PI APPROXIMATION DAY (22/07) QUIZ

 Dear All

On the occasion of Pi Approximation Day being celebrated on 22nd July (22/7) every year, Here is one very interesting quiz dedicated to Pi. There are 40 questions related to Pi. Let's know the mysterious number pi. Don't forget to share with your known/students/teachers/

Just give a TRY

 The story of pi is more than 4000 years old but the race to find its value is still continued.

Interesting Facts:-

1.  

                                             (Courtesy:- From the Tweet of @Cliff Pickover)

2. 22nd July is the birthday of -- GAUSTAV HERTZ      ---- WILHELM BESSEL  and great Indian mathematician - SHREERAM SHANKAR ABHYANKAR 

3. 22nd July 2025 is the 203rd day of the year.  203 is the 6th Bell number, i.e. it is the number of partitions of a set of size 6.

203 is a palindrome in base 3  (21112),   base 6 (535), and base 8(313),

203^2 + 203^3 + 1 is prime. 203 is the number of nondegenerate triangles that can be made from rods of lengths 1,2,3, 4,...,12

                                                      A brief Introduction of Pi

Value of Pi = 22/7 is probably taken because Archimedes (born in 287 BC) calculated the ratio of circumference to diameter coming out to be lying between 223/71 and 22/7.

Aryabhata (born in 476AD) was the first Indian mathematician who calculated the value of pi correct up to 4 decimal places. His value of pi was 3.1416. 

The Mahabharta decodes the value of pi as 3.

योजनानां सहस्राणि विष्कम्भो द्वादशास्य वै ॥ 6-12-40
परिणाहेन षट्त्रिंशद्विपुलत्वेन चानघ ।
षष्टिमाहुः शतान्यस्य बुधाः पौराणिकास्तथा ॥ 6-12-41
चन्द्रमास्तु सहस्राणि राजन्नेकादश स्मृतः ।
विष्कम्भेण कुरुश्रेष्ठ त्रयस्त्रिंशत्तु मण्डलम् ॥ 6-12-42
एकोनषष्टिविष्कम्भं शीतरश्मेर्महात्मनः ॥ 6-12-43
सूर्यस्त्वष्टौ सहस्राणि द्वे चान्ये कुरुनन्दन।
विष्कम्भेण ततो राजन्मण्डलं त्रिंशता समम् ॥ 6-12-44
अष्टपञ्चाशतं राजन्विपुलत्वेन चानघ।
श्रूयते परमोदारः पतगोऽसौ विभावसुः ॥ 6-12-45
एतत्प्रमाणमर्कस्य निर्दिष्टमिह भारत ।

The Moon is handed down by memory to be eleven thousand yojanas in diameter. Its peripheral circle happens to be thirty three thousand yojanas when calculated.

The Sun is eight thousand yojanas and another two thousand yojanas in diameter. From that its peripheral circle comes to be equal to thirty thousand yojanas.

The Bible says -

Also he made a molten sea of ten cubits from brim to brim round in compass and five cubits the height thereof; and a line of thirty cubits and compass it round about.  --- Old Testament

William L Schoff says -

Probably no symbol in mathematics has evolved much mystery, romanticism, misconception and human interest as the number of pi.

      

          Buffon

Buffon calculated the value of pi using needle. Ancient Hebrews who built Solomon's temple used pi = 3 while Shatapatha Brahmin calculated the value of pi equals to 3.085.

In 1901, Italian mathematician Mario Lazzarini Performed the Buffon Needle experiment tossing a needle 3408 times, he obtained the approximation of pi which was a very accurate value. 

Archimedes in 3rd century inscribed and circumscribed regular polygons up to 96 sides and showed the upper limit is 22/7 and lower limit is 223/71.

           Pi  Day = March 14 (3/14)

Aryabhata calculated the value of pi correct  up to 4 decimal places and can be termed as the first mathematician to do so.

Add 4 to 100, multiply it by 8 and then add 62000. The result is approximately the circumference of a circle of diameter 20000.

Madhava, the founder of Kerala School of Mathematics also calculated the value of pi before James Gregory using the infinite series.

व्यासे वारिधिनिहते रूपहृते व्याससागराभिहते।

त्रिशरादिविषमसंख्यामत्तमृणं स्वं पृथक् क्रमात् कुर्यात् ॥

यत्संख्ययात्र हरणे कृते निवृत्ता हृतिस्तु जामितया।

                         तस्या उर्धगताया समसंख्या तद्दालं गुणोऽन्ते स्यात् \\

Ramanujan made several attempt and calculated the value of pi through numerous formula.

You can also calculate the value of pi using his formula.

Yale Bablonian Tablet known as YBC 7302 also approximates pi as 3.125 . . .

Interesting Facts About Pi:- 

At position 763 which is also known as Feynman Point, there are six nines in a row. 

