History of Trigonometry

Trigonometry, derived from the Greek words “trigonon” (“triangle”) and “metron” (“to measure”), focused on computing numerical values of triangle parts or shapes disassembled into triangles. Other parts’ values were given until the 16th Century. Pythagoras, Aristotle, or the ancient civilization of the Greeks, Egyptians, and Babylonians may come to mind while looking at the dawn of trigonometry.

Pythagoras, the author of the Pythagorean Theorem, was afraid of beans and had a cult to worship triangles, his followers were not only vegan but also didn’t eat beans because they believed that a part of their soul escaped every time, they passed gas.

The Pythagorean Theorem, traditionally known as the square of the hypotenuse’s length equalling the sum of squares of the other two sides of a right-angled triangle, formulates as a² + b² = c². For example, (3)² + (4)² = (5)².

The Rhind papyrus (1800 BCE) was an Ancient Egyptian Collection of 84 mathematical problems to the likes as Arithmetic, Algebra, and Geometry. The Geometry portion also consisted of five issues dealing with the seked or what we now refer to as the hypotenuse.

The Rhind papyrus’ 56th problem addressed a pyramid with a height of 250 cubits and a length of 360 cubits. The solution provided the ratio of 51/25 palms per cubit, equivalent to the pure ratio 18/25 considering that one cubit equals 7 palms.

This referred to the “run-to-rise” ratio of the pyramid in question—in effect, the cotangent of the angle between the base and face, from this we can examine the Egyptians’ extent of knowledge of the numerical relations in a triangle along with trigonometry.

The Greeks initiated modern trigonometry, and Hipparchus (120 BCE) formulated the table of values for trigonometric functions. Being an astronomer, he focused on spherical triangles formed by three stars on the celestial sphere. Still, he was also familiar with the basic formulas of plane trigonometry.

The symbols for trigonometry were formulated only in the 17th Century. Ptolemy’s Almagest was the first major ancient work on trigonometry to reach Europe that uses some elementary trigonometry that led to Ptolemy’s geocentric system being a succession of the heliocentric system of Nicolaus Copernicus.

The Babylonians used the Pythagorean Theorem some 1,000 years before Pythagoras was born. They wrote it down on a tablet now known as Plimpton 322.

The ancient Egyptians, Chinese, and Indians all used versions of its centuries before Pythagoras. An ancient Babylonian tablet used the Pythagorean Theorem 1200 years before Pythagoras was born.

India and the Islamic world were also great contributors to trigonometry which makes you wonder about the true importance and value of Mathematics as recent research shows us that 4000 years ago Neanderthals also had a basic sense of Mathematics.

AI is the Future of Education

The Covid-19 pandemic accelerated the shift to tech-enabled learning, even though it may not have been the most desirable driving force. However, the pandemic pushed tech integration into the field of education.

Companies across the world are happy about this since they can now show the world what technology can do if used in its most essential forms. Before we get into how AI technology plays a role in education, we will understand what AI means!

AI System definition, history, and the likes:

Manual effort in certain areas can drive very little change, especially on a larger scale. Automating some human tasks can maximize impact and reach a larger scale.

For all those tasks, we make use of Artificial Intelligence. While AI systems may perform tasks that we generally associate with humans, it is humans who build the framework that allows for AI principles to function!

AI is a determining tool that uses data to make recommendations, and decisions and also arrive at evidence-based research findings all in seconds. It can save time and a lot of valuable human resources that can be used in other domains of functioning. It can also help people make decisions based on risks and rewards. So, these are just a few of the vast capabilities that AI can power. 

With the right frameworks, AI can do things efficiently, very effectively, and on a massive scale.

AI in Education:

Keeping all the aforementioned points in mind there are a few things that we can be sure that AI does- 

  1. It helps teachers understand not just the needs of their students but also more personal things about their students. For instance, teachers can learn through AI where a student’s learning interests are.
  2. AI gives evidence-based reports to teachers rather quickly so teachers can foster collaboration with their students.
  3. AI is what is revamping and revolutionizing assessments right now. What AI does is use assessments as a diagnostic tool that reflects on a child’s learning needs instead of using it as an indicator of their capabilities.
  4. AI as a feedback tool is more reliable, free from bias and cancels out any human error in the estimation process. When feedback is based solely on a student’s performance, they tend to rely on it more than any other form of feedback.
  5. AI helps eliminate boundaries. AI does not see geographical boundaries. It can be used anytime anywhere, truly inspiring the idea that AI is a global experience.

