Maths – Funny Side Up

At QuickerMaths, we have been bringing you some seriously good tips and tricks on tackling maths problems. But it is good to have some fun too every once in a while.

Today, we want to talk about an amazing piece we found on how maths can be funny as well. And we’ve been laughing since we read it. In fact, it is so cool that we thought we will share it with you and spread the joy.

It is called “If you thought maths was boring, this will change your mind” and is on a new website we found cool enough to refer to you. Hope you like it as much as we did. These guys have a lot of other great stuff going on at the site as well, if you want to check it out.

The direct link to the site is mamamiia.com

Enjoy it, and have a proud and happy Independence Day!

Best
QuickerMaths Team

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Was Pythagoras Theorem actually proved by Pythagoras?

With all respect to Pythagoras, the so called Pythagoras’ Theorem was known to the ancient Indians long before the time of Pythagoras. Although Pythagoras introduced his theorem to the Western mathematical and scientific world long after, yet that theorem continues to be known as Pythagoras’ Theorem!

There are several proofs given by Indian mathematicians, everyone of which is much simpler than given by Pythagoras or Euclid. Here, we’re going to discuss few such proofs of the Pythagoras theorem:

First Proof of Pythagoras Theorem

a2 + b2 = c2

Where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides of a right angled triangle.

Here, AE pythagoras theorem= BF = CG = DH = x and ED = HC = BG = FA = y

Now, the square ABCD = square EFGH + the 4 congruent right angled triangles around it.

Therefore, z2 + 4 (1/2*x*y) = (x+y)2 or, z2 = x2 + y2. Hence proved.

Second Proof of Pythagoras Theorem

Here we’ll use the property of similar triangles that the area of similar triangles is proportional to the squares of homologous sides.

Any right triangle can be split into two similar smaller right triangles by drawing a perpendicular from point of the right angle. The similarity can be checked using Angle-Angle-Angle similarity.

It’s also evident from the diagram that: similar triangles

Area (Big) =  Area (Medium) + Area (Small)

Now since the triangles are similar they will have the same area equation.

If the long side is c (5), the middle side b (4), and the small side a (3), our area equation for these triangles is:

 

Area = F * hypotenuse^2   where F is some area factor (6/25 or .24 in this case; the exact number doesn’t matter).Now let’s play with the equation:

Area (Big) = Area (Medium) + Area (Small)

F c^2 = F b^2 + F a^2

Divide by F on both sides and you get:

c^2 = b^2 + a^2

Hence we get the famous Pythagoras theorem.

There are more than 100 ways of proving Pythagoras theorem. Which one is your favorite proof?

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Ask or Answer a Question and Get Rewarded

I am glad that the Maths Question Answer Platform of QuickerMaths.com has reached 135+ users in 2 months time since its launch. It is such a great feeling to see users asking questions and getting answers from registered enthusiasts, mutually helping each other out.

Today’s post is to announce a fun challenge for the month of July. The challenge is to be the highest scorer on the Q&A platform of QuickerMaths.com.

How do you score points?

The highest scorer will be the winner. You get points for activities like asking questions, giving answers, having your answer selected as the best, voting up or down a question or an answer and so on. The scoring pattern is explained in this earlier post – http://www.quickermaths.com/maths-question-answer-forum/

How the Winner will be decided?

There will be 2 winners. The user who scores the highest points by end of the day 31 July 2014 bags the first prize. The second highest scorer becomes eligible for the second prize.  Winners will be announced and their gifts will be sent to them in the month of August.

We can see the points scored in real time by each and every user by visiting the USER section of the Q & A platform. People can check who’s leading at any point of time.

Now the big question, what are the prizes?

What’s the Prize for the Winner?

 

First Prize: DigiFlip Explorer Laptop Backpack

Digiflip Laptop Backpack Explorer Bag
Digiflip Laptop Backpack Explorer Bag

but that’s not all, the first prize also includes 2 fantastic Vedic Math books for the winner.

Book #1: Vedic Mathematics (The Original Book) by Jagadguru Swami Sri Bharati Krsna Tirthaji Maharaja

Vedic Mathematics Book
Vedic Mathematics Book

Book #2: How To Become A Human Calculator?: With The Magic Of Vedic Maths by Aditi Singhal

How to Become a Human Calculator
How to Become a Human Calculator

Second Prize

Book #1: The Power of Vedic Maths by Atul Gupta

Book #2: Vedic Mathematics Made Easy by Dhaval Bathia

Book #3: Vedic Mathematics : The Student Taking Competitive Exams by author Rajesh Kumar Thakur

Any Questions?

