Math Yoga
Ancient Hindu sutras offer intriguing shortcut to solving complex
modern math problems
http://consciouschoice.com/2006/01/img/vedicmath1.jpg
Nikhil Reghunath (left), 11, and P.V.
Sarath Nath, 12, race through a set of practice problems in Vivek
Astunkar's
Vedic math course. Photo: John Myers
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A taste of Vedic math
The "Nikhilam" (by one more
than the one before) sutra
One fun technique derived from this sutra instantly gives squares to
any number ending with 5. So, to find the square of 75:
1) Simply put 25 on the "right-hand side" of your answer.
2) Take the number that precedes five (7, in this case) and add one,
giving you 8. (This is where "by one more than the one before" takes
flight.)
3) Next, multiply 8 by 7 to get 56. This is the "left-hand side" of
your answer.
4) Put the results together, 56 and 25, to form 5,625. Check it!
By John Myers
BOMBAY, INDIA - Math instructor Vivek Astunkar barely caps his pen
before 12-year-old Janhavi Shah calls out "one, three, two, one, six,
double zero!" She has, in mere seconds, correctly answered Astunkar's
whiteboard challenge — multiply 1,120 by 1,180.
Unlike Dustin Hoffman in the film "Rain Man," Janhavi cannot
instantly count toothpicks dropped to the floor. In fact, her nine
classmates — all normal, middle-class Indian youngsters — confirm her
results just seconds later.
They've used a shortcut from Vedic math, an alternative approach to
calculation that Indian ascetics may have devised more than 3,500
years ago. These yogic math techniques are mental exercises that can
waylay the fear of numbers, build confidence and enhance creativity,
says Astunkar.
Vedic math is largely unknown in India, let alone the West. But
that's changing. A local newspaper recently counted more than 40
Bombay schools using it. Astunkar, alone, has tutored thousands of
students, and also supplies newspapers with weekly Vedic problems.
And a few organizations such as Mathvedics, which has franchises in
California and Colorado, are pioneering the approach in America.
"School is just studies. This is fun," says Janhavi, who sits at the
end of a couch, sandwiched by peers, in Astunkar's small apartment,
four floors up in one of New Bombay's mid-rise buildings. It's Sunday
morning and the students are happy, even giggling, as they speed
through multiplication problems that would make the average adult
sweat.
Astunkar, an aeronautical engineer who left his software firm five
years ago to teach Vedic math, excels at making it fun. Using a small
whiteboard, he writes out problems for the kids to race through,
afterwards explaining the Vedic techniques in a flash of scribbling.
He says the methods, derived from devotional Sanskrit verses called
sutras, should not replace classic math practices. But, he adds, they
offer students fresh, and ultimately faster, ways to calculate.
A Hindu holy man, steeped deeply in Sanskrit and math scholarship,
marshaled Vedic math into the modern era. Followers of Bharati
Krishna Tirthaji believe he discovered 16 sutras in a long-lost
appendix to the Vedas, Hinduism's most sacred religious texts. Using
these verses, Tirthaji spent eight years (1911-18) reconstructing
formulas that span math's various realms, from basic arithmetic to
advanced calculus.
Indeed, Tirthaji enthusiasts claim the 16 sutras encompass all
possible mathematical knowledge. But they're left with precious
little guidance from their guru. He supposedly wrote one book for
each sutra and entrusted them to a disciple. Near the end of his
life, however, the works mysteriously disappeared. Tirthaji obliged
frantic devotees and rewrote the works from memory into one
compressed volume, published posthumously in 1965 under the title
Vedic Mathematics.
Average readers will find the book virtually impenetrable. The
sutras, simple phrases loaded with meaning, like "All from nine and
last from 10," and "By one more than the one before," are spelled out
but hardly illuminated. And the resulting math procedures are
recorded but left largely unexplained, notes Astunkar.
"I have read a little last night and not understood a word," says his
student Janhavi. (Her mother, a college professor of commerce, bought
a copy out of curiosity.)
But, for most Indians, the appeal of Vedic math has less to do with
its spiritual and cultural roots and more to do with the intense
competition facing students on college entrance exams, says Atul
Gupta, author of The Power of Vedic Maths.
Gupta's book skims over the underlying sutras, instead featuring more
than 1,000 practice problems with detailed explanations of the math
techniques themselves. In a workshop Gupta offered in November, all
but one of the students were preparing for technical examinations in
the spring.
Still, Gupta waxes poetically about the spiritual nature of Vedic
math. "The simplicity and the brilliance of the techniques will make
you feel humble," he says.
Of course, Vedic math is not without controversy. Many scholars say
it's neither "Vedic" nor "mathematics."
Joining 15 math and Sanskrit scholars, Madhav Deshpande, a Sanskrit
professor at the University of Michigan, argued as much in a signed
letter sent to India's national council on school curriculum.
Advocates hope to add Vedic math to the national curriculum, which
these critics characterize as arithmetic "tricks."
"I believe as a Sanskrit scholar that whatever its intrinsic merits
or lack thereof, the contents of `Vedic Mathematics' have no
historical connection with the Vedas," says Deshpande.
Regardless what Sanskrit scholars make of the Vedic connection, it is
full steam ahead for Astunkar, Gupta and other Vedic math teachers
who hope to spread the practice. The goal is not to get students
mired in Sanskrit, but to get them excited about math, says Astunkar.
Recalling a student who found a way to expand a method for squaring
numbers that end in 5 (see sidebar), Astunkar notes, "With Vedic
math, their hidden creativity just pops up."
Thanks to Vedic math, Chicago-based writer John Myers can instantly
convert any price in rupees to dollars, astounding both chaiwallas
and fellow travelers throughout India.
http://consciouschoice.com/2006/01/vedicmath.html