Johann Lambert proved Pi is irrational in 1768.

I hope you have read the information shared here. It is the time to play quiz to explore your knowledge about pi. 

CLICK HERE FOR QUIZ

A certificate is attached with the quiz provided you score 75% marks so try your luck and win certificate.

Rajesh K Thakur

google.com, pub-5194588720185623, DIRECT, f08c47fec0942fa0 google.com, pub-5194588720185623, DIRECT, f08c47fec0942fa0

Art of Making and Dealing with Questions by Mr K Bhanumoorthy

 

Questions ----CBSE ----- Part I

“Your success and happiness lie in you. “---- Hellen Killer.

Acquiring application of knowledge, understanding and apply in class X, CBSE, what are learnt in precious classes.

Introduction: The curriculum is prepared in such a manner that is horizontal as well as vertical integration in every subject class wise, upward trend, stage by stage, rather to say from class to class. Primary 1to5, middle class vi to vii, secondary class ix to x, higher xi xii. the word primary means important. the fundamental concepts are being thought. foundation has to be strong enough, so that going to the higher level could be easier. I had an opportunity to go through chapter wise question and model paper in math. Here are some questions which are basics (fundamental) being asked. Unless students are familiarized and have understood the concepts, students will not be able to answer the question paper fully. let me discuss and begin from MCQs.

Evaluation tests are being conducted to assess and be aware of, how far students have understood the concepts and be familiarized with competency-based questions, case study questions TESTS. this trust nothing but self-evaluation for teachers’ fraternity.

Number system:

a)Prime number: It’s a number greater than 1, is divisible only by one and number itself.

b)Twin primes: They are pairs of prime numbers those have a difference of two. E.g. (3,5), (5,7) ………

c) Co- prime numbers: They are pairs of numbers that have no common factor other than 1. E.g. (21 and 22 tests), (9and 14), (1,3,9), (2,14,7).

d) Factor: It is a devisor of a given number. E.g. 3and 2 are factors of   6, 6= 3x2, 6=1x6.  factors of 6 are 1,2,3, 6. (The number 1 and number itself included in the factors.)

e) Multiples: the multiples of a number are multiplying a number by the set of natural numbers e.g. multiples of 4 are 4,8,12,16, 20……... (multiplication table of 4)

f) HCF: highest common factor; LCM lowest common multiples. for a given set of numbers say a and b we can find HCF and LCM. there is a relation it goes like this HCF x LCM = the product of the two given numbers.

That is HCF x LCM = a x b

There are statement questions in using the concepts / principles, in HCF and LCM. Students are to be taught where HCF and LCM to be used.

E.g.: 1.  A circular track around a playfield has a circumference of 540m. Two people say A and B do cycling at constant speed of 6m/sec and 9m / sec respectively. Around the track. They do start from a same point. After how many minutes, will they meet again at the starting point.

Time taken by a to complete one round 540/ 6 = 90secs, while B takes to complete one round 540/ 9 = 60 secs.  We have to find the LCM 0f 90 and 60. The least common multiple is 180 secs. So, they meet again after 3 minutes (180/ 60).

2.In a teachers training, the number of teachers who teach the undermentioned subjects, Physics 20, chemistry 30and English 40. In each room the same number of teachers are seated and all of them are teaching same subject. Find the minimum number of rooms required.

Ans: For this question one has to find the HCF of 20,30 and 40. HCF is10. The number of rooms required is 20/10 + 30/10 + 40/10 = 2+3+4 = 9. 

g) Rational numbers: it is a number which can be written in the form of p/q, where p and q are integers and q is not equal to zero e.g. 2/5.

h) Irrational number: it is a number which cannot be written in the form p/q, where p and q are integer and q is not equal to zero. it is non- terminating, non-repeating, non-oscillating. There is various way to prove a given number is an irrational number.

Eg: Ö2, Ö3, Ö21.

 Öa + Öb ≠ Ö a+b, while Öa x Öb = Öaxb = Öab.

2Ö2 +  Ö3 is irrational. 2 Ö5 --Ö2 is also irrational.

i) Prime factorization: it is finding the factors for a given number. E.g. for a given number 48 this can be written as 36= 2 x 2 x 3 x3 = 2² x 3², 400= 2 x 2 x 2 x 2x 5x 5 = 2⁴ x 5²; 120 = 2x2x2x3x5 = 2³ x 3 x 5.

--------------------------------------------------- be continued.

THE JOURNEY OF LEARNING- K Bhanumoorthy

 

THE JOURNEY OF LEARNING

                                                                        K. BHANUMOORTHY

                                                                           (Principal, Retd from KVS)

 INTRODUCTION:

A quote from Ken Robinson.

                               “Curiosity is the engine of achievement.”

