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(1)

The Secret of High-speed

The Secret of High-speed

 mental computations

 mental computations

Vedic Vision

(2)

“There are things which seem incredible to

“There are things which seem incredible to

most men who have not studied

most men who have not studied

mathematics.”

mathematics.”

 – 

 – Archimedes.

Archimedes.

“Spiritually advanced cultures were not ignorant of

“Spiritually advanced cultures were not ignorant of

the principles of mathematics, but they saw no

the principles of mathematics, but they saw no

necessity to explore those principles beyond that

necessity to explore those principles beyond that

which was helpful in the advancement of

which was helpful in the advancement of

God

God

realization.”

realization.”

 – 

(3)

“There are things which seem incredible to

“There are things which seem incredible to

most men who have not studied

most men who have not studied

mathematics.”

mathematics.”

 – 

 – Archimedes.

Archimedes.

“Spiritually advanced cultures were not ignorant of

“Spiritually advanced cultures were not ignorant of

the principles of mathematics, but they saw no

the principles of mathematics, but they saw no

necessity to explore those principles beyond that

necessity to explore those principles beyond that

which was helpful in the advancement of

which was helpful in the advancement of

God

God

realization.”

realization.”

 – 

(4)

4 frailties

4 frailties

We make mistakes.

We make mistakes.

We fall into illusion.

We fall into illusion.

We have cheating propensities.

We have cheating propensities.

Karana-patava

Karana-patava

pramada

pramada

bhrama

bhrama

vipralipsa

vipralipsa

W

We have imperfect se

e have imperfect senses.

nses.

Descending

(5)

Comp

Composeoseddbybysagsageses

Wo

Wordrdingmaychaningmaychangegefrfromomagageetotoagagee

Revealed Absolute Truth

Revealed Absolute Truth

Every word unchanged eternally 

Every word unchanged eternally 

Rajasic

Rajasic

VEDIC KNOWLEDGE

VEDIC KNOWLEDGE

SRUTI

SRUTI

 

 

SMRTI

SMRTI

UPAVEDAS UPAVEDAS Dhanurveda Dhanurveda  Ayurveda,  Ayurveda, Gandharvaveda, Gandharvaveda, Sthapatyaveda Sthapatyaveda VEDAS VEDAS Rg, Yajur, Rg, Yajur, Sama, Atharva Sama, Atharva VEDANGAS

VEDANGAS    PPuurraannaas s ItihasasItihasas SSiix x DDaarrsshhaannaass

Tantras Tantras Spoken by Lord Spoken by Lord Siva to Parvati Siva to Parvati Ritual Sutras Ritual Sutras Connected to Connected to Kalpa-vedanga Kalpa-vedanga Pancaratras Pancaratras Srauta Sutras Srauta Sutras explains explains public yajnas public yajnas Grhya Sutras Grhya Sutras explains explains home yajnas home yajnas Dharma Sutras Dharma Sutras Law books Law books Vedanta Vedanta ( (Vyasa)Vyasa) (Metaphysics (Metaphysics)) theology of  theology of  Upanisads Upanisads Mimamsa Mimamsa (Jaimini) (Jaimini) (Hermeneutics (Hermeneutics)) interpreting interpreting scriptural texts scriptural texts Nyaya Nyaya (Gautama) (Gautama) (Epistemology, logic) (Epistemology, logic) philosophy of  philosophy of  knowledge knowledge including logic including logic Vaisesika Vaisesika (Kanada) (Kanada) (Metaphysics (Metaphysics)) philosophy of  philosophy of  existence existence  Yoga  Yoga (Patanjali) (Patanjali) (Sadhana) (Sadhana) Sankhya Sankhya (Atheist Kapila) (Atheist Kapila) (Metaphysics) (Metaphysics) Dharma Sastras Dharma Sastras including including

Manu-samhita and others

samhita and others

18 Major  18 Major  18 Minor  18 Minor  Samhitas Samhitas mantras mantras Brahmanas Brahmanas ritual explanation ritual explanation of mantras of mantras Aranyakas Aranyakas esoteric explanation esoteric explanation of mantras of mantras Upanisads Upanisads Jnana-kanda Jnana-kanda philosophy of Brahman philosophy of Brahman Kalpa Kalpa ritual details ritual details Siksa Siksa pronunciation pronunciation Vyakarana Vyakarana grammar  grammar  Nirukta Nirukta etymology etymology Chandas Chandas meters meters Jyotisa Jyotisa astronomy-time astronomy-time calculation calculation Vaisnava Vaisnava worship worship Tamasic Tamasic Sattvic Sattvic

Vedic Mathematics

Vedic Mathematics

Srauta Srauta Sutras Sutras Smarta Smarta Sutras Sutras Sulba Sulba Sutras Sutras

(6)