I feel the challenge is pretty straight forward. You just need to actively participate on www.quickermaths.com/questions. The ultimate objective is to make the forum more useful for everyone by having more and more active and enthusiastic users. So go ahead and post your questions or give answers.

If you’ve any queries / suggestions / feedback, post it in the comment section below.

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7 Things to Avoid to Get Good Memory

Having a good memory is essential for becoming proficient in mathematics. It is often necessary to remember theorems (with or without proofs) to solve mathematical problems. To attain speed in solving complex problems, fundamentals of various topics should become part of the memory system. Good memory can be a great asset for learning new things, new subjects including mathematics.

How to Increase Memory Power?

In this article we will discuss things which should be avoided to harness brain power for an excellent memory. So here is the list of 7 things which should be avoided –

  1. Multitasking – Observation is the most important thing to train your memory. One reason people can’t remember things like where they have put their spectacles, keys, etc. is because they are not paying attention while putting them down. To acquire a good memory, stop giving continuous partial attention to everything.

    “The true art of memory is the art of attention” – Samuel Johnson

  2. All work and no playWe should make time in our daily routine for friends and fun. Our mind works best when we are happy and active. Research and studies show that life filled with fun and friends comes with cognitive benefits. If you’re a working professional, small little exercises like neck & shoulder exercises, stretching, frequent walks to water cooler, etc. during work hours relieve you of the pressure which builds up in our muscles. This helps our brain to focus and observe and hence better memory power.  Students should avoid very long hours of continuous study sessions. Breaks should be filled with some physical activities. To exercise your brain, puzzles and riddles are very effective.
  3. Being a Couch Potato – When you exercise the body, you also exercise your brain. Physical exercise enhances the oxygen flow to our brain and reduces the risk for disorders that lead to memory loss. Staring at screen which can be of the television or mobile or PC or tablet is reducing our attention span and capability to remember things. Go get a life.
  4. Being obsessed with Mobile or Tablets – Cell phones are supposed to make our lives easier. However, everything comes with consequences attached to it. Studies have shown that usage of mobile phones is negatively impacting human memory. The cell phone radiation damages the nerve cells in the brain. The effect of mobile phones is slow but its extensive and indisciplined usage over a long period will become a major issue for the mankind. Avoid sleeping with it.
  5. Stress and Tension – Anxiety, mental tension, nervousness, constant worry and pressure are brain’s worst enemies. Disappointments generated by fears and failures is equally dangerous. Avoid stress, stay calm and do your brain good.
  6. Unhealthy Food Habits – Brain is one of the most active part of our body. It works even when we are sleeping. Our brain needs constant adequate supply of energy in the form of glucose in our blood. Since I’m a vegetarian I can only suggest vegetarian foods which can boost your memory. Eat leafy green vegetables (like spinach), blue berries, broccoli, whole grains and tomatoes. Avoid long gaps between meals.
  7. Disturbed or Inadequate Sleep – To operate efficiently brain requires good undisturbed sleep. Imagination, creativity, decision making abilities are hampered due to lack of sleep. Whether you’re studying or working, sleep deprivation can stress out your brain and make your memory system highly ineffective. Learn to put aside all tensions of the day at bay before you retire to bed.

Well these are a few little things that I have discussed which seem to general but their impact is huge if diligently adhered to. Bring these changes to your lifestyle- unwind and uncomplicate. Lead a stressfree and joyful life, relax your mind and watch your brainpower grow phenomenally.

Do you have something else in your mind which can be added to this list?

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List of Mathematics Question Answer Sites

Today I will discuss some platforms where students of maths at various levels can ask questions and get answers. You can get answers to all the problems of mathematics you couldn’t solve yourself. It’s like your maths teacher or a friend expert in mathematics is always available to answer your questions. Isn’t that wonderful?

Get Instant Answers – In most cases you get the answer instantly. Most of the time you get answers from multiple people on the same question. Hence you get exposed to various ways of solving a mathematical problem and you can also compare and decide which way suits you the best.

No Chit-Chat – These sites are all about getting answers. These are not discussion forums and hence not meant for chit-chat.

Good Answers – The voting mechanism on these websites allows good answers to go to the top by getting voted up. The best answers show up first so that they are always easy to find.

Specific Target Audience – These websites are targeted towards students studying math at any level and even professionals in fields related to mathematics. These websites are in most cases are community driven where common people like you and me post questions and give answers to questions posted by someone else.

