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The Abacus: A Brief History

what is an abacus

So, they can be introduced to Abacus training, after that they can start practising addition and subtraction. Ancient Romans utilized stones as counters up and down on a smooth table to do calculations. It was developed to help bankers and money changers, businessmen and engineers. Additionally Romans invented other types of Abacus such as the dust Abacus, the line Abacus, the grooved Abacus.

  • The abacus was used as a counting tool before the advent of the Arabic numeral system.
  • It has endured over time and is still in use in some countries.
  • Furthermore, the abacus improves the overall conception of math, and it also enhances the problem-solving ability and faster calculation skills.
  • The origin of the Abacus has yet to be discovered, but it is believed to have originated in ancient China around 500 BCE.
  • However, China and Japan have the longest history of consistent abacus use and development.

More Powerful than a Calculator

  • This is known to be the modification of the current Abacus to support the learners that have vision disabilities.
  • The abacus is still taught in Asian schools, and a few schools in the West.
  • A horizontal beam separates the structure into two sections, known as the upper deck and the lower deck.
  • As time passed, the design of an Abacus kit has widely varied in terms of style, size and material but the design of Abacus kits remains to be in a combination of rods and pebbles.
  • It is great to see such great calculations being solved efficiently using a tool.
  • The Japanese abacus is called the Soroban which was not used widely until the seventeenth century.
  • It was used in 300 BC by the Babylonians and was discovered in the year 1849 on the island of Salamis.

Abacus is a device consisting of a frame with rows of wires consisting of beads. It is a hand-operated device used for calculation and is bound to have some human error. It can be used for performing calculations such as multiplication, addition, and division. Earlier operations like counting were performed on hands or using Vedic maths but larger operations require more calculations. Therefore there was a need for a development tool for such calculations. It was India’s first calculator used in Asia, Europe, and Russia.

Who invented the first abacus?

The device consists of a series of beads on parallel wires that are arranged in three separate rows. The beads in the Abacus represent a switch on the Computer in either an “on” or “off” position. Abacus is a man-made calculating device invented around 5000 years ago. According to Historians, it was the Chinese people who invented Abacus around 500BC.

Renaissance abacuses

Right below this crack, we come across another set of eleven parallel lines which are again divided into two sections by a line that is perpendicular to them but has a semi-circle at the top of the intersection. The third, sixth and ninth lines are marked with a cross where they go and intersect with the vertical line. The Hindu-Arabic number system made counting, calculating and record-keeping a lot easier than with counting boards which had all but disappeared in Western Europe by the 14 century. Arithmetic brought about the invention of logarithms by John Napier and logarithmic scales by Edmund Gunter. In 1622, William Oughtred used these two inventions together and invented the slide rule which lasted until modern times when the scientific calculator became popular in the early 1970s.

Portable Computing Devices Today

“AbacusandVedicMath” carries out A national and worldwide online course seeks to instill a love of mathematics and dispel math anxiety. The curriculum is created in a way that makes learning more engaging for the kids. Sanchez wrote in Arithmetic in Maya that another base 5, base 4 abacus had been found in the Yucatán Peninsula that also computed calendar data.

The Salamis Tablet (c. 300 BCE)

This was a finger abacus, on one hand, 0, 1, 2, 3, and 4 were used; and on the other hand 0, 1, 2, and 3 were used. Note the use of zero at the beginning and end of the two cycles. It is believed that the first abacus was made by Ancient Mesopotamians of Sumeria .

Which Country used the Abacus first?

When the right hand is used on the abacus, the left side cells of the brain are activated. The left-brain activity is interpreting, and the right brain activity is visualizing. Therefore, both the left and right sides of the brain work commonly and help to whole-brain development. This is known to be the modification of the abacus market tor current Abacus to support the learners that have vision disabilities. The learners can manipulate the beads that would in effect help them in the in-depth understanding of the numbers. This Abacus can be used to calculate various numbers involving arithmetic processes like addition, subtraction, division or multiplication.