There are four types of learning: Visual, Auditory, Kinaesthetic, Reading/Writing. Most of the people have the combination of all the four.

Courtesy:- https://educateradiateelevate.org/the-4-learning-styles/

The word journey means an expedition or an act of travelling or a voyage. In this the destination is important. Learning means gain knowledge or become aware of or discover or observe or grasp.

True learning is not just being literate but it modifies one’s behaviour. After acquiring degrees, one looks for the eligible decent job with respectable salary so that one can be independent. The real reason for study is to gain the knowledge. The more the knowledge, one can take the better decisions which would lead to a better life. One need to understand the WHY of what you do. Study is an integral part of one’s life and it is most important. Just as little drops of water make up an ocean, a little knowledge everyday can make a person wise. This is possible only when we truly learn.

STYLES OF LEARNING:

1.     Implicit: This takes place without one’s knowledge, indirectly takes place.

2.  Explicit: This is acquired when a person uses brain, able to proceed from known to unknown.

3.     Collaborative: Nowadays this method is advocated in schooling. Leadership qualities get developed.

4.     Co-operative: When students interact with one another, they are able to understand better. They learn from others too.

5.     Observation: This is another important kind of learning where one observes another and learns a lot. We can refer the very NATURE.

How to Learn:

There are 3 stages of learning:

1.     Cognitive – This is pertained to an individual working towards developing overall understanding of skills. One use brain more effectively. This skill enables any individual to develop problem solving skills. An individual is be able to link the previous knowledge for updating.

2.     Associative – In this kind of learning, an individual is capable of linking the known ideas to new ideas and it is a continuous process.

3.     Autonomous – In this, learners acquire skills by independent efforts, looks for sources, make efforts for effective learning.

Why to Learn:

              Courtesy:- https://paulgmoss.com/2021/07/23/7-reasons-why-you-should-be-active-in-your-learning/

Knowledge is all around. Everyday learning refreshes our mind. It depends on how one learns. There are voracious readers, some tune to TV, listen to radio, some converse with neighbours, some learn from work place. The under mentioned are the benefits of learning:

i.                    By learning, we are exposed to new things, it expands one’s mind.

ii.                  One may try to experience by involvement in doing a particular job/deed.

iii.                Learning is refreshing.

iv.                One feels happy by acquiring new information and feel to learn more and more.

v.                  One tries to look forward ‘what next?’ for one’s growth.

vi.                By learning every day, it is possible one can influence the lives of others in a positive way.

vii.             The philosopher, Sir. Francis Baron said “Knowledge is Power.” This can be achieved by more learning.

viii.           An individual is intellectually stimulated to know more about area of work.

ix.                The most important to say quality of life shall definitely be enhanced.

x.                  Helps an individual to overcome boredom.

Conclusion:

There is a purpose in life, one has to understand this, then only one’s mind shall not wander here and there, shall be working towards the goal. The purpose could be on many areas either in scholastic or non-scholastic, to say self-development, enlightening others, to validate and update one’s knowledge, to prepare and guide others to face the problems.

A quote from Kirill Korshikov

“Never stop learning, because life never stops teaching.”

Study Habits and Behavioural guidelines in the examination hall

A quote from Alfred Mercier:

“What we learn with pleasure we never forget.”

 Everyone is aware that teachers do teach. The question is how far the learning has taken place. Students’ performance is taken as mark with respect to our system /pattern of examination, the way by which it is being conducted. It is not what one knows the subject how far understands the subject. It is very important how far one has reflected rather to say how far presented the correct (right) answer in the answer paper. There lies the effectiveness of teachers’ fraternity. In brief I can say the teachers can influence a student’s life.

Teachers Role:

 Let me write some more aspects about teachers. Let them have 5 Cs. i.e. to say concern for students, commitment to the profession, cordial in their approach, character, consistency, counselling as and when required. We can add many more. Let every student feel and say “here is the teacher who has a concern about me and progress in academics and non-scholastic areas.” 

Qualities of a Good Teacher

Source: https://lefaemmabuckland.blogspot.com/2022/09/characteristics-of-teacher.html

If portion of a subject is over does not mean everything is over. There are specific objectives in every unit of every chapter, teachers have to know about them, inculcating various competencies, to initiate creativity, to provide open ended questions approach. Teachers do have many responsibilities. Teachers do play an important role on students progress in studies apart from their parents. On some occasions I have heard some students, they say to their parents “my teacher told me to do these activities/ this work. They request parents, allow them, to carry out what the teachers have informed. There lies the effectiveness of teachers’ fraternity. In brief I can say the teachers have such an impact on students and can influence a student’s life.  A life changing teacher is to provide whatever the students need, to help them excel in all space including academics. Students who are inspired by their teachers can accomplish amazing results, and that motivation always stays with them lifelong. 

                                                  Study Habits:

Do you study by laying on bed?