Topic-wise segregation of Questions – This helps students to see all the questions related to a particular topic categorized in one place using categories and tags. 

Here is the list of those Mathematics related Question Answer Websites –

For School Students

For Students of Competitive Examinations – QuickerMaths Question Answer

For Advanced Math Students

General Forums for getting Answers

Have you come across any other maths question answer website?

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QuickerMaths.com launches Question Answer Platform

Quicker Maths has been bringing to you hundreds of free easy mathematics tricks and simple tips. I have shown you the magic of Vedic Maths Sutras in mathematical calculations.

On and off I’ve been getting a lot of maths questions on email, on Facebook profile, while interacting face to face with people and as comments on the posts on QuickerMaths.com. To be frank, I was not able to answer each and every question due to paucity of time or completely missing out on some questions here and there. Hence I decided to add a Question Answer platform on QuickerMaths.com. The usage of this platform is completely free.

The most important purpose of adding the question answer section is to continue helping the readers in their quest for solving mathematical problems. However, there are other equally motivating reasons for adding this platform on QuickerMaths.com

You can Ask any Maths Questions

I will try to answer as many questions as possible. However, the best part is this will not remain completely dependent on any one individual. Anyone can answer questions asked by any one.

Screenshot of Question Answer Platform added on QuickerMaths.com

screenshot

Learn from Questions Asked by Other People

Larger the participation from all readers, larger will be the question bank on each topic. This will help all the learners to get answers to more and more questions. Most of these questions will be either from competitive examinations or from text books of school and college going students. Hence, this can act as a self learning tool for students preparing for quantitative aptitude or mathematics in general.

Topic wise Segregation of Questions

I’ve pre-specified few categories under which you can ask questions. I’ll keep adding more categories as we go along. Categorizing questions topic wise will help you refer to them when preparing for that particular topic. Hence it will help in some amount of self learning of that particular topic.

If the question you want to post doesn’t fall under any of the existing categories, put it under Other category. Later I’ll create appropriate category and put your question(s) under it.

Facebook Login

You can register either by using your email id or by logging in through your Facebook account. Facebook log in is exceptionally simple and convenient – no need to remember separate username and password.

Earn Points on Activities

You’re being given a score for every activity you do on quickermaths.com/questions. Refer to the table below for details –

Points to be Earned

Posting a question:

20

+  points
Selecting an answer for your question:

30

+  points
Per up vote on your question:

10

+  points
Per down vote on your question:

10

–  points
Limit from up votes on each question:

100

+  points
Limit from down votes on each question:

30

–  points
Posting an answer:

50

+  points
Having your answer selected as the best:

300

+  points
Per up vote on your answer:

20

+  points
Per down vote on your answer:

20

–  points
Limit from up votes on each answer:

200

+  points
Limit from down votes on each answer:

50

–  points
Voting up a question:

10

+  points
Voting down a question:

10

+  points
Voting up an answer:

10

+  points
Voting down an answer:

10

+  points
Add for all users:

100

+  points

After a point of time the profiles of individuals with highest score can be highlighted on the sidebar. This will be in essence showcasing the most helpful person who has scored points by answering other people’s questions, by asking relevant questions, etc.

I appreciate the love and affection of all the readers and request all of you to register yourself on Question Answer platform of QuickerMaths.com and starting asking and answering questions!

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8 Tips to Overcome Fear of Maths

“When did you get up this morning? At 6.35. Did you reach your destination in time? Yes, I arrived ten minutes earlier even though I got up five minutes late. I usually walk but today I took a bus. Why not a taxi? Isn’t it faster? Faster, yes. But in my case the speed of the bus was sufficient. Besides I compared the fares of the two means of transport and concluded that taking a taxi would mean incurring unnecessary expenditure.

Wow! What a clever guy! Saves money, saves time.

However he is just an ordinary guy who just is confident about calculations which can be used in day to day life. Let me suggest some ideas which you can use yourself or help your young ones to enhance maths skills and gain similar confidence –

Tip #1: Do calculations mentally in everyday life

You should go grocery shopping and try to beat the shop-keeper in his speed of calculation. Try this especially with fruit or vegetable vendors. Mostly they are very good at basic calculations as they don’t use calculators. Try to understand their way of making mental calculations. The secret of their speed is that they break down the calculations to a level of simplicity they can handle. For example, you purchased 650 grams of bitter gourd priced at Rs.35 per kg. Their mode of calculation will be to start with the price of 100 grams i.e. Rs.3.5. Hence 600 grams will be 3.5*6 = 21 + (price of 50 grams which is 3.5/2) = 21 + 1.75 = 22.75

In super markets or merchandise shops you will often find 50% or 40% or 10% off. Use such small opportunities to learn discounting, rounding off, percentage calculations, etc.