There is a lot about AI that is still under research and development but what we have in the markets and in access these days makes use of some very optimal tools to give students an experience they will enjoy.

Innovation drives artificial intelligence, and with proper coaching, students learn to enjoy the methodology behind it. What AI also does is inspire and it is important now more than ever that students appreciate their opportunities to learn and act on them with performance, drive, and passion!

Help Your Child Manage Their Learning With These Tips!

Students in classroom
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Children require a lot of attention when they are pursuing academic interests and it is not the kind of attention that you think they need. Having parents spend every learning moment with them can cause children to lose focus, feel suffocated and also dislike the process.

For the sake of this article, we researched and put together a list of 5 things that work in helping your child manage their schoolwork and here’s also why these are important.

1. Time management

Children need to be taught time management from early on as it brings discipline to the growing and learning process. Help them build a timetable and hold them accountable for it. Avoid being the one who fills in the timetable for them, that is for them to figure out.

However, you can oversee to ensure there is school-play balance and also time for some extracurricular activities. It would also help if you had a time management chart so that you can lead by example!

2. Create space for open communication

When your child feels burnt out or pressured, they should be able to articulate it to you. Children who cannot do that grow up to entertain more stress and anxiety.

Managing a timetable also means looking at the tasks at hand and being able to say “it is too much for today, I will work on it when I have more mental energy”. This also teaches them the importance of rest.

3. Befriend the school and teachers

Do not be one of those parents who calls their child’s teachers every day. Be friendly enough with the teachers to know how your child is doing in school, if they’ve noticed any behavioural changes or if they have some tips for your child to follow.

It is important you do so primarily because you can intervene wherever necessary without badgering your child too much. It is also good if you communicate regularly with the school so that you are aware of all the developments and opportunities that are available to your child at school.

4. Help them think long-term

Management essentially means building a process today so that the outcomes are fruitful tomorrow. When your child is building their routine or expressing their interests, ask them to think about it long term as well.

For example, if your child wants to learn a new language, first ask them if they can continue pursuing these interests through multiple other engagements and how they seek to benefit from it in the long term. You can also help them by finding the answers to some of these questions for them!

5. Do not overschedule

Your child may be good at multiple things but it is important for them to find time for it. Also, as parents, you may want your child to fulfil each one of their interests but in the worst-case scenario, you may end up turning an interest into a chore. Helping your child manage their time also means teaching them to prioritise their immediate needs and make space for other pursuits in the future.

Parents, learning goes beyond teaching charts and sitting with them while they learn. It is also about giving space, learning when to hold your child accountable and also giving in to their interests if they show interest along with commitment. We hope these tips will help you and your child!

Teach Your Children to Love Maths With These Tips!

Math textbook page
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Mathematics or Maths for short, has been an item of absolute terror for students across generations. There is no easy way to say this, but Math, you are more feared than loved.

Before you read the above sentences and agree with us, remember that this is the fear that you can prevent your children from embodying and you could break the bad spell surrounding Maths. Want to know how? We have a list of five tips you can use!

1. Lead the change you want to see –

If you have had a bad experience with Maths and you constantly narrate it to your children, then they start internalizing a fear for the subject. This is something that you may want to prevent.

Granted that Maths may not have been easy for you but the goal is to make sure your child does not approach the subject with any preconceived fears. Maths anxiety is real and very catchy.

2. Know what they need to know and by when –

We assign a specific set of math skills that a child needs to know for each grade or level. For instance, kindergarten Maths will require number recognition and your child will need to know how to conceptualize numbers through examples; they should be able to count out five apples in a basket of ten. Knowing what they need to know is useful when you want to complement their school learning with activities at home.

3. Allow them to learn through conceptual experiences –

Learn Math as a life skill, not just a textbook concept. If your child is old enough to own a bank account, help them set up one. Additionally, you could ask them to keep track of their savings with the passbook and also teach them to calculate various things such as interest rates. This fun way allows you to see Math being used live in action! It also dispels fear if you reward it through their savings account.

