Free Online Maths Helpdesk for South African learners

May 11, 2015, 2:29 am

≫ Next: Puzzles to Puzzle you by Dr. Thakur

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Vedic Maths Forum South Africa is launching an online Maths help-desk to help learners with Maths problems/questions they have difficulty understanding. This is a free service for South African learners from Grade 4 to 12 and will run for the next 4 weeks to help them with Exam preparation.

How does it work?

Take a picture of the problem.
Tweet it to @VedicMathsSA #MathsHelpDesk
One of our Maths teachers will reply within 24hrs.

It is as simple as that! If the student still doesn’t understand, then we will explain via our virtual classroom. Each learner will receive 1 free online session (60min). So start tweeting now and get the help you need.

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Puzzles to Puzzle you by Dr. Thakur

May 27, 2015, 10:13 am

≫ Next: Number of Buttons in Your Favorite shirt and its Color by Dr. Rajesh Kumar Thakur

≪ Previous: Free Online Maths Helpdesk for South African learners

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It gives me immense pleasure to introduce a new section on our blog today! From today every day you will get puzzles to puzzle you and open your mind! Dr.Rajesh Kumar Thakur will be giving us a new puzzle every day and winners stand a chance to be mentioned on this blog and win gift hampers.

Dr. Rajesh Thakur is a mathematics lover and loves to play with number. He has written 32 books , 100 mathematical articles, 10 Research Papers and Dozens of Hindi Poem.

Send in your answers to rkthakur1974@gmail.com

Here is today's puzzle:

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Three friends were returning from college when they saw a speeding car hitting a man while he was crossing the road and fleeing away. They shouted in desperateness to seek help from the passerbyes but failed.

In the meantime they noticed the registration number of the car and tried to remember in their own style. They rushed the person to the nearby hospital where he was admitted. The doctor called the police as this was a case of road accident and a case was registered.

In order to do proper investigation the police started inquiring the three friends and asked them if they could provide the registration number of car so that the driver who had hit the person can be caught up. All the three friends tried a lot to remember the car number but failed so they altogether decided to zero upon the number of the car as they have remembered the car number with some mathematical properties behind it.

1^stStudent: -- Sir, the first two digits of car number were same.

2^ndStudent: - Sir, the last two digits of car number were same.

3^rdStudent:- The four digit number is a square number.

Can you guess the car number to help the police to nab the guilty?

Send me your valuable comments on rkthakur1974@gmail.com and try to reason this out with algebraic proof ? See you next day till then open up your mind.

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Number of Buttons in Your Favorite shirt and its Color by Dr. Rajesh Kumar Thakur

May 27, 2015, 5:35 pm

≫ Next: Upcoming Workshops in Dubai, June 2015

≪ Previous: Puzzles to Puzzle you by Dr. Thakur

Hey Guys, I am back with another puzzle but this time it is for the students of secondary level to open their mind to take out the mathematician hidden out. The basic aim of this blog is to make you feel mathematically strong by strengthening your fundamentals of mathematics. Mathematics is all about calculation with reason and I am here to explore your brain.

Isn’t it interesting to know the number of buttons in your friend’s shirt without counting it?

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Indeed it will prove you a super hero in the sight of your friend. Your friend will think you a mind reader and appreciate you for your marvelous guessing technique with 100% accuracy.

I am stopping the game here, you can also predict the color of your friend’s shirt kept in his/ her wardrobe and force him to show that shirt and count the number of buttons in front of many of your friends sitting around you.

Here is the color chart that your friend will chose according to his favorite color.

Red	Indigo	Blue	Green	Yellow	Orange	Red	White	Black
1	2	3	4	5	6	7	8	9

Now give a pen and paper to your friend and instruct him to do as instructed.

1. Choose the number of his favorite shirt color from the table given above.

2. Multiply this number by 4

3. Add 5 to it

4. Multiply it by 3

5. Tell him to multiply the number of buttons of his favorite shirt by 5 and add it to the previous result.

6. Multiply the result obtained by 8

7. Divide the result by 4

8. Subtract 30

9. Subtract 23 times the number corresponding to the color of his favorite shirt from the previous result.

The result obtained will have a two digit number where ten’s digit will represent the number of buttons in his shirt and one’s digit will show the color of his favorite shirt.So,did you find it interesting enough? It is based on simple algebra and I want your kids and you even to open your mind and sharpen it. Don't forget to send your mail tome at rkthakur1974@gmail.com.

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Upcoming Workshops in Dubai, June 2015

May 28, 2015, 3:53 pm

≫ Next: Puzzle 3 :- Birthday Puzzle to play with your friends by Dr Rajesh Kumar Thakur

≪ Previous: Number of Buttons in Your Favorite shirt and its Color by Dr. Rajesh Kumar Thakur

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The Vedic Maths Forum India will be conducting full day Workshops on Vedic Maths in Dubai from 26th to 30th June, 2015.

Interested parents and students in Dubai who would like to participate may please get in touch with us at gtekriwal@vedicmathsindia.org to get the further details . We would only be happy to have you as an active participant. See you in Dubai people!

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Puzzle 3 :- Birthday Puzzle to play with your friends by Dr Rajesh Kumar Thakur

May 28, 2015, 11:21 pm

≫ Next: KENKEN - Maths Puzzle Game that develops Maths and Logic Skills

≪ Previous: Upcoming Workshops in Dubai, June 2015

Hey Friends,
Thanks a lot for your continuous answer of Puzzle 1 and 2 posted. I congratulate
Mr.Rupesh Gesota for his correct answer with logic . The answer is obviously 7744 but 99% of the mail I received had posted only 7744 as an answer.

This is another set of Puzzle which you would love to play but the condition remains the same. You have to post me the basic reasoning i.e. the algebraic proof on which the puzzle is based and train your students also to improve his mathematics with logic. This is not the birthday puzzle you generally play so use your brain and be a mathematician.

