SQUARING A CIRCLE AND VICE - VERSA - A new approach

Dear Reader,

We are well aware of the fact that SQUARING A CIRCLE AND VICE - VERSA (using straightedge and compasses only) is impossible because of the trascendency nature of 'pi'  which was proved by German Mathematician Carl Louise Ferdinand Lindemann in 1882. Even after proving this fact, many mathematicians like Jacob de Gelder, Kochansky,  our Indian mathematical legend, Srinivasa Ramanujan who showed his unmatchable ingenuity, tried to construct a square equal in area to the area of the given circle using different rational convergent of 'pi'. They adopted different modes of processes to arrive at the convergent of their choice and their mode provides little chance to reverse the process so that circle can be constructed from the given square.

Viewing these deficiencies, KASIRAO. JAGATHAPU, a retired headmaster from V.C.B.R.M.Z.P.  High School, Nellore Dist., A.P. after years of struggle, devised a method not only answering the deficiencies but also a simple method that can take to the maximum accuracy one wishes.

Here is the pdf version of the method suggested. Please go through this and in case you want to contact the author, you mail directly write an email at kasiraoj@gmail.com

Amit Bajaj

RAMANUJAN'S BIRTHDAY CELEBRATION AT MY HOME

"GANIT UTSAV" - Math's Week Celebrations from 16 - 22 December 2014

Dear Reader,

CRPF Public School, Rohini celebrated Mathematics Week as “Ganit Utsav” from 16 December 2014 to 22 December 2014 to remark the 127^th Birth Anniversary of the great Indian Mathematician Srinivasa Ramanujan.
The inauguration was done by honorable chief guest Anita Sharma Madam, Principal, S.D. Public School, Pitam Pura and respected Principal Sir Sh. H.R. Sharma.

A series of interesting events for different classes were organized. On the Inaugural day i.e. 16 December 2014, lecture on Ramanujan and his life was delivered by honorable chief guest Anita Sharma Madam and also by Mr. Amit Bajaj, HOD (Mathematics).

Many Mathematical competitions were organized on different days.

1.      POSTER MAKING COMPETITION FOR CLASSES VI – VIII (THEME: MATH’S IN DAILY LIFE)

2.     ORIGAMI FOR CLASSES III – V

3.     SCREENING OF VIDEOS BY VIGYAAN PRASAR  for classes VI and VII

4.     ESSAY WRITING COMPETITION FOR CLASSES IX – X

          (TOPIC: WHAT WOULD HAPPEN IF THERE IS NO MATH’S’)

5.     MATHS QUIZ COMPETITION FOR CLASS XI

6.     CREATING FIGURES USING SHAPES FOR CLASSES I – II

7.     EXPERIENCE SHARING ON INNOVATION IN MATHEMATICS BY THE STUDENTS

The culmination ceremony was held on 22^nd December 2014 and was marked by celebrating birthday of Srinivasa Ramanujan. Smt. Anjana Mukharjee, HOD (Mathematics) in DAV School, Pitam Pura graces the occasion and was the chief guest.

About 10 students from VI – XI shared their experiences on innovations in Mathematics. Anant Kumar, A student of VII – A acted as Ramanujan and enlightened the students about the great mathematician. The ceremony ended in magnificence, with students receiving merit certificates(Prize Distribution) for their respective events, by honorable chief guest Smt. Anjana Mukharjee, Mr. Amit Bajaj HOD (Mathematics), Mrs. Vandana Sehgal Primary Incharge and Ms. Hema Batra Pre-Primary Incharge.

The whole week was full of Mathematical Joy with lots of learning for all the students. 

Source: http://www.crpfpsrohini.blogspot.in/

HAPPY BIRTHDAY TO GENIUS MATHEMATICIAN - SRINIVASA RAMANUJAN

Srinivasa Ramanujan (22 December 1887 – 26 April 1920) was an Indian mathematician, who made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions. Ramanujan independently compiled nearly 3900 results (mostly identities and equations). His work continues to inspire mathematicians even today! 

Srinivasa Ramanujan, born into a poor Brahmin family at Erode on Dec. 22, 1887, attended school in nearby Kumbakonam. By the time he was 13, he could solve unaided every problem in Loney's Trigonometry, and at 14 he obtained the theorems for the sine and the cosine that had been anticipated by L. Euler.