4. Board Games are fun when it comes to Maths –

There are plenty of fun board games that require the use of applied Mathematics for victory. Games like Monopoly are not just great family games but will also teach your kids to appreciate the finesse with which Maths is being used everywhere, especially for fun!

5. Avoid Tuitions for performance –

Tuitions the way we have experienced are the most detrimental experiences for students who want to learn Maths. We send students for tuitions in the country only in the event that they are doing very poorly at it. A child forced into tuition will believe that they are incompetent at that subject.

Introduce tuitions as a concept to help them hone their skills instead of a method to discipline learning. It may be difficult to find a teacher who can help your student this way but till you do, avoid standardised tuition practices.

Math is only as scary as we make it, and we must treat it with confidence and respect. There’s no point fretting about a subject like Math that is highly misunderstood.

So much of Maths is a learner’s paradise and it is time we demystify the subject for now and forever! If you need help with that, start using our app, Class Saathi: MCQ Revision App. It’s for students in Class 3-10, free with 30K+ practice questions!

5 Strategies For Building Motivation in Your Child

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Children who score the best marks in exams are not the only smart kids in the class or school. In fact, many students with top-scoring potential are unable to achieve it because they haven’t received training in learning methods that suit them.

Coaching any child to understand their learning styles and recognize their limitations can lead to excellence not only in academics but also in life. Knowing how to work according to your personal style is crucial in long-serving motivation. Want to ensure that your child remains motivated to learn and study? Here are five tips that are ought to help!

1. Allow them to take the lead wherever they can

Teaching your child to articulate their strengths and weaknesses is crucial in ensuring they can express themselves in the best way possible. Ask them what they want to do, what topics they want to study and be open to the possibility of not being involved in everything your child does. Children respond better to learning when they do not feel controlled and when you are fostering an atmosphere that allows them to take charge of their academics.

2. Lead by example

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If you want your child’s curiosity to be nurtured by motivation, you must show them that you are constantly committed to trying or learning new things. For instance, if you take up a hobby and see it through, then you are showing your child that learning is fun and fruitful if supported with discipline and dedication. The best way to do this is to also engage your child in learning a new hobby with you.

3. Make the learning count and not the performance

Regularly associating learning with performance is detrimental to a child. Children tend to stop enjoying learning if everything they do is seen as a road to A+ on their report cards. They lose the value of the learning experience if they are only measured on their final performance. For any big project to come alive, the process is what people tend to refine and that is what leads to the final outcome. So always support the process over the outcome!

4. Recognise them as their own individuals

Children respond to “I told you to do this / I told you so” the same way adults do. The idea that children do not know any better is what keeps them from learning and staying motivated. They will need parental validation on everything they do and won’t be able to make independent decisions on their own. It is important for parents to give them a space to discuss their interests, argue their case and form their own opinions.

5. Discipline and organisation

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Encouraging your child’s interest is simply not enough. They must also be taught to commit themselves to the ideas they express or the interests they want to pursue. For instance, if a child has made a verbal commitment to learning a new language, follow up with them and ask them when they would like to initiate the process and also help them to find a time and space for it. Allowing these interests to hang in the air makes children feel like their parents don’t take their learning needs seriously enough.

As parents, you always want to curate the best experiences for your children and that holds true for academics as well. Children are sponges and they absorb whatever environments they see around them. So, it is important that we provide them with the support and mental stimulation they need as it only helps them stay focused when they grow older!

5 Non-Typical Learning Hacks to Engage Your Child Through the Holiday Season

Welcoming Diwali
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It is that time of the year where everybody is anticipating long weekends and shorter workdays. Slowly but surely, buildings around the country are setting up lights and diyas to hint at the upcoming excitement. Neighbours and relatives drop by with sweets and snacks every morning, accelerating all renovation activities.

The whole country has been in the festival mode for more than a month and once Diwali is over, Christmas and New Year are around the corner to keep the celebrations going. While this is all fun and festive, it is also a dreaded time for parents who have to make sure their children have some amount of facetime in front of their books.

Want your children to learn while also having fun? Read on to find out our top tips to engage children with their learning resources through the long holiday season.