BIRTH DAY PUZZLE
1. Add 18 to the month in which you were born?

January = 1…. July = 7 and December = 12

2. Multiply the result with 25

3. Subtract 333

4. Multiply by 8

5. Subtract 554

6. Divide by 2

7. Add your birthday to the previous result

8. Multiply the result by 5

9. Add 692 to it

10. Multiply the result by 20

11. Add the last two diigts of the year you were born, i.e 75 for 1975 , 99 for 1999

Get confused ! Your wait is over

12. You will have a 5 or 6 digit number

13. Subtract 32940 from your result. It is a 5 or 6 digit number.

Let the number obtained is xyab cd

xy = Month

ab = Date

cd = Year

Do you remember your promise?

I know you do, so please play this puzzle and solve the puzzle algebraically and send mail to

Dr. Rajesh Kumar Thakur

rkthakur1974@gmail.com

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KENKEN - Maths Puzzle Game that develops Maths and Logic Skills

June 4, 2015, 1:45 am

≫ Next: Vedic Maths Club in Cape Town

≪ Previous: Puzzle 3 :- Birthday Puzzle to play with your friends by Dr Rajesh Kumar Thakur

It is always difficult to get children to practice calculations, especially if they are given a worksheet to do. A whole page of sums looks daunting and not very exciting.

I recently came across an interesting puzzle game called “KENKEN”. No, it has nothing to do with the doll!

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Source: www.kenkenpuzzle.com

KENKEN is a numerical puzzle that tests basic operations such as addition, subtraction, multiplication and division, and also challenges logic and problem solving skills. It was developed in 2004 by the Japanese instructor Tetsuya Miyamoto who wanted to improve his students’ Maths and logic skills.

You can find many examples to work through on the official website or download the Mobile App.

The simpler puzzles with just addition will help even children in Grade 2 to practise their number bonds. More difficult puzzles that combine all four operations can be used with the older children.

Be warned though – it can become quite addictive! My 8-year old loves the Mobile App and nags me to allow him to play KENKEN.

Neshni Naidoo

Director: Vedic Maths Forum South Africa

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Vedic Maths Club in Cape Town

June 5, 2015, 1:24 am

≫ Next: Smriti Irani slams critics who accuse her of 'saffronising' education

≪ Previous: KENKEN - Maths Puzzle Game that develops Maths and Logic Skills

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It is a Thursday afternoon and while their peers are outside engaged in sport or at home, these children are still at school – doing Maths. This is not a class they are forced to attend to improve their marks. On the contrary, these children have opted to be members in the Vedic Maths Club launched at their school, Rylands Primary. The Maths Club is facilitated by Mrs Yurashnie Naidoo, the Deputy Principal at the school, using the material supplied by Vedic Maths Forum South Africa. There are currently 14 learners from Grade 4, 5 and 6.

The parents of one the learners told me that her son, who is in Grade 4, was excited about the Vedic Maths Methods shown during the school assembly. He asked to join the Maths Club because he felt that it would improve his Maths scores from a 6 (70-79%) to a 7 (80-100%).

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I conducted a session with the learners and shared with them techniques of multiplying by 11 and finger multiplication. I could see the ‘Eureka’ moment when the light went on in their eyes. It was such a rewarding feeling!

For now, the learners are learning some basic Vedic Maths and how to use this to improve the speed and accuracy of their arithmetic. We have also included strategies for Word Sums and Maths Puzzles in this term's programme.

These learners will go on to compete in the Speed Math Challenge being held on the 1 August 2015.

However, the Vedic Maths Club will still continue after the competition and we will include games and practical applications of Maths in addition to the Vedic Maths techniques.

We are looking forward to taking this to other schools since we know that it will increase interest and skills in Maths.

Neshni Naidoo

Director: Vedic Maths Forum South Africa

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Smriti Irani slams critics who accuse her of 'saffronising' education

June 8, 2015, 4:13 am

≫ Next: The birth of Logartihm

≪ Previous: Vedic Maths Club in Cape Town

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HRD Minister Smriti Irani spoke at a conference organized by Hindu Education Board.

Taking a jibe at critics alleging saffronisation of education, Union HRD Minister Smriti Irani on Monday said the country’s inherent strength in education, ancient concepts and values is hailed and applauded abroad but is described as “saffron” back in the country.

Wondering if India’s inherent strength should not be valued, Ms. Irani, who is accused of ‘saffronising education’, said even in the field of Mathematics there has been accusation of saffronisation when India’s ancient method of maths is explored the world-over.

Speaking at a conference organised by Hindu Education Board, she spoke about the criticism faced by well- Mathematics professor of Princeton University Manjul Bhargava back home who confided learning the concept of maths through Sanskrit poems.

“...he is accused in television shows of saffronisation of mathematics. This is only possible in India that you have an ancient method of maths which is explored and applauded across the world, that becomes saffron back in India,” she said.

“Is everything Indian not to be valued? Is it possible in any country that we shy away from our own inherent strength… that we shy away from our own inherent heritage, our culture, our glorious history,” the minister said.

Referring to the controversy surrounding the yoga day celebration, she said, “I wonder whether all the 175 nations who supported us at the UN for celebrating the day were as saffron as we are.”

She said the new education policy, which would be ready by the year-end would emerge as one that helps in nation building.

