast way of travel, then you can use an aeroplane. Nowadays there are many budget airlines (companies that fly passengers by plane) and you can fly to many destinations relatively cheap.  If you are travelling to an island, you might prefer to take a ferry (a boat or ship that transports passengers and/or goods, especially over a relatively short distance and as a regular service). If you happen to travel overnight, then you sleep in a cabin.If you have travelled in Asia you will be familiar with the very small Tuk Tuk  a mix of a motor bike and small car. A great way to travel and sometimes the only means of transport in rural areas.And I am sure most of you are familiar with a bicycle, you pedal your bicycle and get from A to B easily. It is also a great exercise! Public Transport in English - Infographic Enjoyed this infographic? Here’s what you can do next:

Introducing Tutorfairs Online Classroom

Introducing Tutorfair's Online Classroom As Head of Operations at Tutorfair, I get to be involved with lots of really exciting projects that help both tutors and clients get the most out of the platform. Our big project in the second half of 2018 has been developing Tutorfair’s online classroom, an online learning platform! Why did we want to provide an online classroom for Tutorfair users? On Tutorfair, more lessons than ever before are online - making up to 50% of Tutorfair lessons, on some days! Many tutors enjoy the online lesson format, finding it as engaging as in-person lessons, and now, more and more students are also opting for the online learning experience. We know that at the moment, our tutors and students use a mixture of online platforms and teaching resources, such as Zoom, Skype, and bitpaper.io, to conduct lessons. With this in mind, we wanted to provide tutors and students with a resource to make online learning even easier and more effective, which is why we’ve been working on the Tutorfair online classroom. Tutorfair’s online classroom is an e-learning platform available and free to use for Tutorfair’s tutors and students. It features a variety of teaching tools and will be easily accessible for lessons directly through your Tutorfair account. What have we done? After lots of research with our development team, we have chosen a fantastic, versatile online classroom to integrate into the Tutorfair website. It was chosen because it has all the features tutors told us they would need to conduct great lessons online - and all in one place! Since integrating the classroom, we have run pilot tests with some fantastic tutors (thanks for the help guys!) and collected LOTS of feedback. We have since been working on improving the classroom experience for all users. What’s new and exciting the classroom? The online classroom is specifically designed to enhance the experience of online learning.  It has a range of teaching tools and features that will help tutors conduct engaging lessons for students. These include: Video, audio and chat facilities A whiteboard to draw on The ability to incorporate documents, images and videos onto the whiteboard Screenshare Learning tools such as Wolfram Alpha and LaTeX tool The work done in the classroom can be saved as images straight to the user’s computer. What’s great is that both the tutor and student will be able to access the classroom directly from their Tutorfair account - either from their messages, or lessons/bookings pages. How we are moving forward We’ve had some really lovely feedback from our pilot tutors so far! Katherine was very excited about all of the features of the classroom. She particularly liked the whiteboard, the video embed feature, the screenshare and the ability to upload pictures/documents and write on them. Luke, a Science and Maths tutor, really likes the Wolfram Alpha feature. He considers this to be a big advantage to the classroom and says that things will be much easier. Juliette observed that the classroom is very user-friendly and thinks it’s a great piece of technology! With the feedback collected from our pilot period, we’re implementing some small changes to improve the online classroom experience. The one big project we’re working on is being able to provide a lesson recording, so that tutors and students can go back and watch/listen to their lesson. In the meantime, we’re inviting tutors to get in touch if they would like to trial the classroom. Just send us an email to support@tutorfair.com! The online classroom is an incredibly exciting project that is giving us lots of scope for future development, so if you would like to be kept updated, please don’t hesitate to get in touch with us.

Importance of Early College Preparation

Importance of Early College Preparation College preparation  is extremely  important  to  college  success for students.  Although many decisions are made during the senior year, it is best to begin the college process as early  as high school freshman year. Knowing this, it’s crucial for freshman students to complete these tasks before the end of the school year: Answer the questions: How are you doing academically? How would you rate your current academic performance? If you feel as if you are struggling, now is the time to get some help from a tutor and make sure you will be able to pass your tests. If you are unprepared, you  can fail an assignment or class, which leads to stress and hopelessness. Get involved in a school activity.  Being a member of the chess club, art club, sports, etc.  is a great way to dive into your passions and interests outside the classroom. If you are having difficulty, talk to someone (teacher, tutor, or counsellor). Make a plan for next years courses.  Advanced classes should certainly be a part of this plan. Choose an inspiring community service project  such as collecting toys for a local shelter, planting a community garden etc. Make some preliminary college visits. Wander around, explore the campuses, talk to students. Find out what you like and dont like about the campuses.  It’s never too early to  visit colleges ??