1. Fix a schedule –

Entrust your child with a firm and compulsory schedule. Make sure they spend a fixed amount of time in front of their books and learning resources based on their attention span. Keep the schedule brief – it is unfair to expect them to sit for longer than 5 hours when everybody else is emulating the festival season. For instance, you can encourage your child to spend 2-3 hours revising and learning. It also helps if you encourage them to make their own plan of actions for the day.

2. Stock up on worksheets and question banks –

Student sitting cross-legged and doing rough work on a piece of paper supporting it on a register.
Photo by Mary Taylor from Pexels

Engage your child productively with worksheets and question banks. If they find it difficult to sit and revise with all that’s going on around them, allow them to use this time to practise and test their knowledge.

3. Involve them in the festival prep work –

Most households in the country are doing DIY projects at home to make ornaments and decorations for the festival. This is time you can use to enlist your child’s imagination! It also helps children improve their focus, refine their fine motor skills and it also gives them an outlet to relax while also learning something new!

4. Give them a designated space to work out of-

Please do not disturb sign on door knob
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This may be a fairly huge challenge since households get busy with tonnes of people and activities. If you don’t encourage your child to maintain their learning routine, it becomes easier to cement them in a permanent festival mood. Give them a designated space and request the other members of your house to not enter that area during their study time. 

5. Be flexible with what they’re learning –

It can be daunting for children to sit and study while everybody else is out there bringing in the festival season. It is not important that they sit and learn only their Maths-Science subjects. However, it is important for them to have a routine that festivals or celebrations do not easily disturb. Allow them to pick their learning material on their own. For instance, if your child wants to learn about the history and origins of festivals in India, encourage them to do that too!

The idea is not to make sure your child is constantly studying. However, it is to instil in them a keen sense of routine that becomes so entrenched that they grow not to be distracted by the various stimulating activities that are constantly a part of life in India and everywhere else.

Festivals are for fun and joy and children must experience that without having to compromise on their learning. It is also a time to show your children that festivals are also a lot of hard work along with a lot of fun. 

If you have great tips on how to engage your children with learning activities during the holidays, please share the same!

5 Useful Tips to Study Smarter, Not Longer

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Many students study for so many hours, but sometimes it doesn’t pay off as they expected. Is there any solution for this? The answer is “there is.” For decades, scientists and psychologists have been snooping on the top students and doing research on which study habits are most efficient.

Here are some tips you can apply for your future study plan.

1. Test yourself

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Your teachers use quizzes and tests to check on your progress. But you don’t want to find it out at the same time as your teacher. Better to know sooner, so you have time to correct it. Check for yourself before your teachers do. Try to quiz yourself the way the teacher asks questions. Figure out what stuff you don’t quite understand before the test. And check your work for accuracy before you turn it in.

2. Mix it up

In many cases, it helps to mix up your self-studying. Don’t just focus on one thing. Drill yourself on different concepts. Psychologists call this interleaving. Actually, your tests usually will have questions mixed up. More importantly, interleaving can help you learn better. If you practice one concept over and over, your attention decreases because you know what’s coming up next.

Mix up your practice, and you now space the concepts apart. You can also see how concepts differ, form trends, or fit together in some other way. Studies have shown that interleaving can help students with both strong and weak working memory. Working memory lets you remember where you are in an activity, such as following a recipe.

3. Don’t just reread the materials

One of the most common bad study skills that students have is reading their textbooks, worksheets, and notebooks over and over and over again. Too often, when students reread materials, it’s superficial. Rereading is like looking at the answer to a puzzle, rather than doing it yourself.

It looks like it makes sense. But until you try it yourself, you don’t really know if you understand it. This is because you’re not processing it deeply or picking more out of it. It gives you the illusion that you know the material very well, when in fact there are gaps.

4. Use pictures

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Making information visual is useful because it forms associations between bits of information. Images are much richer in information than language, and you must think about all the associations that go into generating an image.

So, with images, you’re actually growing more connections as you learn. Images can encapsulate a lot of information in a very small amount of visual display. Yet, that’s not to say that text is not important.

The key concept here is known as “dual coding”, presenting information in written and visual formats. Consuming information in this way can boost learning.

5. Use examples

Abstract concepts can be hard to understand. It tends to be far easier to form a mental image if you have a concrete example of something. For instance, sour foods usually taste that way because they contain acid.