“Education is also not limited to policy draft, or school or university. It defines the existence of human being, the society,” she said.

http://www.thehindu.com/news/national/while-abroad-hails-our-education-we-ridicule-it-as-saffronisation-irani/article7294449.ece

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The birth of Logartihm

June 13, 2015, 5:44 am

≫ Next: Fascinating Number Pattern

≪ Previous: Smriti Irani slams critics who accuse her of 'saffronising' education

How can you shorten the subject ? That stern struggle with the multiplication table, for many people not yet ended in victory, how can you make it less? Square root, as obdurate as a hardwood stump in a pasture nothing but years of efforts can extract it. you can''t hurry the process or pass from the arithmetic to algebra, you can't shoulder your way past quadratic equations or ripple through the binomial theorem. Instead , the other way ; your feet are impeded in the tangled growth, your pace slackens, you sink and fall somewhere near the binomial theorem with the calculus in sight on horizon. So died, for each of us, still bravely, lighting our mathematical training; except for a set of people called " mathematician" - born so , like crooks.

- Stephen Leacock

The word Logarithm is the combination of two words- Logos and arithmos. The meaning of these two Greek words are ration and number respectively. Hence logarithm means ration number. During the later part of 16th century, sea voyages were taken in large scales by the western countries like Great Britain, Portugal and Denmark. So the correct position of stars, planets and constellation were needed and therefore it was necessary to prepare accurate trigonometric tables for which complicated calculations were necessary.

In 1593, the great work of two Danish mathematicians Wittich and Calvin’s De – Astrolabo was published, who suggested the use of trigonometric table for shortening calculation. Moreover, Stevinus had published a table for calculations in commercial mathematics, which helped the person taking voyages to calculate the wealth collected during the voyages.

The birth of logarithm was therefore to shorten the length of calculation.

Take one example –

256 + 225 = 481

256 x 225 = 57600 and it involves three steps.

It is clear from the examples that number of operations involved in multiplication is greater than the number of operations involved in adding them. The bigger the number is the amount of labor in involved in calculation. Hence an effort was made to reduce all multiplication or division into addition or subtraction problems, and thus had the birth of logarithms possible.

John Napier is called the father of logarithms. John Napier was born in Scotland in 1550. Although he was not a professional mathematician but he had a strong interest in simplifying calculations, he worked for 20 years to prepare the table of logarithms. Napier published Mirfici Logarithmorum canonies Descripto in 1614 which was translated in English by Edward Wright.

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John Napier

Napier approached logarithm form the stand point of geometry and probably he might have used the formula –

2 Sin A Sin B = Cos(A – B) – Cos(A + B)

To prepare the logarigthm table. But presently we take

a^mx aⁿ = a^m+ ⁿ

to understand the log. The fact that in Napier’s log table the value of log1 does not equal to zero brought a major difficulty in its use. In a meeting of 1615, Napier suggested Briggs to construct a log table with a base 10 and with log1 = 0. Henry Briggs, a professor of geometry at Gresham College, London upon reading the Napier’s Descripto wrote –

Napier, Lord of Mar Kinston, hath set my head and hands at work with his new and admirable logarithms. I hope to see him this summer, if it pleases God; for I never saw a book which pleased me better and made me more wonder.

Prof. Briggs in his Arithmetica Logarithmica writes about Napier in the following words –

I journeyed to Edinburgh where being most hospitably received by him, I lingered for a whole month. But as we talked over the changes in logarithm, he said that he had for some times been of the same opinion and had wished to accomplish it …. He was of the opinion --- that 0 should be the logarithm of unity.

Napier in his book Mirfici Logarithmorum canonies Descripto wrote a work on the construction of a table published in 1619 posthumously. Prof. Briggs in 1624 published his Arithmetica Logarithmica gave the logarithms of all numbers from 1 to 1000 correct to 14 decimal places.

We all know

2 Sin A Cos B = Sin(A+B) + Sin(A- B)

Suppose we have to multiply -- 0.7072 x 0.9781

From the trigonometric table

Sin45 = 0.7072 and Cos12 = 0.9781

Hence,

Sin45 x Cos12 = ½ (Sin57 + Sin33)

Sin 57 = 0.8387 and Sin33 = 0.5446

Hence,

Sin45 x Cos12 = ½ (0.8387 + 0.5446) = 0.69165

By general multiplication - 0.7072 x 0.9781 = 0.69171232

If we compare both the result we see both the results are true to the 3 decimal places. The inaccuracy is due to the fact the table used here is for four-figure table. Had we consulted the eight figure table we would have the seven figure correct answer.

The present day log table is based on indices-

a^x = n

log aⁿ = x

n = antilog a^x

here the operator log written in front of number means – Look up in the table the power to which a has to be raised to give the number , whereas operator Antilog says – Look up in the table the value of the base when raised to the power represented by the number.

How can you construct a log table by your own?

We know

10⁰ = 1

log10¹= 0

2¹⁰ = 1024 = 10³ approximately

Since 1024 – 1000 = 24 , i.e a difference of 2 ½ %

Hence,

2 = (10³)^1/10 = 10^0.3 approximately

Therefore, log ₁₀² = 0.3

Similarly,

Since 3⁹ = 19683 = nearly equal to 20000

= 2 x 10000 approximately

= 10^0.3 x 10⁴ = 10^4.3approximately

3 = (10^4.3)^{1 / 9} = 10^0.48

log₁₀3 = 0.48

In the same way you can prepare a log table.

Rule of log:-

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Check some more rules on logarithms

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Rajesh Kumar Thakur

rkthakur1974@gmail.com

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Fascinating Number Pattern

June 17, 2015, 5:54 am

≫ Next: The Journey of Figurative Number

≪ Previous: The birth of Logartihm

Hello Readers,

Please read mathematical blogs of mine at -- www.mathspearl.blogspot.in

Fascinating Number Pattern

Number pattern is my weakness. The moment I see the pyramid of number pattern I start jumping and these pattern which I have collected from different sources is presented here for your enjoyment. I do hope you will love it and enjoy.

