**Vedic Mathematics Newsletter No. 119**

A warm welcome to our new subscribers.

This issue’s article (at the end of the newsletter) is an inspiring account, by Virgilio Y. Prudente, of upcoming events in the Philippines.

“…500 teachers and 2,000 students are expected to attend the seminar series…… One hundred thirty Filipino elementary and high school teachers are currently enrolled in the Vedic Mathematics Teacher Training Course…”

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**NEWS**

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**3 ^{RD} INTERNATIONAL VM CONFERENCE – REGISTRATION**

This Conference is from 23rd - 25th August 2018 at RV College of Engineering, Bengaluru, India.

There will be scholarly speakers presenting their research and many workshops for students and teachers.

Details can be seen at the link below, and registrations are now being taken.

https://instituteavm.wixsite.com/conf2018

**PROCEEDINGS OF THE 2 ^{ND} INTERNATIONAL CONFERENCE**

The research papers from this conference in December 2017 at St Stephen’s College, New Delhi, can be requested after paying a $10 donation.

http://www.instavm.org/research-papers-1

**AN INTERESTING APPLICATION OF THE SUTRAS “THE FIRST BY THE FIRST AND THE LAST BY THE LAST” AND “THE PRODUCT OF THE SUMS IS THE SUM OF THE PRODUCT” **

While studying Pythagorean Triples, I came across an article about two consecutive odd (or even) numbers being the basis for the lengths of the sides of right triangles. The sum of these numbers would be one of the legs of a right triangle, and their product would be the other leg. Out of curiosity, I tried to prove it to myself.

So, I let x = the first odd (or even number)

And (x + 2) = the next odd (or even number)

One leg would be their sum, x + (x + 2) = (2x + 2)

The other leg would be their product, x (x + 2) = (x^{2} + 2x)

By the Pythagorean Theorem, we have

C^{2} = (x^{2} + 2x)^{2} + (2x + 2)^{2}

= (x^{4} + 4x^{3} + 4x^{2}) + (4x^{2} + 8x + 4)

= x^{4} + 4x^{3} + 8x^{2} + 8x + 4

I was momentarily stumped. How can I extract the square root of that expression? I said “momentarily”, because I immediately remembered the Vedic sutras.

Using “The First by the First”, the square root of x^{4 }is x^{2}.

Using “The Last by the Last”, the square root of 4 is 2. We now have

C^{2} = x^{4} + 4x^{3} + 8x^{2} + 8x + 4 = (x^{2 }+ Bx + 2)^{2}

We need only to determine the value of B. By using “The Product of the Sums is the Sum of the Product” we know that the digit sum of the hypotenuse is the square root of the digit sum of C^{2}.

The digit sum of C^{2} is 1 + 4 + 8 + 8 + 4 = 25 and the square root of 25 is 5. (1 + B + 2) must be 5, then B = 2. The hypotenuse is thus (x^{2 }+ 2x + 2) or just 2 more than the other leg.

From Virgilio Y. Prudente, The Philippines

**‘GEOMETRY FOR AN ORAL TRADITION’**

This book by Andrew Nicholas is available again in hard copy:

http://www.vedicmaths.org/shop/books

(item 12)

This book presents direct, immediate and easily understood proofs. These proofs are based on only one assumption (that magnitudes are unchanged by motion) and three additional provisions (a means of drawing figures, the language used and the ability to recognise valid reasoning). Starting from these first principles it leads to theorems on elementary properties of circles. It includes discussion on the relevant philosophy of mathematics and is written both for mathematicians and for a wider audience.

**VM BOOK PRICES TO INCREASE**

Please note that prices of most books in our Bookstore at:

http://www.vedicmaths.org/shop/books

will increase at the end of August 2018.

The prices have not been increased since the Bookstore was originally formed but due to increasing costs of printing and postage it is no longer possible to sustain the current prices.

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**ARTICLE FOR NEWSLETTER 119**

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**Vedic Math Activities in the Philippines**

**Inspirational Maths from India by IAVM**

**by Virgilio Y. Prudente**

The Institute for the Advancement of Vedic Mathematics (IAVM) will be conducting “Inspirational Maths from India”, a series of seminar workshops in three cities in the Philippines. James T. Glover of the United Kingdom, chair and co-founder of IAVM, together with trustee Swati Dave of the United States, trustee Marianne Fletcher of South Africa and member Gowri Ramachandran of the Philippines, will conduct parallel sessions for elementary and high school teachers in:

- Puerto Princesa City, Palawan on August 1-3;
- San Pablo City, Laguna on August 4-5; and
- Quezon City, Metro Manila on August 9.

Separate sessions for students of all ages are also scheduled.

A teacher’s handbook, also entitled “Inspirational Maths from India,” was specially written for this occasion by IAVM members and will be given to the participants. It contains topics that will be discussed in the seminars.

A total of 500 teachers and 2,000 students are expected to attend the seminar series organized by MATH-Inic Philippines in cooperation with the Palawan State University, Department of Education, Division of San Pablo City, and the World of Outbound. Among the main sponsors are Palawan Pawnshop-Express Pera Padala and the City Government of San Pablo City.

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**Continuing cooperation**

Upon the request of the College of Teacher Education of Palawan State University (PSU), the IAVM sent a “Proposal of Cooperation for the Introduction and Maintenance of Vedic Mathematics into the Curriculum of the Philippines.” A Memorandum of Agreement to be signed by the PSU, IAVM, the Vedic Mathematics Academy, and Vedic Maths Inc. is currently in the works.

The Division of Schools, San Pablo City is considering a similar agreement. These partnerships will help popularize VM in the Philippines and is a step towards strengthening Math skills in the country.

**IAVM in the 2018 MTAP-Tl Convention**

The Institute for the Advancement of Vedic Mathematics (IAVM) Chair and co-founder James T. Glover will be the closing plenary speaker at the 2018 Mathematics Teacher’s Association of the Philippines – Tertiary Level on July 27 at the Cebu Grand Hotel, Cebu City. He will talk about “Vedic Maths as a Pedagogical Tool “, a paper co-authored by Mr. Glover and Vedic Mathematics Academy founder Kenneth R. Williams in 2015.

IAVM member and MATH-Inic Philippines president, Virgilio Y. Prudente will also discuss the “Various Applications of The First and Last Digits and Digit sums in Arithmetic and Algebra” during the closing plenary session.

A Speed Math contest sponsored by Math-Inic Philippines will highlight the closing ceremonies of the convention.

**Vedic Math Teacher Training**

One hundred thirty Filipino elementary and high school teachers are currently enrolled in the Vedic Mathematics Teacher Training Course under Vedic Maths Academy founder Kenneth R. Williams. Upon completion of the course, these teachers plan to organize training teams to introduce VM not only to their co-teachers in their localities but also to the other regions in the Philippines.

End of article.

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Editor: Kenneth Williams

The Vedic Mathematics web site is at: http://www.vedicmaths.org

26^{th} July 2018