On its own, that concept might be hard to remember. But if you think about lemon or vinegar, it’s easier to understand and remember that acids and sour go together. And the examples might help you to identify other foods’ tastes as being due to acids.

With these tips, you can save a lot of time while studying and process the materials way more efficiently.

If you have your secret study tips as well, share them with us in the comments below!

5 Tips to Achieve What You’ve Always Wanted

Cardboard boxes
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Are you someone who aspires to achieve things but finds it difficult to take any action? Most likely you are stuck in the overthinking cycle, where you are too cautious before taking a step ahead.

Thoughts are essential, but you also need action. Taking action isn’t easy, especially if external factors affect you more than your internal drive. Zig Ziglar rightly said, “You don’t have to be great to start, but you have to start to be great”. You may get nervous and feel like procrastinating. It is okay to feel that way and you cannot do much about it.

But once you start acting, this feeling can automatically convert to that of adrenaline. For example, do you remember when you plan to go jogging early in the morning, but you just find it difficult to get out of bed? Once you are out of bed and running, you begin to feel the runner’s high. The same goes for any other action. The mood will follow the action.

So here are some tips to get you going:

1. Deliver on your promises

Quite often we promise ourselves or those around us that we will do something. But over a period of time if we don’t see immediate results, we get less enthusiastic. Don’t let that happen. Deliver on your promises in terms of the efforts you put in, irrespective of the final result.

2. Show up

Hand to the elbow holding a grey bag
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The biggest indicator of a winning attitude is showing up no matter how you feel. This attitude should be a core value to you. For example, there might be days when you don’t feel like attending your regular classes. Do it anyhow. It may happen that you are not focused during the class. But make sure you write down the notes so that you can go back and study on your own.

3. Put things into perspective

Most of the time overthinking makes you exaggerate things and circumstances in your mind. So instead of worrying about everything, categorize them based on whether they really matter to you in the long term. For example, if you score less in a school exam, don’t feel disheartened. Don’t give up just yet. Think from the long term perspective. If you were considering the next 5 years, would your scores matter more or your learning?

4. Stop waiting for perfection

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We grow up in a society where we worship perfection. It doesn’t have to be the best or nothing at all. Things are not black and white. So, stop waiting for the day when you are perfect. Instead, start to get better at doing something while you’re doing it. The only thing that matters is how better you are today as compared to yesterday.

For example, most of us fear solving past year papers because we are scared that we are not fully prepared for them. That day of perfection might never occur. That doesn’t mean you should give up on solving those papers. In fact, the learnings you get from those papers will help you in scoring better at the exams. The mistakes you commit will help you avoid them in the future.

5. Put a timer to work

Hard work is not bad, but it has to be time-bound. Without any timeline, you may end up spending more time on something where it was not required and less time on something where it was required. So, plan your day in the morning or the previous night and try to stick to the plan as far as possible.

Even if you can follow just 50% of it, you will still be better off than without a plan. If you find yourself losing focus or overthink while studying, write down your thoughts on a piece of paper, set aside 5-10 minutes just for thinking and think only during that time. This will allow your mind to fully focus on the task at hand and finish it within time.

Of course, you’ve got to know what you are doing and you’ve got to plan. But you’ve got to also do it. So get into action, and results will follow! What are you waiting for?

If you found these tips useful please do let us know in the comments below.

Science Isn’t Just For Nerds Anymore!

Science is part of every aspect of our lives, whether we realize it or not. However, no matter how hard our teachers try, our school textbooks simply are unsuccessful in developing our interest in it. Certainly, studying science is part of our curriculum, but what if there was a way to enjoy studying it?

Here are some hacks that will make science more interesting to you.

Kid experimenting with circuit board
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1. Focus on the problem solving:

Science, just like other subjects, may seem boring if you focus only on the theory. The real beauty of science lies in its application. So, focus more on solving problems that can help you understand science better.

For example, instead of just reading theory about projectile motion, try to solve a real-world problem that needs you to calculate the distance a ball will travel when thrown horizontally with a certain speed.

2. Find science camps and workshops:

Science camps are great ways for you to explore science while interacting with other children. These camps provide hands-on learning opportunities by involving you in extracurricular activities and experiments.