Amazing Number 142857

While solving the problem of mensuration we generally take the value of pi to be equal to 22/7 which in mixed fraction gives 3 ¹/_7.This fractional part ¹/₇ when changed it will be a non- terminating decimal which is equal to 0.142857 142857…

The number 142857 shows an explicit feature; when multiplied by 1, 2, 3, 4, 5 and 6.

142857 × 1 = 142857

142857 × 2 = 285714

142857 × 3 = 428571

142857 × 4 = 571428

142857 × 5 = 714285

142857 × 6 = 857142

This is not the end of the story. The sum of every digit of the number (if written in a table) column wise or row wise comes to be equal to 27.

×	1	4	2	8	5	7	Row wise sum
1	1	4	2	8	5	7	27
2	2	8	5	7	1	4	27
3	4	2	8	5	7	1	27
4	5	7	1	4	2	8	27
5	7	1	4	2	8	5	27
6	8	5	7	1	4	2	27
Column wise sum	27	27	27	27	27	27

You will be astonished to see more feature of this number. Let’s do the division process of number 1, 2, 3, 4, 5 and 6 by 7 and see the beauty of the number obtained.

1/ 7 = 0.142857 … and 142 + 857 = 999

2/7 = 0.428571 … and 428 + 571 = 999

3/7 = 0.285714 and 285 + 714 = 999

4/ 7 = 0. 857142 and 857 + 142 = 999

5 / 7 = 0.571428 and 571 + 428 = 999

6/ 7 = 0.714285 and 714 + 285 = 999

So far, we did multiplication of number 142857 by number from 1 to 6, let’s do the multiplication of this number by 7.

142857 × 7 = 999, 999

Moreover, 142 + 857 = 999 and 14 + 28 + 57 = 99

(142857)² = 20408122449 and 20408 + 122449 = 142857.

Pattern 2:- Multiplication of Number in recurrence of 9 with 2

Numbers like 9, 99, 999, 9999 … etc. are amazing numbers and it shows a beautiful relation when multiplied by 2. Enjoy the beauty here:-

9 × 2 = 18

99 × 2 = 198

999 × 2 = 1998

9999 × 2 = 19998

99999 × 2 = 199998

999999 × 2 = 1999998

9999999 × 2 = 19999998

99999999 × 2 = 199999998

999999999 × 2 = 1999999998

Pattern 3:- Multiplication of 987654321 by multiples of 9

987654321 is a number written in reverse order from the highest one digit number 9 to the least one digit number 1. This number when multiplied by the multiples of 9 it shows an exceptional beautiful pattern of number. Are you ready to enjoy the beauty?

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Did you notice the beauty of pattern?

The sum of digit at both the extreme is 9 and the multiple is placed at both the extreme. As far as the middle part of the product is concerned it is the recurring of number that is 1 less than the number at the unit digit of the multiplier.

Pattern 4: Here is a pyramid of multiplication of two numbers with equal number of 1’s and 8’s and the result obtained is amazing.

1 × 8 = 8

11 × 88 = 968

111 × 888 = 98568

1111 × 8888 = 9874568

11111 × 88888 = 987634568

111111 × 888888 = 98765234568

1111111 × 8888888 = 9876541234568

11111111 × 88888888 = 987654301234568

Pattern 5:- The below pattern is a very beautiful pattern of numbers that involves the multiplication of number 1, 12, 123 …. 123456789 by 8 and adding number 1, 2, 9 to it making a beautiful decorative pattern.

1 × 8 + 1 = 9

12 × 8 + 2 = 98

123 × 8 + 3 = 987

1234 × 8 + 4 = 9876

12345 × 8 + 5 = 98765

123456 × 8 + 6 = 987654

1234567 × 8 + 7 = 9876543

12345678 × 8 + 8 = 98765432

123456789 × 8 + 9 = 987654321

Pattern 6:- Pyramid of 8

This beautiful pyramid of 8’s is formed with the number 9, 98, 987 … multiplied by 9 and adding 7, 6, 5 ….

9 × 9 + 7 = 88

98 × 9 + 6 = 888

987 × 9 + 5 = 8888

9876 × 9 + 4 = 88888

98765 × 9 + 3 = 888888

987654 × 9 + 2 = 8888888

9876543 x 9 + 1 = 88888888

98765432 × 9 + 0 = 888888888

Pattern 7:- Multiplication of number 12345679 with the multiples of 9’s:- If you multiply 12345679 with the multiples of 9’s the result will be the recurring of the as many times the multiples of 9’s.

12345679 × 9 = 111 111 111

12345679 × 18 = 222 222 222

12345679 × 27 = 333 333 333

12345679 × 36 = 444 444 444

12345679 × 45 = 555 555 555

12345679 × 54 = 666 666 666

12345679 × 63 = 777 777 777

12345679 × 72 = 888 888 888

12345679 × 81 = 999 999 999

Pattern 8:- Multiplication of number 65359477124183 with multiples of 17:- Number 65359477124183 makes astonishing pattern when multiplied with the multiples of 17.

65359477124183 × 17 = 1111 1111 1111 1111

65359477124183 × 34 = 2222 2222 2222 2222

65359477124183 × 51 = 3333 3333 3333 3333

65359477124183 × 68 = 4444 4444 4444 4444

65359477124183 × 85 = 5555 5555 5555 5555

65359477124183 × 102 = 6666 6666 6666 6666

65359477124183 × 119 = 7777 7777 7777 7777

65359477124183 × 136 = 8888 8888 8888 8888

65359477124183 × 153 = 9999 9999 9999 9999

Pattern 9:- Palindrome Number Pattern with the multiples of 11, 111 ….:- Here is a beautiful pattern formed with the multiples of 11, 111, 1111 …. with itself.