  • Various portable counting devices were invented to keep tallies.
  • On this instrument, calculations are made with beads, or counters, instead of numerals.
  • For example, the Roman Abacus, used in ancient Rome, was similar to the Chinese Abacus but had slight differences in design.
  • Though it can’t be stated clearly but the Ancient china is attributed for the early use of abacus.
  • In fact, people who regularly do mental abacus math show higher numerical memory capacity, quicker mental retrieval speeds, and overall increased neural connectivity / processing abilities.
  • In the Middle Ages, the Abacus was further developed in Europe, and merchants and traders used it for bookkeeping and accounting.
  • An abacus is a manual calculating tool used for adding, subtracting, multiplying, and dividing.

Who Invented Abacus? Types and Uses

  • Digital devices need not replace manipulative tools like the abacus that build mathematical thinking.
  • It is easier to use one’s thumb to move the beads in the top row, and the index finger to move the beads in the bottom row.
  • The suanpan can be reset to the starting position instantly by a quick movement along the horizontal axis to spin all the beads away from the horizontal beam at the center.
  • This origin, whether in Ancient China or Babylon, has been used throughout history and is continued to be used as a convenient calculator for commercial transactions.
  • Removes the fear of mathematics by making arithmetic calculations easier.
  • Despite the advances of digital technology, abacuses remain popular tools in education and mental math training despite its advanced use.
  • In many countries abacus is taught to early school goers as it has been seen that it helps subtends have a better understanding of numbers.
  • From Greece and Rome to Russia, China, and Japan, abacus design and precision evolved.

The abacus was in use in Europe, China, and Russia, centuries before the adoption of the written Hindu-Arabic numeral system. When the Hindu-Arabic number system was widely accepted, abaci were adapted to use place-value counting, a system in which the position of a digit in a number determines its value. In the standard system, base ten, each place represents ten times the value of the place to its right. Since the first abacus, the physical structure of abaci has changed, but the concept has survived almost five millennia, and is still in use today. The abacus, generally in the form of a large calculating board, was in universal use in Europe in the Middle Ages, as well as in the Arab world and in Asia. The introduction of the Hindu-Arabic notation, with its place value and zero, gradually replaced the abacus, though it was still widely used in Europe as late as the 17th century.

Pascaline Calculator Explained — Everything You Need To Know

It is advised that the students are introduced to Abacus at a very young age, to provide them with enough exposure so that they do not find mathematics as difficult as they earlier did. Learning Abacus is fun, as it helps the students explore their creative abilities while also putting them to practical use. All of this makes the learning of the Abacus easy and fun for the candidates. The main difference that one witness between the Chinese Abacus and the Russian Abacus is the position of its rods. These rods are placed horizontally in the case of the Russian Abacus and beads are slid from the right to left. A typical Russian Abacus would measure 28 cm wide and 46 cm in height.

Where Are Abacuses Used Worldwide?

After learning the basics of counting on the abacus, you can quickly perform arithmetic like addition, subtraction, multiplication, and division. Long before the invention of the electronic calculator or the computer, people counted and did calculations with a device called an abacus. On this instrument, calculations are made with beads, or counters, instead of numerals. The beads that slide along a series of wires or rods set in a frame to represent the decimal places.

For instance, to add two numbers, drag the appropriate number of beads on each row towards the centre and then count the number of dots. Similarly, to subtract two numbers, you move the proper number of beads away from each other and then measure the remaining beads. The Abacus may seem like a primitive tool compared to today’s modern math calculators and computers.

Discover Abacus: Understand its Definition, Types & History

It was a very basic invention which did not look like today’s abacus being used. It has been proved by many pieces of researches that the abacus learners can use both sides left and right hemisphere of their mind. The Cranmer abacus is a modified version of the Japanese abacus or sorobon. Shortly thereafter, the American Printing House for the Blind began selling the device, and they continue to sell it today.

A brief history of Abacus

The Schoty is a Russian abacus invented in the 17th century and still used today in some parts. The accountant sits in the middle of his side of the table, so that everybody can see him, and so that his hand can move freely at its work. When the sum demanded of the sheriff has been set out in heaps of counters, the payments made into the Treasury or otherwise are similarly set out in heaps underneath. The lower line is simply subtracted from the upper.” —The Dialogue on the Exchequer, 1177. “The Exchequer is an oblong board measuring about 10 feet by 5…with a rim around it about four finger breadths in height, to prevent anything set on it from falling off.

Seki Kowa removed one bead all from upper and lower decks for making the abacus to 1/4 decks. It became popular after globalization when there was intense competition in the world on a common platform. It also influenced the education system of different countries. Furthermore, the abacus improves the overall conception of math, and it also enhances the problem-solving ability and faster calculation skills.