During the pandemic, camps might not be conducted offline, but there are a lot of programs that take place virtually. Just look up ‘kids science camps’ on the internet or event listing pages and you will be able to find some good ones.

3. Follow science channels:

What better way to cultivate an interest in science than by exploring interesting facts and staying updated on the latest developments? You can find plenty of online resources for free. Based on your interest you can choose to follow the technical ones or even the ones for the general public. You can check out some of the below links for reference:
– Veritasium on YouTube
– TedEd on YouTube

4. Form a study group:

Science is more fun when you have a group of like-minded people. Form a small study group with friends who share an interest in science. You can make it fun by deciding a weekly topic and having a discussion on it on the weekends.

Another way is to find some good science-related documentaries and watch them together. At the end of it, you can discuss the learnings you had or what fascinated you about it.
5. Take a hike:

Just go for a walk-in nature with your friends or family. If you have an interest in nature or biology, actively observing habitats, geology, and more can provide valuable knowledge. It is a great way to have fun while learning science.

You can also note down your observations in a journal. If you are on the creative side, you can also take some pictures or even draw them. Engaging in this interactive form of learning will undoubtedly benefit you in the long run.

Science is a subject that doesn’t always come easy, but it can be fun if you approach it in interesting ways as shared above. Are you using textbooks as your only source of study? What are some innovative ways you use while studying science? Let us know in the comments below.

A Power Nap Can Actually Boost Your Productivity

On a long stressful day, what’s a better way to recharge than to take a quick power nap? Despite its known benefits, most of us feel guilty about adopting this unique productivity tool. However, even famous people like Einstein, Winston Churchill, JFK, and Leonardo da Vinci were all fans of the afternoon brain shut down.

So obviously it must not be a completely bad thing, right? In this article, we will cover the top benefits and some tips that can help you make the best out of this productivity practice.

cat taking a nap
Take a power nap
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Benefits of Power Napping:

1. Reduces sleepiness:

It might not be possible for all of us to get a continuous 8–9 hours of sleep every day. A lot of times even if we do manage to get that sleep, we do not feel that refreshed in the morning. A quick power nap can help you overcome this energy downfall and rejuvenate you for the day ahead.

2. Improves memory and cognition:

Research shows that an afternoon nap can help you feel more rested and alert. Longer naps can also help in improving your memory and cognition. So, for example, if you are thinking of really stretching your day just before exams, that might not be useful for you. When you feel really tired and drowsy during the afternoon, taking a short nap might benefit you more.

3. Regulates emotions:

Remember feeling cranky due to lack of sleep and having a lot of tasks at hand? A quick power nap does a better job in this situation rather than having coffee. Having coffee or anything that can instantly boost your energy might actually worsen your mood. So don’t hesitate to invest those 10–20 minutes at least in order to feel better.

Power Napping Tips:

1. Nap at the right time and for the right duration:

For most people, the duration of 10–20 minutes works the best, typically known as the power nap. The reasoning lies in the sleep cycle. The more you increase the duration the worse you will feel after waking up from the nap. This is because they may wake up from a deeper stage of sleep, which occurs later in the cycle, and feel fuzzy-headed.

Also, try to take a nap in the early afternoon. Research shows a nap taken any time between 1:00 pm to 4:00 PM will coincide with one of the energy dips you feel throughout the day. Thus, it will not have a negative impact on your overall sleep cycle and you will maintain a fine balance of your sleep cycles.

2. You don’t need to fall asleep:

For a lot of people falling asleep doesn’t happen in the flip of a moment. It might take up to 14 minutes or even more to actually fall asleep. So don’t worry about it.

What actually matters is that you close your eyes and let your body and mind relax. Also napping is a skill you will be able to develop over a period of time as and how you practice.

3. Find the right place:

The quality of sleep or nap also depends on how comfortable you are in the sleeping position. So, it matters where you are sleeping and what your body posture is while sleeping.

Choose a place that has minimal noise and more comfort. You need not always be in bed to take a nap. A comfortable chair or just lying down on the desk can do an equally good job.

For most people sleeping adequately and taking rest when required helps them feel better and improve their productivity. Instead of avoiding napping altogether, doing it with certain things in mind can help you get the most out of it.

Are you a napper or a non-napper? Do let us know in the comments below!