11 × 11 = 121

111 × 111 = 12321

1111 × 1111 = 1234321

11111 × 11111 = 123454321

111111 × 111111 = 12345654321

1111111 × 1111111 = 1234567654321

11111111 × 11111111 = 123456787654321

111111111 × 111111111 = 12345678987654321

Pattern 10:- Beautiful pattern of multiplication of 9, 99 …:- Multiplication of number 9 shows a beautiful pattern. Enjoy the beauty of pattern.

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Pattern 11:- Pattern of square making a beautiful pyramid: - There are certain numbers which presents a beautiful pyramid pattern when its square is formed. Let’s enjoy the beauty.

4² = 16 7² = 49 9² = 81

34² = 1156 67² = 4489 99² = 9801

334²=111556 667²= 444889 999² = 998001

3334² = 1115556 6667² = 4444889 9999²= 99980001

33334² = 1111155556 66667² = 4444488889 99999² = 9999800001

Pattern 12:- Multiplication pattern with number 76923:- If you multiply 76923 with 1, 10, 9, 12, 3 and 4 you will see a beautiful pattern of result obtained. The number obtained in each case contains the same number of digit.

76923 × 1 = 076923

76923 × 10 = 769230

76923 × 9 = 692307

76923 × 12 = 923076

76923 × 3 = 230769

76923 × 4 = 307692

Pattern 13:- Pyramid of square of number in the recurring of 9:- Square of number 9, 99, 999, 9999, 99999, 999999 … etc. will form a pattern that looks like a pyramid. See the beauty.

9² = 81

99 ²= 9801

999²= 998001

9999²= 99980001

99999² = 9999800001

999999² = 999998000001

9999999² = 99999980000001

Pattern 13: - Circular Prime Pattern: - This is a circular Prime pattern :-A circular prime is a prime number that remains prime as each leftmost digit in turn is moved to the right hand side. For more information you can visit www.

19937

99371

93719

37199

71993

19937

Pattern 14:- Multiplication pattern with the primes makes a beautiful pattern.

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Pattern 15:- Division of number 1 to 9 by 11:- Number 1 to 9 divided by 11 gives non ending decimal expansion.

1/11 =0.09090909…. 2/ 11 = 0.18181818…

3/11 = 0.27272727… 4/11 = 0.36363636—

5/11 = 0.45454545… 6/11 = 0.54545454….

7/11 = 0.63636363… 8/11 = 0.72727272…

Pattern 16:- Division of number 1 to 9 by 9:- Number 1 to 9 divided by 9 gives non ending decimal expansion.

1 /9 = 0.11111… 2 /9 = 0.22222…

3/9 = 0.33333… 4/9 = 0.44444….

5/9 = 0.55555…. 6/9 = 0.66666…..

7/ 9 = 0.77777…. 8/9 = 0.88888…

Pattern 17:- Palindrome Pattern:-

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Pattern 18:- Square of Palindrome number giving the palindrome result

11² =121

101² = 10201

1001² = 1002001

10001² = 100020001

100001² = 10000200001

1000001² = 1000002000001

10000001² = 100000020000001

100000001² = 10000000200000001

Pattern 19: Product of Palindrome number making a beautiful pyramid: Here palindrome number made with recurring of 1 and 8 are shown making a beautiful pyramid of number.

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Pattern 20:- Pattern with number 987654321 :- Number 987654321 when multiplied by the multiple of 9 gives a beautiful pattern of number where the number placed at the extreme left and extreme right are the digit by which the number is multiplied whereas the middle recurring digits are one less than the number placed at the extreme right.

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Pattern 21:- Pascal Triangle: - In Algebra, you must have used the Pascal triangle to obtain the coefficient of binomial expansion. But this is not the end of the game, Pascal triangle when expended for 9 -10 rows shows different number pattern itself. If I say that Pascal triangle has natural number, triangular number, square number, Pentagonal number, Hexagonal number, Fibonacci number etc. then you will simply not believe my words but it is true.

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In the above diagram, you can see the second diagonal showing you the Natural numbers like 1, 2, 3, 4, 5 …. Whereas the third diagonal from either side shows you the triangular number 1, 3, 6, 10 … The Square number (1, 4, 9, 16, 25 …), Pentagonal number (1, 5, 12, 22, 35,…) Hexagonal number (1, 6, 15. 28, 45,…) and Fibonacci sequence (1, 1, 2, 3, 5, 8, 11, …) can be witnessed in this triangle.

Pattern 22:- Pyramid of 1:- See the beauty of number in increasing order making the pyramid of 1’s.

1 × 9 + 2 = 11

12 × 9 + 3 = 111

123 × 9 + 4 = 1111

1234 × 9 + 5 = 11111

12345 × 9 + 6 = 111111

123456 × 9 + 7 = 1111111

1234567 × 9 + 8 = 11111111

12345678 × 9 + 9 = 111111111

123456789 × 9 + 10 = 1111111111

So Explore the beauty and never forget to inform me about your sweet reaction.

Rajesh Kumar Thakur

rkthakur1974@gmail.com

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The Journey of Figurative Number

June 22, 2015, 7:05 am

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Figurative Numbers

Pythagoreans discovered the figurative numbers. The Greeks were deeply interested in numbers especially to those connected with the geometric shapes, and given the name therefore figurative numbers. Since Pythagoreans as the early custom of Greeks used to play with the pebbles to form the different shapes, so they were more fascinated with the relationship that emerged with the different shapes of pebble like Triangular, Square, Cubic, Pyramid, Hexagonal ...etc

The Greek word for pebble was pséphoi, meant to calculate. The pebbles made it possible for Pythagoreans to identify different shapes, the simplest being the two dimensional figure the triangle and simplest three dimensional figures was the tetrahedron.

Aristotle in his Metaphysics writes “They (the Pythagoreans) supposed the elements of numbers to be the elements of all things and the whole heaven to be a musical scale and a number ...Evidently then these thinkers also consider that number as the principal both as matter for things and as forming both their modification end their permanent states.”