Ramanujan became so absorbed in mathematics that when he entered the local government college in 1904 with a merit scholarship, he neglected his other subjects and lost the scholarship. Ramanujan married in 1909, and while working as a clerk he continued his mathematical investigations.

In January 1913 Ramanujan sent some of his work to G. H. Hardy, Cayley lecturer in mathematics at Cambridge. Hardy noticed that Ramanujan had rediscovered, and gone far beyond, some of the latest conclusions of Western mathematicians.

In 1914 Ramanujan went to Cambridge. The university experience gave him considerable sophistication, but intuition still played a more important role than argument. In Hardy's opinion, if Ramanujan's gift had been recognized early, he could have become one of the greatest mathematicians of all time. His patience, memory, power of calculation, and intuition made him the greatest formalist of his day.

In 1918 Ramanujan was elected a fellow of the Royal Society and a Fellow of Trinity College, Cambridge.

However, the story goes that, Ramanujan’s health deteriorated greatly while he was in England, and he eventually had to travel back to India in 1919. He died a year later, when he was only 33 years of age, although his work will be remembered for a long time. He dealt with Riemann series, the elliptic integrals, hyper geometric series, and functional equations of the zeta function. Hardy liked to rank mathematicians on a scale of 1 to 100, and he gave himself 25, Littlewood 30, David Hilbert 80, and Ramanujan 100, which shows just how great Ramanujan was.

XII CLASS CBSE MATHEMATICS 2013-14 PAPERS AND SAMPLE PAPER FOR 2014-15

Dear class XII Students,

I hope that all of you are doing well in ongoing Pre-Board Exams 2014.

For your reference I am providing the links to 2014 Math’s CBSE Papers as well as latest Sample Paper issued by CBSE.

Click on the following link and download all the papers.
For other subjects, please check this link.

All the best

Amit Sir

Second Term Exam 2014- 15 Mathematics Class XII (SOLUTION KEY)

Dear class XII Students,

I hope that all of you must have performed well in the Second Term Exam held today i.e. 16 December 2014. 

For your reference I am providing both the sets of the question paper and the solution key. 

Question Papers:

Set A      Set B

Solution Key

All the best...

Amit Sir

Fifth Intra School Mathematics Olympiad - RESULT

Dear Reader,

The Fifth Intra School Mathematics Olympiad was held on 7 November 2014.

Hopefully, it was a great learning experience for all. It surely provided an extended platform for all the participating students and it is wished that it is utilized to its fullest.

Here are many young Ramanujan’s and Shakuntala Devi’s in our school who had performed very well in the exam.

Check out the result here:

V-VIII RANK HOLDERS    

V-VIII MERIT HOLDERS

IX-XII RANK HOLDERS  

IX-XII MERIT HOLDERS 

Congratulations to all the rank and merit holders for their brilliant performance in the  Olympiad.

You may again like to see the question papers and their solutions.

Fifth Intra School Mathematics Olympiad - Solution Key

Dear All,

Mathematics, often called as language of nature has become an integral part of everyone’s life. In today's highly competitive world, one has to bear a lot of mental stress and also have to get involved in so many things in order to acquire knowledge. This is where co-scholastic activities play a very significant role. They provide the much needed exposure for a student.

CRPF Public School has fulfilled its motto of striving towards excellence by organizing and successfully completing its Fifth Intra School Mathematics Olympiad on 7 November 2014. Around 250 students enthusiastically participated in the Olympiad held in school premises.

Such Olympiads and events provide a great and extended platform for the students to nurture and showcase their ability and talent. It was a towering learning experience for the students of the school from class VI to XII. To encourage students, merit certificates will be given to those scoring at least 60% along with the normal prizes for the top scorers.

I hope that all the participating students must have done well in the exam. To access your performance, check out the solution keys of the question papers below:-

Question papers:-

Class VI      Class VII     Class VIII

Class IX      Class X        Class XI     Class XII

Solutions keys:-

Class VI      Class VII     Class VIII

Class IX      Class X        Class XI      Class XII

The result would be declared on 21  November 2014 and would be available here on the blog.

Wishing you all the best!!!