Comp

Composeoseddbybysagsageses

Wo

Wordrdingmaychaningmaychangegefrfromomagageetotoagagee

Revealed Absolute Truth

Revealed Absolute Truth

Every word unchanged eternally 

Every word unchanged eternally 

Rajasic

Rajasic

VEDIC KNOWLEDGE

VEDIC KNOWLEDGE

SRUTI

SRUTI

 

 

SMRTI

SMRTI

UPAVEDAS UPAVEDAS Dhanurveda Dhanurveda  Ayurveda,  Ayurveda, Gandharvaveda, Gandharvaveda, Sthapatyaveda Sthapatyaveda VEDAS VEDAS Rg, Yajur, Rg, Yajur, Sama, Atharva Sama, Atharva VEDANGAS

VEDANGAS    PPuurraannaas s ItihasasItihasas SSiix x DDaarrsshhaannaass

Tantras Tantras Spoken by Lord Spoken by Lord Siva to Parvati Siva to Parvati Ritual Sutras Ritual Sutras Connected to Connected to Kalpa-vedanga Kalpa-vedanga Pancaratras Pancaratras Srauta Sutras Srauta Sutras explains explains public yajnas public yajnas Grhya Sutras Grhya Sutras explains explains home yajnas home yajnas Dharma Sutras Dharma Sutras Law books Law books Vedanta Vedanta ( (Vyasa)Vyasa) (Metaphysics (Metaphysics)) theology of  theology of  Upanisads Upanisads Mimamsa Mimamsa (Jaimini) (Jaimini) (Hermeneutics (Hermeneutics)) interpreting interpreting scriptural texts scriptural texts Nyaya Nyaya (Gautama) (Gautama) (Epistemology, logic) (Epistemology, logic) philosophy of  philosophy of  knowledge knowledge including logic including logic Vaisesika Vaisesika (Kanada) (Kanada) (Metaphysics (Metaphysics)) philosophy of  philosophy of  existence existence  Yoga  Yoga (Patanjali) (Patanjali) (Sadhana) (Sadhana) Sankhya Sankhya (Atheist Kapila) (Atheist Kapila) (Metaphysics) (Metaphysics) Dharma Sastras Dharma Sastras including including

Manu-samhita and others

samhita and others

18 Major  18 Major  18 Minor  18 Minor  Samhitas Samhitas mantras mantras Brahmanas Brahmanas ritual explanation ritual explanation of mantras of mantras Aranyakas Aranyakas esoteric explanation esoteric explanation of mantras of mantras Upanisads Upanisads Jnana-kanda Jnana-kanda philosophy of Brahman philosophy of Brahman Kalpa Kalpa ritual details ritual details Siksa Siksa pronunciation pronunciation Vyakarana Vyakarana grammar  grammar  Nirukta Nirukta etymology etymology Chandas Chandas meters meters Jyotisa Jyotisa astronomy-time astronomy-time calculation calculation Vaisnava Vaisnava worship worship Tamasic Tamasic Sattvic Sattvic

Vedic Mathematics

Vedic Mathematics

Srauta Srauta Sutras Sutras Smarta Smarta Sutras Sutras Shulba Shulba Sutras Sutras

““Shulba

Shulba Sutras” is the name given to those portions or

Sutras” is the name given to those portions or

supplement

supplements of the

s of the Kalpasutras, whic

Kalpasutras, which deal

h deal with the

with the

measurem

measurement and construction of

ent and construction of the different altars

the different altars

or arenas for religious rites.

(7)

In order to help the pupil to memorize the material studied and assimilated, they

made it a general rule of practice to write even the most technical and abstruse

textbooks in sutras or in verse (which is so much easier-even for the children-to

memorize). And this is why we find not only theological, philosophical, medical,

astronomical, and other such treatises, but even huge dictionaries in Sanskrit

verse! So from this standpoint, they used verse, sutras and codes for lightening

the burden and facilitating the work (by versifying scientific and even

mathematical material in a readily assimilatable form)!

(8)

Translation

: Lord anointed with the yogurt of the milkmaids’

worship (Krishna), O savior of the fallen, master of Shiva,

please protect me.

(9)

Ref.

“Vedic Mathematics and the Spiritual Dimension” by B.B. Visnu Swami 

Spiritually advanced cultures were not ignorant of the principles of mathematics,

but they saw no necessity to explore those principles beyond that which was

helpful in the advancement of God realization. Intoxicated by the gross power

inherent in mathematical principles, later civilizations, succumbing to the

all-inviting arms of illusion, employed these principles and further explored them in

an attempt to conquer nature. The folly of this, as demonstrated in modern

society today, points to the fact that

“wisdom” is more than the exercise of

intelligence. Modern man's worship of intelligence blinds him from the obvious:

the superiority of love over reason.