This part of the chapter deals with only the figurative numbers and its different properties.

Triangular Numbers:- This is a kind of Polygonal number. It is the number of dots required to draw a triangle. The triangular numbers are formed by the partial sum of the series 1+ 2 + 3+ … + n.

The Greeks also noted that these triangular numbers are the sum of consecutive natural numbers, as they appear in the number sequence. If the process continues till n th array then numbers of pebbles in the nth array is 1+2+3+...+n=n* (n+1)/2

1 first triangular number

1+2=3 second triangular number

1+2+3=6 third triangular number

1+2+3+4=10 fourth triangular number

1+2+3+4+5=15 fifth triangular number

And so on...

Here is a picture of first few triangular numbers.

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Properties of Triangular Numbers:-

v A triangular number can never end with 2, 4, 7, or 9.

v The sum of the two consecutive triangular numbers is always a square number. T₁ +T₂ = 1 + 3 = 4 = 2²T₂ + T₃ = 3 + 6 = 9 = 3² T₃ + T₄ = 6 + 10 = 16 = 4²

v All perfect numbers are triangular numbers.

v A triangular number greater than 1 can not be a cube, a fourth Power or a fifth Power.

v The only triangular number which is also a prime is 3.

v The only triangular number which is also a Fermat number is 3

v The only Fibonacci numbers which are also triangular are 1, 3, 21, and 55.

v Some triangular numbers are the product of three consecutive numbers. T₃ = 6 = 1* 2 * 3 T₁₅ = 120 = 4* 5* 6 T₂₀ = 210 = 5 * 6 * 7 T₄₄= 990 =9 * 10 * 11 T₆₀₈= 185136 = 56 * 57 * 58 ---------------------- ---------------------

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

Triangular number can be seen in Pascal’s triangle. Look at the Pascal’s Triangle and you will find that the third diagonal is all triangular numbers.

Square Numbers:- The number 1, 4, 9,16,25,36... are called the square numbers. It is the numbers of dots arranged in such a way that it represent a square shape. These are the square of the natural numbers 1, 2, 3, 4, 5, 6….. respectively.

The Greeks also have discovered that if consecutive odd numbers are added they become square numbers. 1=1*1

1+3=4=2²

1+3+5=9=3²

1+3+5+7=16=4²

1+3+5+7+9=25=5²

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More interestingly each higher square number is formed by adding L shaped set of pebbles to the previous number. The L-shape was called gnomon by the Greeks which referred to an instrument imported to Greece from Babylon for measuring time.

Note that the square number can be found by addition of all triangular number in the following manner—

1 3 6 10 15 21 28 36...

1 3 6 10 15 21 28 36 ...

1 4 9 16 25 36 49 64....

Properties of Square Numbers:-

o Every square number can end with 00, 1, 4, 5, 6, or9.

o No square number ends in 2, 3, 7, or 8.

o Look at the following pattern 1² = 1 11² = 121 and 1 + 2 + 1 = 4 = 2² 111² = 12321 and 1 + 2 + 3 + 2 + 1 =9 = 3²

1111² = 1234321 and 1 + 2 + 3 + 4 + 3 + 2 + 1 = 16 = 4²

11111² = 123454321 and 1 + 2 + 3 + 4 + 5 + 4 + 3 +2 +1 = 25 = 5^{2 --------------------------------------------------------------------------------------------------------------------------------------------------------------------}

Cube Numbers:- The numbers which can be represented by three dimensional cubes are called cubic number. 1,8,27,64,125...are cubic numbers which are obviously the cubes of 1,2,3,4,5,....

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Properties of Cubic Numbers:-

1³=1 first odd number

2³=8=3+5 sum of next two odd numbers

3³=27=7+9+11 sum of next three odd numbers

4³=64=13+15+17+19 sum of next four odd numbers

5³=125=21+23+25+27+29 sum of next five odd numbers

Between 1 and 100 there are only two numbers 1 and64 that are also square numbers.
If C_1,C_2,C₃ ….are the first, second, third… cubic number then they exhibit a unique property:- C₁= ( T₁)² C₁ + C₂ = 1 + 8 =( T₂) ² C₁ + C₂ +C₃ = 1 + 8 + 27 = 36 = ( T₃) ² C₁ + C₂ +C₃+C₄ = 1 + 8 + 27 + 64 = 100 = (T₄)²
Tetrahedral Numbers:- The numbers that can be represented by the layers of triangles forming a tetrahedron shape are called tetrahedral numbers. It is a figurative numbers of the form Tn = nC3 where n = 3, 4, 5,….4, 10, 20...are the example of tetrahedral numbers.

Properties of Tetrahedral Numbers:-

The tetrahedral numbers are the sums of the consecutive triangular numbers beginning from 1. T₁= 1 T₂= 1 + 3 = 4T₃= 1 + 3 + 6 = 10 T₄ = 1 + 3 + 6 + 10 = 20T₅ =1 + 3 + 6+ 10 + 15 = 35 T₆= 1 + 3 + 6 + 10 + 15 + 21 = 56 -------------------------------------------------

The sum of two consecutive numbers is a Pyramidal number. T₁ + T₂ = 1 + 4 = 5 T₂ + T₃ = 4 + 10 = 14 T₃+ T₄ = 10 + 20 = 35 T₄+ T₅ = 20 + 35 = 55 T₅+ T₆= 35 + 56 = 91

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

The tetrahedral numbers can be seen in the fourth diagonal of a Pascal’s triangle

Pentagonal Numbers:- Those numbers which represent the shape of pentagon are called pentagonal number. In the pentagonal numbers the lower base is a square with a triangle on the top. 1, 5,12,22,35...are its example. The nth pentagonal number Pn is given by the formula:-

P_n = n ( 3n – 1 )

If we represent the pentagonal numbers by P₁,P₂ ,.... then the n th number P_n =n(n-1)/2+n²

Properties:-

Every nth pentagonal number is one third of the 3n – 1 th triangular number.

