VISVESVARAYA TECHNOLOGICAL UNIVERSITY

Jnana Sangama, Belgaum-590018

EXPERIENTIAL LEARNING REPORT ON

“INDIAN KNOWLEDGE SYSTEM”

Submitted in Partial fulfillment of the Requirements for the VI Semester of the Degree of

Bachelor of Engineering
in
Electronics and Communication
Engineering
By

AMULYA S RAO (1CR22EC016)

ANJANEYA BASAVARAJ GUGGARI (1CR22EC018)
ANURAG (1CR22EC019)
ANUSHREE J(1CR22EC020)

DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING

CMR INSTITUTE OF TECHNOLOGY

#132, AECS LAYOUT, IT PARK ROAD, KUNDALAHALLI, BANGALORE-560037

 CMR INSTITUTE OF TECHNOLOGY
#132, AECS LAYOUT, IT PARK ROAD, KUNDALAHALLI, BANGALORE-560037
DEPARTMENT OF ELECTRONICS AND COMMUNICATIONENGINEERING

CERTIFICATE

Certified that the experiential report on “INDIAN KNOWLEDGE SYSTEM” carried out by Ms.
Amulya S Rao, Mr. Anjaneya Basavaraj Guggari, Mr. Anurag, Ms. Anushree J bearing USN
1CR22EC016, 1CR22EC018, 1CR22EC019, 1CR22EC020, Bonafide student of CMR Institute of
Technology, Bengaluru in partial fulfillment for the award of Bachelor of Engineering in
Electronics and Communication Engineering of the Visvesvaraya Technological University,
Belagavi-590018 during the academic year 2024-2025.

The project report has been approved as it satisfies the academic requirements in respect of activity
prescribed for the said degree.

Dr. Eisha Akanksha Dr. Pappa M

Associate Professor Head Of Department
Dept. of ECE Dept. of ECE
CMRIT Bengaluru CMRIT Bengaluru

ii
 DECLARATION

We, the students of Electronics Of Communication Engineering, CMR Institute of

Technology, Bangalore declare that the work related to “Experiential Learning” has been
successfully completed under self-paced learning, Electronics Of Communication
Engineering Department, CMR Institute of technology, Bangalore. This dissertation work
is submitted in partial fulfillment of the requirements for the award of Degree of Bachelor
of Engineering in Electronics Of Communication Engineering during the academic year
2024 - 2025.

Place: Bengaluru, Karnataka

Date: 29-05-2025

Team members: Signature

AMULYA S RAO (1CR22EC016)

ANJANEYA BASAVARAJ GUGGARI (1CR22EC018)
ANURAG (1CR22EC019)
ANUSHREE J(1CR22EC020)

I
Module 2: Traditional Knowledge in Humanities and
Sciences

1CR22EC016[Amulya S Rao]

Q4) Analyze the contributions of ancient Indian scholars to

mathematics and astronomy. Highlight key concepts
introduced in these fields.

MATHEMATICS

Introduction:

Ancient India made many important contributions to the world of mathematics. Long before
modern times, Indian scholars developed new ideas that helped shape how we understand and
use math today. Their work was used in areas like astronomy, trade, and building construction.

This report looks at the achievements of famous Indian mathematicians such as Āryabhaṭa,
Brahmagupta, and Bhāskara II. They introduced key concepts like the use of zero, the decimal
number system, algebra, and basic trigonometry. Many of these ideas were discovered in India
long before they were known in other parts of the world.

By studying these early contributions, we can better understand the important role ancient India
played in the development of mathematics.

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Unique aspects of Indian Mathematics :

Indian mathematics has several unique features that set it apart from other ancient mathematical
traditions. One of the most remarkable contributions is the invention of zero as a number and the
development of the decimal place-value system, which allowed for more efficient calculations
and number representation. Indian mathematicians also integrated mathematics closely with
astronomy, using it to predict eclipses and planetary movements with impressive accuracy.
Unlike other cultures that focused on specific problems, Indian scholars emphasized general
methods and rules, often expressed in the form of Sanskrit verses, making complex concepts
easier to memorize and share. Another unique aspect was the early development of ideas similar
to calculus, especially in Bhāskara II’s work on motion and change. Additionally, the logical and
structured format of Indian mathematical texts—starting from definitions to rules, examples, and
proofs—shows a high level of organization that resembles modern mathematical writing.