(10)

Composed by sages

Wordingmaychange from age to age Revealed Absolute Truth

Every word unchanged eternally 

Rajasic

VEDIC KNOWLEDGE

SRUTI

 

SMRTI

UPAVEDAS Dhanurveda  Ayurveda, Gandharvaveda, Sthapatyaveda VEDAS Rg, Yajur, Sama, Atharva

VEDANGAS   Puranas Itihasas Six Darshanas

Tantras Spoken by Lord Siva to Parvati Ritual Sutras Connected to Kalpa-vedanga Pancaratras Srauta Sutras explains public yajnas Grhya Sutras explains home yajnas Dharma Sutras Law books Vedanta (Vyasa) (Metaphysics) theology of  Upanisads Mimamsa (Jaimini) (Hermeneutics) interpreting scriptural texts Nyaya (Gautama) (Epistemology, logic) philosophy of  knowledge including logic Vaisesika (Kanada) (Metaphysics) philosophy of  existence  Yoga (Patanjali) (Sadhana) Sankhya (Atheist Kapila) (Metaphysics) Dharma Sastras including Manu-samhita and others

18 Major  18 Minor  Samhitas mantras Brahmanas ritual explanation of mantras Aranyakas esoteric explanation of mantras Upanisads Jnana-kanda philosophy of Brahman Kalpa ritual details Siksa pronunciation Vyakarana grammar  Nirukta etymology Chandas meters Jyotisa astronomy-time calculation Vaisnava worship Tamasic Sattvic

Vedanta

Sutra

Srimad

Bhagavatam

(11)
(12)

Double the number.

Pick a number.

Add 10.

Divide by 2.

(13)

Reverse the digits and subtract it from the

first number.

Write down a 3-digit number where digits

are in decreasing order.

Reverse the digits of the result and add it

to the result.

(14)
(15)

Digit

Cube

1

1

2

8

3

27

4

64

5

125

6

216

7

343

8

512

9

729

10

1000

(16)

Digit

Cube

Last digit

1

1

1

2

8

8

3

27

7

4

64

4

5

125

5

6

216

6

7

343

3

8

512

2

9

729

9

10

1000

0

(17)

389017

3

7

(18)

175616

704969

970299

238328

103823

39304

10648

Exercises

(19)
(20)
(21)

4

5

4

5

X

25

20

(22)

4

2

4

8

X

16

20

(23)

(10a + b)(10a + c)

= 100a(a + 1) + bc

(24)

Exercises

Set 4 in the handout.

(25)
(26)
(27)

Digit

Square

Last digit

1

1

1

2

4

4

3

9

9

4

16

6

5

25

5

6

36

6

7

49

9

8

64

4

9

81

1

10

100

0

(28)

7396

6

8

(29)

784

1296

1849

2809

4761

5041

8649

Exercises

(30)

What’re the two kinds of approaches

(31)
(32)

nikhilam navatas caramam dasatah

(33)

4 2 3 5 7 2 7

5 7 6 4 2 7 3

(34)

9

2

X

9

6

8

4

8

8

3

2

(35)

-(x ± a) -(x ± b)

= x(x ± a ± b) ± ab

(36)

1

0

2

X

9

6

2

4

9

8

0

8

+

-9

2

9

7

-1

(37)

Exercises

Set 1 in the handout.

(38)

anurupyena

(39)

6

3

X

4

5

3

15

4

8

5

+

-Base = 60 = 6 X 10

4

6 X

2

8

8

-5

5

2

8

3

5

Proportionately

(40)

6

3

X

4

5

23

5

6

8

5

+

+

Base = 40 = 4 X 10

11

4 X

2

7

2

+11

5

2

8

3

5

Proportionately

(41)

6

3

X

4

5

13

5

5

8

5

+

-Base = 50 = 5 X 10

6

5 X

2

9

0

-7

5

2

8

3

5

Proportionately

(42)

6

3

X

4

5

1

3

5

5

8

6

5

+

-Base = 50 = 100/2

2 )

2

9

-1

3

5

2

8

3

5

Proportionately

(43)

Exercises

Set 2 in the handout.

(44)

Yavadunam tavadunikrtya varga ca yojayet

“Whatever the extent of its deficit or surplus, subtract or

add still further to that extent respectively”

(45)

9

2

X

9

2

8

8

8

4

6

4

-Base = 100

Surplus and Deficit squares

(46)

2

9

X

2

9

1

1

2

8

1

-Base = 30 = 10 X 3

Surplus and Deficit + Proportionately

3X

(47)

a

2

= (a + b)(a

 –

b) + b

2

(48)

Exercises

Set 3 in the handout.

(49)

Why are there seeming contradictions

across different approaches to spirituality?

(50)

Urdhva tiryagbhyam

(51)

7

8

5

X

3

6

2

21

6

7

6

0

6

7

4

1

Vertically and cross-wise

28

4

1

7

0

Need second row

when computing

left to right

(52)

1

2

112 X 99

Multiplying by all 9’s

1

2

-+1

1

2

1

1

0

8

8

(53)

Exercises

Set 5 and 6 in the handout.

References

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