Hexagonal Number:- Those numbers which form a shape of hexagon are called hexagonal numbers. 1, 6, 15, 28, 45…. are the few examples of hexagonal numbers.

Hexagonal numbers are of the form n (2n-1).

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Properties:-

· Every hexagonal numbers is a triangular number.

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1,7,19,37,61,91... are the centered hexagonal numbers.

· 11 and 26 are the only numbers that can be represented by the sum using the maximum possible of six hexagonal numbers.

11 = 1 + 1 + 1 + 1 + 1 + 6 26 = 1 + 1 + 6 + 6 + 6 + 6

Pyramidal Number:- Those numbers which can be represented as layers of squares forming a pyramid are called pyramidal numbers. The pyramid class can be formed by adding successive layers of which the next above the nth is the (n-1)th member of the same figurative number series.

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35 55

There are many more figurative numbers which are not discussed here but one thing is clear that they are really very- very interesting. Though in the initial phase; the study of such numbers produced no immediate results but certainly they are important as it led to the study of series, which provided the clue to an understanding of numbers which are not full grown. The credit certainly goes to the Pythagoreans who dealt with such numbers. Even in the history triangular numbers played an important role in suggesting rules for forming and adding the terms of series. A relic of such numbers is seen in the problems relating to the pilling of round shot, still to be found in algebras. Ovid in his poem De Nuce talks about pyramidal number. So the journey which Pythagoreans began with pebbles has now reached many mile stone in the mathematics and mathematicians are also looking for other figurative numbers making their journey endless.

Drop your comments here

Rajesh Kumar Thakur

rkthakur1974@gmail.com

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The Vedic Maths Workshop at Dubai

July 4, 2015, 12:16 pm

≫ Next: TIME 2015 by IIT Bombay

≪ Previous: The Journey of Figurative Number

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The Vedic Maths Workshop at Jumeirah Islands, Dubai

This summer we conducted a private workshop at Jumeirah Islands, Dubai. The Workshop was organized by Mr.Saha from Dubai. It was a pleasure conducting the workshop for 8 hours every day. Hats off to the children who sat patiently and learnt the concepts of Vedic Maths everyday.Apart from the vedic concepts which were taught we had a Maths Quiz, Debates ,Puzzles, Chart making and other interesting facets around vedic maths. Application of Vedic Maths in real time mathematics was discussed as well.

The students were diligent and were very enthusiastic after learning the new methods. We even had 2 teams debate the topic 'Relevance of Vedic Maths in current times'. Some kids wondered why isn't VM taught in schools?

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Fun with Shapes - at the Vedic Maths Workshop

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Kids Enjoying at the Vedic Maths Workshop

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The Digit Sum Man

Overall everybody learnt, enjoyed and was happy about the Maths taught. It was also a learning experience for us and we had a few breakthrough moments during the course of the workshop.

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TIME 2015 by IIT Bombay

July 6, 2015, 12:02 am

≫ Next: Vedic Maths discussed with HRD Minister Smriti Irani

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TIME 2015, IIT Bombay's biennial conference on math education:Technology & Innovations in Math Education" is scheduled from December 4-7, 2015 at VPCOE, Baramati (Pune).

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You can make a presentation in TIME 2015:
Themes for presentation (select one)
• Use of technology in the mathematics classroom – Presentations in this strand may include the use of Dynamic Geometry Software, Spreadsheets, Graphics Calculators Computer Algebra Systems. mobile apps, etc for teaching and learning mathematics at various levels of school and college mathematics.
• Use of innovative teaching aids - Presentations in this strand may include any innovation which has a positive impact on teaching and learning mathematics at any level, be it primary, upper primary (middle school), secondary, senior secondary or college level.
• Mathematics Modelling and Applications in School Mathematics – Presentations in this strand may focus on how modelling and applications of mathematics can be included in the school curriculum to help student appreciate the relevance of mathematics to various subject disciplines and also to solve problems in real life.
• Mathematics Laboratory Activities – This strand will focus on specific activities that can be conducted in a mathematics laboratory which either highlights a mathematical concept or some important aspects of a topic of school mathematics.
• Mathematics Curriculum and Assessment– This strand will focus on presentations which emphasize the relevance of various topics in the curriculum and on how assessment of learning in these topics may be done through innovative means.

Pls contact Prof.Rana for Registration and Participation details.

Dr. Inder K. Rana

Emeritus Fellow

Department of Mathematics

Indian Institute of Technology, Powai

Mumbai 400076, India

Phone: 091+022+25767462

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Vedic Maths discussed with HRD Minister Smriti Irani

July 18, 2015, 10:19 am

≫ Next: Grand Launch of Vedic Maths Forum Mumbai Chapter in association with Fun Gurukool

≪ Previous: TIME 2015 by IIT Bombay

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NEW DELHI: Union HRD Minister Smriti Irani is understood to have held deliberations with functionaries of some RSS-affiliated education bodies today as her ministry is in the midst of drafting a new education policy.

Sources said inputs were shared during the deliberation regarding the new education policy and about giving thrust to a revamped education system which instills nationalism, pride and ancient Indian values in modern education.

The interaction came ahead of RSS' three-day annual meeting in Nainital next week.

The meeting also assumes significance as education bodies have come out with resolutions in recent past supporting the promotion of Sanskrit and vedic values in course curriculum.

The Bhartiya Shikshan Mandal, an RSS body, had in a draft outline on education last week had recommended that from classes 9 to 12, students should be taught mother tongue and a classical language which could be Sanskrit or other languages like Arabic, Persian, Latin or Greek etc.