National Test of Math Knowledge

National Test of Math Knowledge Level 1
Eligibility: All students of class 9 to 12 who are enrolled on full-time basis with a CBSE school are eligible to take NTMK.
 Date: 11 December 2014 (Thursday)
Fee: Rs 250
 Syllabus For level 1, students will be assessed on the following chapters:
Class 9 - Number Systems, Polynomials, Coordinate Geometry, Lines and Angles, Triangles
Class 10 - Real Numbers, Polynomials, Pair of Linear Equations, Triangles, Trigonometry
Class 11- Sets, Relations and Functions, Trigonometry, Complex Numbers, Mathematical Induction, Linear In-equations
Class 12 - Relations and Functions, Inverse Trigonometric Functions, Matrices & Determinants, Differential Calculus
DoK Level Distribution and Marks Student gets 90 minutes to attempt 30 questions worth 60 marks distributed as follows: ·
 10 questions of 1 mark each for DoK 1 ·
 15 questions of 2 mark each for DoK 2 ·
 5 questions of 4 mark each for DoK 3
MathBuster Book of Problems (MRP: Rs. 250)
Each student will get a FREE copy of the MathBuster Book of problems that has:
1000+ problems covering the entire year's curriculum for each class; and ·
 Problems based on DoK 1, DoK 2 and DoK 3 levels; and
 Answers to all problems for self-assessment.
 The book is an excellent source to prepare for PSA exams, formative tests, CCE and CBSE and competitive examinations.
Last Date of Registration: 10 November 2014
Visit www.mathbuster.in for details and Sample Papers.

Inter-House Mathematics Competition - RESULTS

Dear Reader,

Mathematics Department has organised Mathematics Week successfully. Students took part enthusiastically and had a great learning experience.

CLASS VI - GREAT MATHEMATICIAN

CLASS - VII MATHEMATICS BOOK COVER DESIGN

CLASS - VIII MATHEMATICS QUIZ

CLASS IX - MATHS MODEL MAKING

CLASS X,XI,XII - SUDOKU

Mathematics Week Celebrations

Class XII First Term Exam(2014-15) Mathematics - SOLUTIONS

Dear class XII Students,

Hope you all must have done your Math’s paper well. Here is the Question Paper.

Please check out the Solutions here.

(Right click the above link and choose the option "Save link/target as")

