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4 Frailties: Karana-patava, Pramada, Bhrama,
Vipralipsa.
Vedic Knowledge,
Vedanta Sutra,
Srimad Bhagavatam,
Cubic roots,
Exercises,
Where did Vedas come from?
Squares,
What’s the goal of Vedas?
Square roots,
What’re the two kinds of approaches enjoined in the Vedas?
Multiplication techniques,
Proportionately,
Surplus and Deficit squares,
Surplus and Deficit + Proportionately,
Why are there seeming contradictions across different approaches to spirituality?
Vertically and cross-wise.
1.
The Secret of High-speed
mental computations
Vedic Vision
2.
“There are things which seem incredible to
most men who have not studied
mathematics.” – Archimedes.
“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
– Vedic Mathematics and the Spiritual Dimension.
3.
4 frailties
We have imperfect senses. Karana-patava
We fall into illusion. pramada
We make mistakes. bhrama
We have cheating propensities. vipralipsa
Descending Vedic knowledge Perfect
[CC Adi 2.86, CC Adi 7.107]
4.
VEDIC KNOWLEDGE
Revealed Absolute Truth Composed by sages
Every word unchanged eternally SRUTI SMRTI Wording may change from age to age
VEDAS UPAVEDAS Ritual Sutras Tantras
Rg, Yajur, Dhanurveda VEDANGAS Connected to Spoken by Lord Pancaratras Puranas Itihasas Six Darshanas
Sama, Atharva Ayurveda, Kalpa-vedanga Siva to Parvati
Gandharvaveda,
Sthapatyaveda
Smarta
Sutras
Srauta Sutras Vaisnava
Samhitas Kalpa
explains 18 Major
mantras ritual details worship
public yajnas
Srauta
Brahmanas Sutras Grhya Sutras
Siksa
ritual explanation
pronunciation
explains 18 Minor
of mantras home yajnas Tamasic
Aranyakas Sulba
Vyakarana Dharma Sutras
esoteric explanation
grammar Sutras Law books
of mantras Rajasic
Upanisads Nirukta
Jnana-kanda
etymology Dharma Sastras
philosophy of Brahman including Manu- Sattvic
samhita and others
Chandas
meters
Jyotisa Vedanta Mimamsa Nyaya Vaisesika
astronomy-time (Gautama)
(Vyasa) (Jaimini) (Kanada) Yoga Sankhya
calculation (Epistemology, logic)
(Metaphysics) (Hermeneutics) (Metaphysics) (Patanjali) (Atheist Kapila)
philosophy of
theology of interpreting philosophy of (Sadhana) (Metaphysics)
knowledge
Upanisads scriptural texts existence
including logic
Vedic Mathematics
sisters sisters sisters
5.
VEDIC KNOWLEDGE
Revealed Absolute Truth Composed by sages
Every word unchanged eternally SRUTI SMRTI Wording may change from age to age
VEDAS UPAVEDAS Ritual Sutras Tantras
Rg, Yajur, Dhanurveda VEDANGAS Connected to Spoken by Lord Pancaratras Puranas Itihasas Six Darshanas
Sama, Atharva Ayurveda, Kalpa-vedanga Siva to Parvati
Gandharvaveda,
Sthapatyaveda
Smarta
Sutras
Srauta Sutras Vaisnava
Samhitas Kalpa
explains 18 Major
mantras ritual details worship
public yajnas
Srauta
Brahmanas Sutras Grhya Sutras
Siksa
ritual explanation
pronunciation
explains 18 Minor
of mantras home yajnas Tamasic
Aranyakas Shulba
Vyakarana Dharma Sutras
esoteric explanation
grammar Sutras Law books
of mantras Rajasic
Upanisads Nirukta
Jnana-kanda
etymology Dharma Sastras
philosophy of Brahman
“Shulba Sutras” is the name
including Manu-
samhita and others given Sattvic
to those portions or
supplements
Chandas
meters
of the Kalpasutras, which deal with the
measurement
Jyotisa
and construction of the Nyaya
different altars
Vedanta Mimamsa Vaisesika
or arenas
calculation for religious
astronomy-time
rites.(Hermeneutics) (Epistemology, logic) (Metaphysics)
(Vyasa)
(Metaphysics)
(Jaimini)
(Gautama)
(Kanada) Yoga
(Patanjali)
Sankhya
(Atheist Kapila)
philosophy of
theology of interpreting philosophy of (Sadhana) (Metaphysics)
knowledge
Upanisads scriptural texts existence
including logic
Vedic Mathematics
sisters sisters sisters
6.
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)!
Ref. “Vedic Mathematics” by Bharati Krishna Tirtha Maharaja
7.
Translation: Lord anointed with the yogurt of the milkmaids’
worship (Krishna), O savior of the fallen, master of Shiva,
please protect me.
∏ = 3.1415926535897932384626433832792
8.
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.
Ref. “Vedic Mathematics and the Spiritual Dimension” by B.B. Visnu Swami
9.