The draft titled 'Bhartiya Education Outline' also suggests that after eight years of primary education, student will have to "compulsorily" study one economic activity based subject for the next four years.

In June, the Dinanath Batra-headed Shiksha Sanskriti Utthan Nyas had proposed introduction of vedic maths in schools across the country and sought effective implementation of the three-language formula in all states.

It had favoured incorporating vedic maths along with regular mathematic courses in classes so as to improve the level of "competency" among students in the subject.

"We have prepared a syllabus on vedic maths and have reached out to a few private schools across the country including a school in Delhi to impart it in classes," the body's secretary Atul Kothari had said.

Meanwhile, slamming the current education system in the country for lacking "Indianness", joint general secretary of RSS Krishna Gopal had said an education system should be such which connects students with their roots, their culture and provides an spiritual integration.

The new national education policy, the consultation of which started in January this year, could be ready for consideration by the end of this year.

The thrust of the Ministry is to reach out to all the stakeholders at the grassroot level to seek their views and suggestions during the consultation stage.

Source: http://www.ndtv.com/india-news/union-minister-smriti-irani-holds-talks-with-rss-bodies-on-education-policy-782848

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Grand Launch of Vedic Maths Forum Mumbai Chapter in association with Fun Gurukool

July 21, 2015, 5:07 am

≫ Next: Speed Maths Challenge 2015 (Cape Town, 1 August 2015)

≪ Previous: Vedic Maths discussed with HRD Minister Smriti Irani

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With Mrs.Shah, Director VMFI Mumbai Chapter

It is my pleasure to announce the Grand Launch of our Mumbai Chapter in Kandivali in association with Fun Gurukool,Mumbai.

All our Vedic Maths online and offline programs are offered for Teachers, Students and Math Enthusiasts.

We wish Mrs.Shah, the Proprietor of Fun Gurukool and the Director of VMFI, Mumbai Chapter, the very best in future endeavors.

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Speed Maths Challenge 2015 (Cape Town, 1 August 2015)

July 23, 2015, 2:26 am

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How can we change Maths from being described as boring, tedious and difficult to fun, creative and exciting? One way is to show learners simpler, alternate ways of doing Maths, turning the lesson into a game. This is the objective of the Speed Maths Challenge initiated by Vedic Maths Forum SA (VMFSA) in 2014.

VMFSA provides School Maths tutoring to learners in Grade 4 to 12 and offers courses in Vedic Maths (a Mental Maths programme) via an online platform. We wanted to take this a step further though - to reach more learners and teachers and demonstrate to them that Maths can be fun. This is how the Speed Maths Challenge was born – a Quiz competition that tests learners’ knowledge and application of Mental Maths through Maths Puzzles and speed challenges.

Over the last 6 months, we have worked with Grade 4, 5, and 6 learners in 4 schools – Habibia Primary, Rylands Primary, Surrey Primary and Vanguard Primary. The learners were taught a few Vedic Maths techniques and given the opportunity to work through Maths puzzles. This was done through workshops with learners, self-study notes and a Vedic Maths Club. The Vedic Maths Club is an extra-mural activity run at Rylands Primary and Vanguard Primary and facilitated by teachers with guidance and support from VMFSA.

On the 1^st August 2015, 3 teams from each of these 4 schools will compete against each other in 3 categories (Grade 4, 5 and 6) in Speed Maths Challenge 2015. The event is being held at Rylands Primary School in Rylands, Cape Town from 9:30am to 12:30pm.

Based on our experience from 2014, we have seen that this type of competition not only enhances Mental Maths ability, but encourages teamwork, builds confidence, increases concentration and develops logic and strategic thinking skills.

Feedback received from the schools that participated last year, demonstrates that a competition such as this one, can be an intrinsic motivator and encourage learners to try harder and challenge themselves.

"Learners were very thrilled with the methods taught - especially once they mastered it.

The learners definitely benefited from the methods. It made them aware that there is more than one way to solve problems.

As for the competition learners were very excited and eager to participate. It also gave them a chance to test their newly acquired skills against other learners. Many of them also came to me and mentioned that if they had put in more effort they would have been able to do even better - which is good. They realise if they work hard they will more be successful."

Rylands Primary School – Mr M.S. Hendricks

Our vision is to take this competition to more schools next year and use this as a tool to create a more positive perception of Maths in the minds of our learners and teachers.

VEDIC MATHS FORUM SOUTH AFRICA

Making Maths Fun

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Prime Minister Shri Narendra Modi invites inputs on Maths

July 27, 2015, 6:51 am

≫ Next: News from Bangalore

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Prime Minister Shri Narendra Modi has invited suggestions as below on his Twitter Account.

How can we create a curiosity among young minds towards science and mathematics? Share your inputs here. https://t.co/FiCcU0vQuJ
— Narendra Modi (@narendramodi) July 26, 2015

So now is the time to show some love to Vedic Maths people! Please share your inputs on the above links.

Thanks

The Vedic Maths Forum India Team.

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News from Bangalore

July 31, 2015, 2:25 am

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Shri V.G.Unkalkar at the Vedic Maths Workshop

Sahyadri Kannada Sangha from Kaiga Nuclear Power Corporation, India ltd., Karnataka organized a 2 day workshop on Vedic Mathematics on 11 &12 July 2015.

The workshop was conducted by Shri V. G. Unkalkar, author of many books on Vedic Mathematics. The gathering comprised of about 100 participants including high school & college students , teachers, & employees of that area. It was appreciated by one & all. Shri V.G.Unkalkar was felicitated by Sahyadri Kannada Sangha after the workshop.

Principal K. Sharma, Sangha president Amol Revankar, v.p. Jeetendrakumar, Mahantesh Oshimath,& all members of sangha made efforts to make the Vedic Mathematics workshop a grand success.

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