Tip #2: Do not stick to text books

Text books can be monotonous and hence make things boring at times. Use newspapers and magazines to read and interpret and explain the usage of graphs and charts like bar chart, pie chart, line chart, histogram, etc. Regular exposure to such things can make understanding statistics simpler in future.

Tip #3: Memorize few things

If you want to achieve the speed of a train, you can’t use wheels that are fit for a bullock cart. What I want to say is that if you want to achieve good speed in calculations you need to mug up few things listed below to make your foundation strong –

  • Memorize tables up till 20×20. This multiplication method can come handy.
  • Squares of numbers up till 25
  • Cube of numbers up till 15
  • Powers of 2 up till 10
  • Powers of 3 up till 5

Tip #4: Play Number Games

Some board games like Monopoly can help in strategic thinking as well as improve basic calculation skills. Playing cards games which involve certain amount of calculations can help you in improving your speed of calculation without you realizing about it.

Permutation & Combination and Probability can be taught using coins, dice and playing cards. To make it more challenging use two or more coins, dice, etc. Start with listing down all possibilities. Then try to answer questions like, what is more likely 7 or 12 when 2 dices are rolled.

Play number guessing games with your friends. Make it time bound. One example to start with can be, the number is between 50 and 100 and it is a multiple of both 8 and 9. It can be real fun playing such games.

Tip #5: Get Help from Internet

There are a lot of resources available for free on the internet. You must use these websites to improve your maths skills. Most of them make it very interesting material and are available for free.

Tip #6: Read Quicker Maths Books

In one of the past articles I’ve given a list of quick math books which will make you fall in love with numbers and various intricacies of mathematics without becoming boring at any stage.

Tip #7: Solve Puzzles and Riddles Regularly

Solving puzzles gives a feeling of handling a real life problem. It gives us the enthusiasm to think logically, do required calculations, to look at all the possibilities, reject few and make decisions. All these are prerequisites for acquiring good mathematics skills. This is one of the reasons why I chose to put up a separate section on puzzles and riddles on Quicker Maths

You can also start solving Sudokus, if you are not already doing that. Do it for the fun of it.

Tip #8: Keep Learning New Mathematics Memory Tricks

Not being able to recall important maths formula at the time of application is one of the big deterrents for students. To become good at remembering such formulae mnemonic, memory tricks and methods like these can be used –

This list is by no means an exhaustive list. You can keep trying new things to overcome the fear of maths. However, the first step is to acknowledge the fear and take it heads on. Don’t be scared of making mistakes. Even when you’re helping someone, don’t discourage them when mistakes happen. Tell them to explain the steps adopted by them to solve the problem. Let them figure out where they made the mistake.  Once that is taken care of explore this list to overcome the fear of Mathematics gradually.

Let us know how you overcame your fear for maths?

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How to Develop Effective Thinking through Puzzles

While going through an online course on EDX (Massive Open Online Courses) named Effective Thinking through Mathematics with Professor Michael Starbird, I came across couple of interesting puzzles. This course basically talks about how one can improve his thinking and make it very effective using mathematical reasoning in decision making. I am sharing those with you here in this post.

Puzzle 1: Gem in the Stone

Here are nine identical-looking stones. One can’t differentiate any one from the others. Eight of the stones weigh the same, but one of the stone containing the jewel weighs slightly more than the others

For your help you have got 2 balance scales. You may use each of the two balance scales exactly once. Is it possible for you to select the slightly heavier stone containing the gem (jewel) from among the nine identical-looking stones? Explain why or why not.

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Contribution of Indian Mathematicians

Famous Indian Mathematicians and their Contributions

History of mathematics will remain indebted forever to the contribution of Indian mathematicians. In this post I will like to draw your attention towards the contribution of some famous Indian mathematicians dating from the Vedic period to the modern times. They have contributed significantly. However, many of them did not get their due recognition due to insufficient follow up by the later generations.

Baudhayana

It was Baudhayana who discovered the Pythagoras Theorem 1000 years before Pythagoras was born! He stated that a rope stretched along the length of the diagonal produces an area which the vertical and horizontal sides make together. This is such an incredible way of visualizing Pythagoras theorem.