Who invented the abacus?

During the brief period when pocket calculators rose in popularity, the Sorocal/Sorokaru, a hybrid abacus digital calculator was manufactured to help abacus users in the transition. Three sets of Greek symbols (numbers from the acrophonic system) are arranged along the left, right and bottom edges ofthe tablet. There are two beads in the top row, and five beads in the bottom one.

Abacus History

In fact, people who regularly do mental abacus math show higher numerical memory capacity, quicker mental retrieval speeds, and overall increased neural connectivity / processing abilities. Although there are various abacuses worldwide, one of the best-known is the soroban, a Japanese version distinguished by an odd number of rods and its sliding beads. Its rich history spans cultures, from ancient civilizations to its continued relevance in modern education.

  • We can mention that, for example, in Greek language the term was used as “ἄβαξ” or abax and there was also a second Greek word which, applied to the term, “ἄβακoς” or abakos, meant flat surface or table.
  • It has been proved by many pieces of researches that the abacus learners can use both sides left and right hemisphere of their mind.
  • It is used to show how numbers, letters, and signs can be stored in a binary system on a Computer, or using an ASCII number.
  • Abacus, also known as “Suanpan”, is a Chinese calculator that has been around for over 2,000 years.
  • Therefore there was a need for a development tool for such calculations.
  • It is advised that the students are introduced to Abacus at a very young age, to provide them with enough exposure so that they do not find mathematics as difficult as they earlier did.

So, the farthest column on the right would be the “ones” place (1-9), the second farthest the “tens” place (10-99), the third farthest the hundreds ( ), and so on. Even today, in the modern world of computers and calculators, it is used by traders, merchants, etc. in many parts of the world. The term originated with the Arabic ‘abq’, which refers to dust or sand.

Do the same thing in the ones place, “borrowing” a bead from the tens place (making it 6) to subtract 7 from 12 instead of 2. Eight removed from nine is one, so a single bead is left up in the hundreds place. It is easier to use one’s thumb to move the beads in the top row, and the index finger to move the beads in the bottom row.

Still, its simplicity and functionality have made it a valuable asset in mathematical education for centuries. Using the Abacus helped early civilizations advance in trade, architecture, and engineering. Today, the Abacus is still widely used in some parts of the world, especially in Asia, to teach children how to perform mathematical calculations. Some experts believe learning to use an abacus can help children develop better mental math skills and a deeper understanding of mathematical concepts. Whether you’re interested in the history of mathematics or want to improve your mathematical abilities, understanding the Abacus and its role in mathematical education is an essential step.

In the Middle Ages, the Abacus was further developed in Europe, and merchants and traders used it for bookkeeping and accounting. In the 17th century, the Abacus was introduced to Japan, where it was embraced and further refined, resulting in the development of a unique style of Abacus called the Soroban. Today, the Abacus is still used in many parts of the world, particularly in Asia, as a teaching and learning arithmetic tool.

what is an abacus

Some historians believe that the abacus was the first instrument created to perform calculations. Invention and technological innovation have relegated the use of the abacus and caused it to lose popularity in schools and homes, where it was previously used to educate children. As Abacus became more widespread, various versions of the device emerged in different parts of the world. For example, the Roman Abacus, used in ancient Rome, was similar to the Chinese Abacus but had slight differences in design.

From Greece and Rome to Russia, China, and Japan, abacus design and precision evolved. The approximate timeline of abacus like instruments can be given and no specific date can be given. Sumeria , the calculator by Mesopotamians, has the earliest records during the time 2700 and 2300 BC. Though it can’t be stated clearly but the Ancient china is attributed for the early use of abacus.

In austere field environments, rudimentary abaci have been commonly used by infantry soldiers among many of the worlds’ armed forces up to the present day. Another popular use of abaci around the world is to teach arithmetic to children, especially multiplication; the abacus can substitute for rote memorization of multiplication tables. So in many Asian countries, the abacus remains a point of cultural pride and mathematical skill. So while the exact origin is uncertain, abacuses developed across Eurasia over thousands of years as an efficient calculation tool.