Do you listen music while reading?

Do you watch TV while reading?

Do you eat or take snacks while reading?

 If the answer of your questions are - YES then you are on wrong track. Improve your habits.

 A few tips are to be given by the teachers, to tackle any one’s tasks., for a success. These aspects and undermentioned points are to be clearly told to student to have these qualities, be inculcated, carryout in letter and spirit. Let them be asked to note down.

1.Be confident: Confident comes when one prepares well enough. Have faith in yourself. (self-faith) If you think you can, YOU CAN.

2.Never compare yourself with others: Everyone is unique in nature, possesses some abilities or other. It is the question of know them and develop those skills. Do your best. You are what you are.

3. Be consistent: During examination, one shouldn’t have any kind of distortion. It is very essential to avoid such as watching Tv, seeing movies. Meeting friends only on academic matters for a discussion. In brief keep away all sorts of distraction.

4.Understand what you study: Kindly not to cram matters, contents. Write and practice. When you write, have full concentration. One time writing is three times studying.

5. Do not study only for marks.: First of all, understand subject matters. Absorb the ideas what you study and retain the knowledge, how applied in our daily life, it’s applications in other subjects too.

6.Picturise what you study: The point is to visualize whatever you study, save it in the mind. Try to re-collect in your mind. Re-collecting is the need for retention I feel.

7. Keep/ set your Goals: Let your goals be, not small. Keep your goals large in numbers. Let not getting marks or admission in joining a particular course be your goal, plenty of options are available. In present days quite lots of courses on correspondence, vocational courses are available One has to search for them. One can easily join the course of his/her choice.  

8. Plan: There is a saying, “plan your work, work for your plan.”  Once get a job / work, have desire to serve the community, society, in turn to the nation. In brief I would say to the humanity. Our education is value based; it is the preparation for one’s life. Retain values, no compromise in sustaining values.

9. Attitude: One has to have right attitude., positive thoughts. The right attitude takes anyone to the highest altitude.

10.Outcome: There is no short cut to achieve success; consistency in hard work shall fetch anyone fruitful outcome.

An abbreviation for student:

 S > studious

           T> think

          U > unique

          D > Discipline

          E> enthusiastic

          N> Natural

          T> Thrive.

In the examination hall the right kind of behavior and duties (ways and means)to follow:

1.To reach the venue of the examination Centre Hall well on time at least 30 minutes before the schedule of examination. The examination may be in the school where the student studies or the allotted center.

2.Student should have a relaxed mind without any tension /fear. To keep things whatever brought for the examination purpose be kept on the desk / table (hall ticket) if it is board examination.

3. Write the examination number i.e. that is allotted number correctly with correct subject code and with proper set of question paper.

4. students have to write his/ her exam number in the question paper and go through the questions properly.

5. Answers have to be written neatly without any cutting/ over writing. To say one must write very clearly.

6. The answer to the questions has to be neither too long nor too short, to be specific as per the question.

7.It is suggested religious symbols be avoided in answer paper.

8.To start with, write down answers to questions which students know thoroughly.

9. Student should not underline in red or green colour in any part of answers, since it is prohibited in the system.

10. Students have to answer all the questions, not to leave any question.

11. One has to keep some time for revision at least for 10min. This has to be done without fail.

12. Make full use of time available for the designed question paper. One should not be in a hurry to finish off. This is very essential factor to remember.

13.If additional sheets are used, there also the exam number should be written. They are to be tied up with the main answer sheet. Tying should not be neither too tight nor too loose.

14. For the subject like mathematics a rough column, be made on the answer sheet where all the rough works (not untidy work) can be carried out. I mean neat work.

15. The most important is to keep one’s health proper (no health issues) and good   enough in order to do well in the examination.

The author of this article is Sri K Bhanumoorthy, a retired Principal from KVS. He lives in Bangluru. If you have any suggestion regarding the article, do comment after reading it.

 

Apology for Maths Quiz/relay link

 Dear students, teachers & parents

I hope this message finds you well. I sincerely apologize for the inappropriate Maths relay/Quiz link shared to you through the link that takes you to my blog post. I understand this may have caused confusion and inconvenience, and I am truly sorry for that. 

I was busy at the 18th National Maths Convention, Science City Ahmedabad since 19th December, and therefore, gave some access to the known persons but they cheated me as well as you all(asked for money). 

The sooner I knew about this fraud through my friends or call of the participants, I-----

a) deactivated the link 

b) Removed the person from the collaboration and stopped taking response from each google form. 

Till now more than 300 quizzes have been conducted by me but all were free of cost. From next time, I'll be careful and appreciate your understanding and patience as I work to ensure such errors do not occur in the future.

Once again sorry!.

Thank you for your continued support and readership.

Yours

Rajesh Kumar Thakur 

Hyderabad Teachers Workshop