ALL THE BEST

Amit Sir

Indian-origin mathematician Manjul Bhargava wins Fields Medal

Dear Reader,

Manjul Bhargava, a Canadian mathematician of Indian origin, has been awarded the prestigious 2014 Fields Medal at the International Mathematical Union’s (IMU) International Congress of Mathematicians held in Seoul. Bhargava, 40, is the first person of Indian origin to receive the prestigious medal, which has been awarded since 1936 and recognizes outstanding mathematical achievement for existing work and the “promise of future achievement”. Known to colleagues as a gifted mathematician who would devise new and simple methods to prove centuries-old theorems in number theory, Bhargava’s work has been described by IMU as based both on a deep understanding of the representations of arithmetic groups and a unique blend of algebraic and analytic expertise. Bhargava was awarded the medal “for developing powerful new methods in geometry of numbers, which he applied to count rings of small rank and to bound the average rank of elliptic curves”, IMU said. One of Bhargava’s most prominent discoveries was a thesis that threw a new light on Gauss’s Law for the composition of two binary quadratic forms. When Bhargava was a graduate student, he read Disquisitiones Arithmeticae, where Gauss developed his composition law which gives a method for composing two binary quadratic forms to obtain a third one. According to IMU’s description of his work, Bhargava one day came up with the idea that if he cut off the Rubik’s mini-cube into half and labelled each corner of the cube with two sets of numbers, that would lead to a cubic analogue of the Gauss Composition. After being cut, a Rubic’s mini-cube could generate three quadratic forms. From the three ways of slicing the cube, three binary forms emerged, and so Bhargava had discovered a simple way to prove the law. “It’s all about contributing to the understanding of ourselves and the world around us. One of the keys to understanding mathematical problems that people have been thinking about for years is to think about them in a totally different way,” said Bhargava in an interview with Simons Foundation and IMU. He went on to discover 12 other analogues of Gauss compositions over the years. He received his Ph.D in 2001 from Princeton University for a thesis that has been described as “stunning” and a “breakthrough”. It generalized the classical Gauss composition law for quadratic forms to many other situations, according to the Tata Institute of Fundamental Research. By 2003, Bhargava had become a professor at Princeton . Born in 1974 in Canada, Manjul Bhargava grew up in the US and often visited Jaipur to stay with his grandparents. His grandfather was a professor in Sanskrit from whom Bhargava learnt Sanskrit poetry, while his mother was a mathematics professor who allowed Bhargava to attend her college-level classes as a child, according to interviews. “He is an extremely original mathematician, who has developed a style which is distinctly his own,” said Benedict Gross, professor of mathematics at Harvard University, who has known Bhargava since his days as a Harvard undergraduate. “His method—combining the arithmetic interpretation of integral orbits with their enumeration, using the geometry of numbers—has led to the solution of a large number of problems in number theory. I think his mathematical work is tremendously important, and has changed the face of the subject,” added Gross, who himself is a renowned mathematician for his work on the Gross-Zagier Theorem that won him the Cole Prize along with his collaborators. Bhargava has also collaborated with mathematicians to increase the understanding of elliptic curves, which are one of the fundamental objects in number theory with applications in the fields of cryptography and data security. Describing the uniqueness of his work, Gross said, “He obtains results ‘on average’ that we can’t obtain in individual cases. For example, for a cubic equation (an elliptic curve), it is quite difficult to determine the size of the group of rational solutions. Bhargava determines an upper bound on the average size, over all cubic equations with rational coefficients.” Bhargava is an accomplished tabla player, having trained under Ustad Zakir Hussain, one of the greatest exponents of the percussion instrument. He is also an impressive and lucid orator. “He is a very kind person, who shares his ideas freely with others. He is also a talented tabla player, who loves music and other arts,” said Gross. Peter Sarnak, professor in the department of mathematics at Princeton University, said, “Bhargava has developed fundamental new tools geometric and diophantine, to count objects in algebraic number theory, that before his work seemed hopeless. His work reminds me of the great German mathematician Hermann Minkowski’s work in number theory: it is brilliant, clear and beautiful and has reshaped the landscape.” Three others received the Fields medal—Maryam Mirzakhani, the first Iranian and the first woman to be awarded the medal; Artur Avila, the first Brazilian to be awarded, and Martin Hairer, the first Austrian to win the medal. Subhash Khot, an Indian-origin scientist from New York University, was awarded the Nevanlinna Prize in Seoul for his prescient definition of the “Unique Games” problem, and his efforts to understand its role in the study of efficient approximation of optimization problems, which have produced breakthroughs in algorithmic design and approximation hardness, according to ICM.

 Source: http://www.livemint.com/

Weekly Test XI and XII Class - Paper and Solution Key

Dear Reader,

Weekly test was held in the classes XI and XII. Hope that all the students have performed well. Here is the test paper and its answer key.

Class XI : Test Paper     Solution Key

Class XII : Test Paper     Solution Key

In case any doubt, kindly drop a small email at amitbajajcrpf@gmail.com

Amit Sir

Do you know what’s special about today, 22 July?

Dear Reader,

Well, today is Pi Approximation Day.

Pi Approximation Day celebrates the mathematical constant π (pi). It is observed on July 22, due to π being roughly equal to 22/7.

The fractional approximation of π ,22⁄7, resembles the date July 22 in the day/month format, where it is written 22/7. Pi Approximation Day is therefore celebrated on July 22.

In geometry, pi is defined as the ratio of a circle's circumference to its diameter. July 22, often written as 22/7, is an appropriate day to explore pi, since 22 divided by 7 is an approximation of pi.

Pi Approximation Day is celebrated in a number of ways, including contests to memorize pi to the most decimal places, solving math problems involving pi, discovering the history of pi, ruminating on how life would be different without pi and—of course—eating pie.

So, enjoy this mathematical day ...

Amit Sir

THREE DAYS MATH'S WORKSHOP CONDUCTED BY ME AT SAINIK SCHOOL, TILAIYA

Dear All

I am delighted to share with you all that I was invited by Sainik School,Tilaiya, Jharkhand to conduct a three days workshop for teachers from all the 24 Sainik Schools across the country. 

In those three days I along with another Math’s expert Mrs. Shuchi Goyal discussed Mathematics beyond Curriculum, Problem Solving, Model Making, and various Hands-on-activities etc.

It was really a fun-filled great learning and sharing experience. All the participants enjoyed the sessions and took part in each activity enthusiastically. It is obvious that if teachers of any age or many years experience can enjoy this Mathematics, I am certain the students will also enjoy the same with more zeal and enthusiasm. The only pre-requisite condition is that as a Mathematics teacher we are passionate learner, flexible, ready to change for betterment and have will and desire to do best for the students.