In the 21st century, portable counting devices rarely exist as separate entities. Instead they are simulated as Apps running on desktop computers, smartphones and tablets. Civilization, which began recording history with a stylus and a clay tablet thousands of years ago is re-using those original terms today. In the Middle Ages, wood became the primary material for manufacturing counting boards; the orientation of the beads also switched from vertical to horizontal. In Western Europe, as arithmetic (calculating using written numbers) gained in popularity in the latter part of the Middle Ages, the use of counting boards began to diminish and eventually disappear by 1500. Both the abacus and the counting board are mechanical aids used for counting; they are not calculators in the sense we use the word today.

Due to fundamental similarities in their core functions, computers are sometimes referred to as an abacus due to their striking resemblance. More recently, the use of the abacus has been shown to produce a number of changes in the grey matter and brain matter, helping to maintain integration and accelerate learning through training. It also helps us to solve arithmetic problems through calculation and memory, as long as the operations are done with simple numbers. Today, this ancient instrument is used as a type of didactic toy to teach mathematics in a simple way to children, as it functions as a multiplication table. This calculating tool uses a counting frame and a series of beads on an upper and lower set of rods. Beads are pushed to the center to mark numbers in different place values, making it easy to make complex calculations.

Careful observers will note that the metal rods, on which the beads slide, have a slight curvature to prevent the “counted” beads from accidently sliding back to the home-position. The design of the schoty is based on a pair of human hands (each row has ten beads, corresponding to ten fingers). Despite the abacus being ancient in its origin, it is still in use today. It has been a boon for the visually challenged as learning placement value, and other calculations can be done by touch. In many countries abacus is taught to early school goers as it has been seen that it helps subtends have a better understanding of numbers.

This Abacus is still in use, however, it is overshadowed by the use of electronic calculators. The Abacus is constructed of various types of hardwoods and comes in various sizes. The frame consists of a series of vertical rods on which several wooden beads are allowed to slide freely. A horizontal beam is used to separate the frame into two sections i.e the upper deck and the lower deck. Each rod consists of beads, which we can move up and down, with the help of the index and the thumb finger. Fibonacci learned of the Arabic numbering system when he accompanied his father, a merchant, to various Arab ports in the Mediterranean Sea.

An abacus is a calculation tool used by sliding counters along rods or grooves, used to perform mathematical functions. In addition to calculating the basic functions of addition, subtraction, multiplication and division, the abacus can calculate roots up to the cubic degree. The abacus (the suanpan is the most useful variety) is a deceptively simple calculating tool still used all over the world. It’s a useful learning device for the visually impaired, as well as for anyone who wants to learn the roots of the modern calculator.

The Chinese abacus was known as the suanpan, it is believed to have been in use since at least the 2nd century BCE. It is believed that Mesopotamia used an abacus for going back during 2700 B.C. Additionally, it was also used in other civilizations such as Greek, Egyptian, Chinese, Persian, Roman, etc. The invention of a numeral system allowed numbers to be broken up into units, tens, hundreds, and so on.

It has also become a symbol of cultural heritage and a reminder of the vital role that ancient mathematical tools have played in shaping the modern world. The Chinese abacus, also known as the suanpan (算盤/算盘, lit. “calculating tray”), comes in various lengths and widths, depending on the operator. There are two beads on each rod in the upper deck and five beads each in the bottom one, to represent numbers in a bi-quinary coded decimal-like system. The suanpan can be reset to the starting position instantly by a quick movement along the horizontal axis to spin all the beads away from the horizontal beam at the center. The beads that are located at the lower of the frame are called “Earthly beads,” and these contain one value in the first column. The beads are counted when they move towards the reckoning bar, and if any bead does not touch the reckoning bar, that column contains value zero.

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Встречи 1:1 Почему не работает такой простой и понятный инструмент

Синхронизация документов быстрее и безопаснее, чем в Google Drive. Бесплатно планировщик встреч можно пользоваться 15GB для хранения файлов на облаке. Если вы используете платформу в компании и нужно больше памяти, то Google предлагает заплатить $0,04 за GB и $8 в месяц за каждого активного пользователя.

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ATS-системы: Централизованное управление процессом рекрутинга

инструменты для планирования встреч

Говоря про приоритизацию и распределение задач, то лучше всего начать с разделения на группы по срочности, важности и сложности. Таким образом, если после трабла с железом не появилась публичная и прозрачная процедура запроса нового железа с её оглашением перед всеми, то проблема (с менеджерской точки зрения) не была решена, т.к. Завязывать решение на себя («хорошего парня») и тем самым усуглублять человеческий фактор — не sustainable решение. Так должно решаться по возможности всё, что не совсем специфическое, ибо, как правильно ниже написали, болит у всех одно и то же, в основном.