Aryabhatta

He is probably the most celebrated Indian mathematician. He approximated the value of pi correctly upto five decimal places and discussed the concept of sine.

He gave the area of a triangle as the result of perpendicular multiplied by half-side.

In algebra, Aryabhatta summed series of squares and cubes and also solved indeterminate equations of the type ax -by = c.

He was the first one to calculate the time period of earth’s rotation as 365 days!

Brahmagupta

He is the one who gave us the concept of zero and negative numbers.

He proposed rules for the solution of quadratic and simultaneous equations and calculated area of a cyclic quadrilateral with ‘s’ as semiperimeter.

Founder of the branch of higher mathematics known as “Numerical Analysis”, he gave the solution of the indeterminate equation Nx²+1 = y².

The identity x²- y² = (x+y)(x-y) is attributed to him.

Bhaskara

He expanded the work of Aryabhatta and found a rational approximation of the sine function.

First to write Hindu-Arabic numerals and zero(as ‘0’), he declared that any number divided by zero is infinity and that the sum of any number and infinity is also infinity!!

Bhaskara introduced chakrawal, or the cyclic method, to solve algebraic equations. Six centuries later, European mathematicians like Galois, Euler and Lagrange rediscovered this method and called it “inverse cyclic”.

Bhaskara laid the foundation of differential calculus. He gave an example of what is now called “differential coefficient” and the basic idea of what is now called “Rolle’s theorem”. Unfortunately, later Indian mathematicians did not take any notice of this. Five centuries later, Newton and Leibniz developed this subject.

Mahavira

A Jain mathematician, Mahavira gave the derivation of the volume of a frustum by a sort of infinite procedure.He worked with the concept of ardhaccheda: the number of times a number could be divided by 2; effectively logarithms to base 2.He also worked with logarithms in base 3 and base 4.

Varahamihira

His mathematical contributions include the discovery of trigonometric formulas:

Bhaskara II

He was a mathematician-astronomer who gave a proof for division by zero being infinity. He declared that a positive number has two square roots and also discovered the derivative and the differential coefficient.

Srinivasa Aaiyangar Ramanujan

In modern India, Ramanujan has gained substantial fame as a mathematician. Hardy-Ramanujan-Littlewood circle method in number theory, Roger-Ramanujan’s identities in partition of numbers, work on algebra of inequalities, elliptic functions, continued fractions, partial sums and products of hypergeometric series are his main contribution.

1729 is popularly called Ramanujan Number. Click to know more about Ramanujan Number

P.C. Mahalanobis

He founded the Indian Statistical Research Institute in Calcutta. In 1958, he started the National Sample Surveys which gained international fame.

C.R. Rao

A well known statistician, famous for his “theory of estimation”(1945). His formulae and theory include ‘Cramer -Rao inequality’, ‘Fischer -Rao theorem’ and ‘Rao – Blackwellisation’.

D.R. Kaprekar

Dattaray Ramachandra Kaprekar, was a school teacher in Devlali near Nashik, Maharashtra. He never received  a masters degree and was laughed at by his contemporary mathematicians for his work being too trivial and unimportant. But today he is hailed as a great recreational mathematicians of India. Fond of numbers, Kaprekar is well known for “Kaprekar Constant” 6174. Take any four digit number in which all digits are not alike. Arrange its digits in descending order and subtract from it the number formed by arranging the digits in ascending order. If this process is repeated with reminders, ultimately number 6174 is obtained, which then generates itself. Apart from that he discovered Kaprekar Numbers, Harshad Numbers, Self-Numbers and much more.

Harish Chandra

He greatly developed the branch of higher mathematics known as the infinite dimensional group representation theory.

Narendra Karmarkar

He, working at Bell Labs USA, stunned the world in 1984 with his new algorithm to solve linear programming problems. This made the complex calculations much faster, and had immediate applications in airports, warehouses, communication networks etc.

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Free Mathematics Resources Available Online

During our student life (school or post-school), search for useful knowledge resources for learning arithmetic, algebra, trigonometry or some other stream of mathematics is never ending.  Here let us discuss few such online free sites, which can be very useful in learning maths. These resources available for free on internet can help us learn fundamentals of various basic to advanced level topics of mathematics. Some of these also provide online tests for practice and solutions to thousands of questions.

Khan Academy – According to me nothing on internet can beat the zeal of Mr. Salman Khan who has produced more than 3400 videos on diverse topic and has extensively covered Mathematics from basic to advanced level in his wonderful video lectures. Best part is all the lessons are absolutely free for everyone.

www.khanacademy.org Read More

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