It is hoped that all the teachers who attended these sessions are now ready to create fun based mathematical classroom where no student is phobic towards Mathematics.

As promised during the sessions I am providing the photographs of all the sessions day-wise.

MEDIA COVERAGE

DAY 1

DAY 2

DAY 3

Happy Learning!

MCQ TEST - INVERSE TRIGONOMETRY

Dear class XII students,

A multiple choice questions based test was held in all the sections of XII. Hope you have performed well in the same.

Here is the test paper and its answer key.

In case any doubt, kindly drop a small email at amitbajajcrpf@gmail.com

Next scheduled test: Continuity and Differentiation on 19 May (Monday)

Amit Sir

MCQ BASED TEST MATRICES AND DETERMINANTS

Dear class XII students,

A multiple choice questions based test was held today in the classes. Hope you have performed well in the same.
Here is the test paper and its answer key.
These files are password protected which was shared with the students in the classroom.
In case any other person wishes to see the paper, kindly drop a small email at amitbajajcrpf@gmail.com
I will share the password with you.

Next scheduled test: Inverse Trigonometry on 25 April (Friday)

Amit Sir

Change in Pattern of CBSE XII Maths Paper for session 2014-15

Dear All,

I hope that most of you are aware of certain changes in the pattern of CBSE math's paper class XII from this session onward. For your ready reference I am providing the same.

(click on images to enlarge)

Download curriculum for class XI and XII from here.

For Class XII Mathematics Students

Dear class XII Students,

Hope you have done well in your exams held till date. I am providing links of previous year's papers held in school for past 4-5 years (with solutions). I hope it will help you to prepare better for the examination.
All the best!

Links for All helpful Resources for class XII Mathematics

Value based:

http://amitbajajcrpf.files.wordpress.com/2013/12/vb_maths_eng_12.pdf

Latest Sample Paper by CBSE:

 http://amitbajajcrpf.files.wordpress.com/2013/12/mathematics_xii.pdf

Sample Papers by Directorate of Education (given to every Government School Students): http://amitbajajcrpf.files.wordpress.com/2013/12/12_math_english_2013-page-136-172-for-sp.pdf

(Also check two Sample papers from page number 136 onward)

Previous year’s papers (held in School)

http://amitbajajmaths.blogspot.in/2012/03/addition-in-mathematics-syllabus-in.html

http://amitbajajmaths.blogspot.in/2013/09/class-xii-first-term-exam2013-14.html

http://amitbajajmaths.blogspot.in/2012/01/practice-material-for-class-xii-maths.html

http://amitbajajmaths.blogspot.in/2013/08/assignmentresources-for-class-xi-and.html

http://amitbajajmaths.blogspot.in/2012/01/solution-key-class-xii-pre-board-2011.html

http://amitbajajmaths.blogspot.in/2012/09/class-xii-first-term-exam-mathematics.html

http://amitbajajmaths.blogspot.in/2010/12/class-xii-maths-answer-key.html

http://amitbajajmaths.blogspot.in/2011/03/class-xii-mathematics-paper-solution.html

http://amitbajajmaths.blogspot.in/2011/01/class-xii-maths-pre-board-2011-answer.html

http://amitbajajmaths.blogspot.in/2011/10/class-xii-first-term-exam-mathematics.html

http://amitbajajmaths.blogspot.in/2011/01/class-xii-special-lecture-by-sh-j-c.html

http://amitbajajmaths.blogspot.in/2010/12/class-xii-maths-answer-key.html

http://amitbajajmaths.blogspot.in/2011/09/practice-material-for-class-xii-maths.html

http://amitbajajmaths.blogspot.in/2013/03/more-practice-papers-xii-mathematics.html

http://amitbajajmaths.blogspot.in/2011/01/cbse-sample-papers-mathematics-class-x.html

http://amitbajajmaths.blogspot.in/2009/11/cbse-sample-papers-mathematics-class-x.html

http://edudel.nic.in/welcome_folder/support_material_13_14.htm

Solution Key -- Class XII Mathematics (Pre-Board 2013-14)

Dear class XII Students,

Hope this time all of you must have performed well in the exam. 
I am providing you with both the sets of the question paper and the solution key.

Question Papers:
Set A     Set B
Solution Key

All the best for board examination.
Amit Sir