инструменты для планирования встреч

Как планировать дела, чтобы повысить личную эффективность

Компания ООО «АЛЛСОФТ Украина» как поставщик программного обеспечения с большим опытом стремится сделать процесс приобретения лицензий максимально удобным и прозрачным. В связи с чем, ниже приведены основные типы поставляемой продукции и сроки получения лицензий. Упростить работу помогают многочисленные методики, разработанные специалистами и экспертами в области управления временем. К примеру, если можете, назначайте встречи в местах, которые близко к дому или офису, чтобы не тратить на дорогу драгоценные минуты. С помощью инструментов автоматизации гораздо проще организовать себя и свою деятельность. Сложность в управлении своим временем и делами, в первую очередь, состоит в том, что нам постоянно что-то мешает, отвлекает, забирает внимание, расфокусирует и т.д.

Негласные правила дистанционной работы

Моя цель — найти подход к каждому сотруднику, с которым я работаю. Есть мнение, когда на шхуне дела плохи, все бегут, и нет бюджета чтоб это остановить, заходят экспериментальные методики по мотивации весляров. Весь этот бред с саморазвитием и мотивацией настолько не вяжется с действительностью и процессами в Украине, что даже смешно. Давно уже пора понять что единственное что действительно мотивирует людей это $ Видимо по этому в US конторах этим стараются мотивировать, предлагая акции компании, на определенных условиях.

Шість маловідомих функцій Google Календаря

Лучше всего с этим справляется полноценный сон и питание с приоритетом в сторону углеводов, если речь про умственный труд. В таких ситуациях нужно вовремя зафиксировать то, что человек поменялся, а отношение к нему — еще нет. Пару раз приходилось это корректировать, и через пару месяцев люди сами не могли понять, почему ранее относились к сотруднику «как-то криво». — это как раз один из инструментов, чтобы выявить что работнику так, а что не так. Когда вы доверяете сотрудникам, вы точно знаете, что они поступают правильно, даже когда вас нет в офисе. Вам не нужно постоянно проверять их, чтобы убедиться, что все идет так, как было задумано.

  • В результате в расписание будет добавлена новая активность с типом “Визит”.
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  • Сам Uber Conference позиционирует свой сервис, как «конференц-звонки без стресса».
  • Asana — функциональная альтернатива Trello для управления командами средних размеров и разработкой проектов разной сложности, которую нетрудно адаптировать под собственные рабочие процессы.
  • Еще один важный инструмент, без которого трудно представить мою работу, – это Calendly.
  • Так PM могут получать четкую картину о том, как команда использует время и находить способы улучшить общие процессы.

Приложения и сервисы для работы

Главные особенности — «заточенность» под Agile-проекты, высокая адаптация Jira к работе с проектами любой сложности и кастомизация. Программа предлагает широкий выбор готовых шаблонов, возможность выбрать проекты под управлением командой или компанией, продвинутый функционал для работы менеджера в роли администратора. Asana — сервис управления проектами, который визуально и по функциональности в базовой версии похож на Trello. Задачи ставятся на Kanban-доске, принцип управления которой стандартный для данного вида инструментов. Из интересных фич — отображение собственного списка задач сотрудника на день, неделю и так далее в формате списка, календаря или доски.

Весь секрет в планировании, которое так часто недооценивается и пренебрегается. Уже сегодня вы можете стать на путь высокой продуктивности, для этого вам нужно всего лишь купить блокнот UTIME и ручку. Хотим отметить, что это не просто записная книжка, в которую заносится список дел и важные отметки. UTIME — это оригинальная авторская методика, которая помогает быть эффективными на работе, дома, в бизнесе.

Польза календарей для бизнеса и маркетинга

Ставя дедлайн себе, давайте обещание представить свое решение к конкретному сроку другим участникам команды или причастным коллегам. Понимаете, в какой период дня вы наиболее продуктивны, а когда – активность снижается. Мы собрали для вас несколько действенных советов и лайфхаков для ежедневного планирования задач. С таким подходом тайм-менеджмент действительно открывает больше возможностей и повышает эффективность. Календари позволяют учитывать сезонные тренды и праздничные периоды.