VEDIC KNOWLEDGE
Revealed Absolute Truth Composed by sages
Every word unchanged eternally SRUTI SMRTI Wording may change from age to age
VEDAS
Rg, Yajur,
UPAVEDAS
VEDANGAS
Vedanta
Ritual Sutras
Connected to
Tantras
Spoken by Lord Pancaratras Puranas Itihasas Six Darshanas
Dhanurveda
Sama, Atharva Ayurveda,
Gandharvaveda,
Sthapatyaveda
Sutra
Kalpa-vedanga Siva to Parvati
Srauta Sutras Vaisnava
Samhitas Kalpa
explains 18 Major
mantras ritual details worship
public yajnas
Brahmanas Grhya Sutras
Siksa
ritual explanation
pronunciation
explains 18 Minor
of mantras home yajnas Tamasic
Aranyakas
Vyakarana Dharma Sutras
esoteric explanation
grammar Law books
of mantras
Upanisads
Jnana-kanda
Nirukta
Srimad Dharma Sastras
Rajasic
etymology
philosophy of Brahman
Chandas
Bhagavatamincluding Manu-
samhita and others
Sattvic
meters
Jyotisa Vedanta Mimamsa Nyaya Vaisesika
astronomy-time (Gautama)
(Vyasa) (Jaimini) (Kanada) Yoga Sankhya
calculation (Epistemology, logic)
(Metaphysics) (Hermeneutics) (Metaphysics) (Patanjali) (Atheist Kapila)
The ripened fruit of all Vedic literatures
theology of interpreting
philosophy of
knowledge
philosophy of (Sadhana) (Metaphysics)
Upanisads scriptural texts existence
including logic
sisters sisters sisters
11.
Pick a number.
Double the number.
Add 10.
Divide by 2.
Subtract original number.
12.
Write down a 3-digit number where digits
are in decreasing order.
Reverse the digits and subtract it from the
first number.
Reverse the digits of the result and add it
to the result.
14.
Digit Cube
1 1
2 8
3 27
4 64
5 125
6 216
7 343
8 512
9 729
10 1000
15.
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.
Exercises
175616 238328
704969 103823
970299 39304
10648
18.
Where did Vedas come from?
22.
How does it work?
(10a + b)(10a + c)
= 100a(a + 1) + bc
23.
Exercises
Set 4 in the handout.
24.
What’s the goal of Vedas?
26.
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.
Exercises
784 2809
1296 4761
1849 5041
8649
29.
What’re the two kinds of approaches
enjoined in the Vedas?
30.
Multiplication techniques
31.
nikhilam navatas caramam dasatah
“All from 9, the last from 10”
32.
All from 9, the last from 10
4 2 3 5 7 2 7
5 7 6 4 2 7 3
33.
9 2 - 8
X 9 6 - 4
8 8 3 2
34.
How does it work?
(x ± a) (x ± b)
= x(x ± a ± b) ± ab
35.
All from 9, the last from 10
1 0 2 + 2
X 9 6 - 4
9 8 -1 0 8
9 7 9 2
36.
Exercises
Set 1 in the handout.
38.
Proportionately
Base = 60 = 6 X 10
6 3 + 3
X 4 5 - 15
6X 4 8 4 5
2 8 8 -5 5
2 8 3 5
39.
Proportionately
Base = 40 = 4 X 10
6 3 + 23
X 4 5 + 5
4X 6 8 11 5
2 7 2 +11 5
2 8 3 5
40.
Proportionately
Base = 50 = 5 X 10
6 3 + 13
X 4 5 - 5
5X 5 8 6 5
2 9 0 -7 5
2 8 3 5
41.
Proportionately
Base = 50 = 100/2
6 3 + 1 3
X 4 5 - 5
2) 5 8 6 5
2 9 -1 3 5
2 8 3 5
42.
Exercises
Set 2 in the handout.
43.
Yavadunam tavadunikrtya varga ca yojayet
“Whatever the extent of its deficit or surplus, subtract or
add still further to that extent respectively”
44.
Surplus and Deficit squares
Base = 100
9 2 - 8
X 9 2 - 8
8 4 6 4
45.
Surplus and Deficit + Proportionately
Base = 30 = 10 X 3
2 9 - 1
X 2 9 - 1
3X 2 8 1
8 4 1
46.
How does it work?
= (a + b)(a – b) + b2
47.
Exercises
Set 3 in the handout.
48.
Why are there seeming contradictions
across different approaches to spirituality?
49.
Urdhva tiryagbhyam
“vertically and cross-wise”
50.
Vertically and cross-wise
7 8 5
X 3 6 2
21 6 7 6 0
Need second row
6 7 4 1 when computing
left to right
28 4 1 7 0
Vinculum can be used to ease the process
51.
Multiplying by all 9’s
112 X 99
1 1 2
- 2 1 2
1 1 0 8 8
52.
Exercises
Set 5 and 6 in the handout.
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