И очень зря, ведь тайм-менджемент на бумаге, при грамотном подходе, может увеличить вашу продуктивность в несколько раз. Вы и сами не заметите, как начнете все успевать и станете хозяином собственного времени, которого раньше так не хватало. Этот сервис можно не просто использовать в роли хранилища документов и файлов, но и дополнить полезными расширениями.

Trello – веб-приложение для удобного управления проектами, позволяет координировать поставленные задачи и их выполнение, а также коммуницировать с коллегами. Отображает задачи в виде списков, которые прикреплены к доске. Участники команды могут добавлять свои комментарии, вложения, чек-листы и пользовательские заметки к картам, вмещая все эти данные на одной странице. Google Workspace – это комплекс облачных инструментов и приложений от Google, предназначенный для совместной работы, общения и управления задачами в бизнесе. Для эффективной организации рабочего процесса сегодня не обойтись без автоматизации. Мы уже упоминали о пользе CRM-системы для планирования и контроля.

Хорошо помогает чтение, прослушивание музыки и прогулки на воздухе. Повышенная физическая активность и гимнастика будет только в плюс, особенно, если акцент делается на спину и глаза. В некоторых крупных компаниях практикуются сеансы йоги и короткого сна во время рабочих перерывов, так что тоже можете взять на заметку. Как бы тщательно вы не прорабатывали свой график, всегда есть вероятность переноса задач, их отмены или корректировки из-за внешних обстоятельств или какой-то неучтенной детали в начале.

О том, с чем работает SMM-менеджер, рассказывает Вика Богомаз из SMM-агентства wishdo. Jira — один из самых популярных сервисов для IT-команд, предлагающий большой арсенал инструментов для ведения проектов. По факту представляет из себя комплекс IT-решений, которые в большинстве случаев полностью закрывают все рабочие запросы PM-ов. Если вы фрилансер, помните, что даже без дорогостоящих систем можно эффективно организовать свою работу. Используйте Google Docs для хранения информации, Magical для автоматизации рутинных задач, а Calendly для удобной планировки встреч.

Trello — приложение-планировщик на основе идеи Kanban-доски для совместной работы команды (сервис часто используют в качестве первого пробного таск-менеджера). В базовой версии каждый проект представлен в формате доски, которая разбита на колонки с названием этапов рабочего процесса. Этот быстрорастущий стартап отлично подходит для коммуникации в реальном времени и парных или командных обсуждений. С ним вы можете организовать чаты по темам и интегрировать свою работу с Github, Trello, Pingdom, и другими инструментами. В нашей редакции с июня мы тоже начали использовать Slack и как-нибудь расскажем об этом подробнее. Google Workspace представляет собой мощный комплекс инструментов, который может значительно улучшить производительность и эффективность бизнеса любого размера.

Эти планы варьируются от базовых, предоставляющих основные инструменты, до расширенных, включающих дополнительные функции безопасности и управления. При интеграции CRM с Google Workspace могут возникать различные проблемы, такие как конфликты данных или проблемы совместимости. Важно тщательно планировать процесс интеграции и выбирать проверенные инструменты и расширения, а также предусмотреть регулярное обслуживание и поддержку системы.

Нужно лишь загрузить документы в папки по месяцам и писать, когда в них появляется новая информация. Kato позволяет использовать чат, видео, аудио и делиться экранами с коллегами, и всё это — бесплатно. Скриншоты и визуальные заметки делаю через Awesome Screenshot – работает быстро, позволяет редактировать картинку, добавлять текст, пометки, делиться ссылкой или скачивать файл.

Роскошное расширение, которое проверяет мои ошибки в английском тексте прямо в процессе написания (работает на любой странице браузера – в том же Gmail и Google Docs в том числе). И удобно, когда кто-то тебя страхует, вычитывая опечатки и предлагая поставить пропущенные запятые. Иногда я даже вхожу в топ-5% самых грамотных людей недели, которые используют Grammarly (буду надеяться, что мне не врут). А чтобы найти в своем или новом городе кофейню для работы, место для бизнес-встречи или ужина активно пользуюсь приложением FourSquare, которое выручает меня почти каждый день последние 7 лет или даже больше.

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