Great Mathematicians and their Contributions:

Mathematician Period Key Contributions

Aryabhata 476–550 CE Approximation of π, place value system, zero

concept, Aryabhata’s algorithm

Brahmagupta 598–668 CE Rules for zero & negative numbers, quadratic

equations, Brahmagupta’s formula for cyclic
quadrilaterals

Bhaskara I 600–680 CE Approximation of sine function, improvements in

place value system

Bhaskara II 1114–1185 CE Early calculus, solutions of algebraic equations,

(Bhaskaracharya) Lilavati, Siddhanta Shiromani

III
 Madhava of 1340–1425 CE Infinite series expansions, early calculus concepts,
Sangamagrama Madhava-Leibniz series for π

Pingala circa 3rd–1st Binary numeral system, combinatorics, prosody

century BCE

Srinivasa Ramanujan 1887–1920 Infinite series, partition theory, modular forms,

original theorems & conjectures

Harish-Chandra 1923–1983 Representation theory, harmonic analysis on Lie

groups

C. R. Rao Born 1920 Statistical theory, Cramér-Rao inequality, Rao-

Blackwell theorem

fig: Great Mathematicians and their Contributions:

This table highlights the brilliance and lasting impact of ancient Indian mathematicians whose
ideas were far ahead of their time. Their works laid the groundwork for many concepts used in
modern mathematics and inspired scholars across the world. These contributions remain a source
of pride and a testament to India’s rich scientific heritage.

Key Concepts Introduced:

1. Zero as a Number

One of the most groundbreaking ideas from ancient Indian mathematics is the concept of zero as
a number, not just a placeholder. Brahmagupta was the first to define arithmetic operations
involving zero, such as addition, subtraction, and multiplication. This concept was revolutionary
and later became the cornerstone of modern mathematics and computing systems.

2. Decimal Place-Value System

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Indian mathematicians were pioneers of the decimal place-value system, where the value of a
digit depends on its position in the number. This system allowed the use of digits from 0 to 9 to
represent any number, simplifying calculations and record-keeping. It replaced older, more
complex number systems used in other civilizations.

3. Algebra

India made major contributions to the development of algebra. Mathematicians like

Brahmagupta and Bhāskara II worked on solving linear and quadratic equations, and also
introduced the use of negative numbers and variables. Their texts included general methods
(sutras) for solving algebraic problems, laying the foundation for symbolic algebra.

4. Trigonometry

The science of trigonometry was well developed in ancient India. Āryabhaṭa introduced the sine
function (called jya) and produced accurate sine tables. Indian scholars later extended this work
with functions similar to cosine and tangent, which played a crucial role in astronomical
calculations.

5. Geometry

In geometry, Indian mathematicians studied shapes, symmetry, angles, and the properties of
triangles and quadrilaterals. They were particularly interested in geometric problems related to
construction, altars, and astronomy. Bhāskara II also explored the geometry of cyclic
quadrilaterals, contributing significantly to the understanding of plane geometry.

6. Early Ideas of Calculus

Centuries before calculus was formalized in Europe, Indian scholars like Bhāskara II and
Madhava of Sangamagrama explored related ideas. Bhāskara II discussed concepts of
instantaneous motion and rate of change, while Madhava developed infinite series expansions for
sine and cosine functions. These were early forms of differential and integral calculus, showing a
deep understanding of mathematical change.

V
Pictures:

Fig: Aryabhata

VI
ASTRONOMY

Introduction:
We are all fascinated by the sky above, right from our childhood. The stars, sun, moon,
meteors, phenomena such as sunrise, sunset, monsoon rains, days getting longer and shorter in a
year, and so on, trigger several questions in our mind. Astronomy is a branch of science that
studies celestial objects, space, and the physical universe as a whole using concepts mainly from
Mathematics. It has been a branch of study right from pre-historic times. All ancient civilizations
have made a methodical observation of the night sky and developed their understanding of the
celestial phenomena. Intense observation of the patterns in the sky using some instruments
designed for this purpose has contributed to a better understanding of astronomy.

Unique aspects of Indian Astronomy :

Knowledge of astronomy was widely used by all sections of Indian society, not just by the
subject matter experts. Villagers, farmers, arts, and craftsmen and householders would know the
meaning of Rasi (Zodiac Sign), Nakṣatra (Star), and months of the calendar, and certain details
about every day (Pañcānga). They developed some understanding of how seasons are formed, as
seasonal changes affect economic activities such as farming, and the general health of
individuals. There are cultural-religious aspects too. In India, it is a common tradition for the
newly married couple to be shown the pair of stars known as Vasistha and Arundhati
(corresponding to the visual binary system in the constellation of 'Ursa Major') as part of the
marriage ceremony by the priest or the family elders. The celestial binary is held up as a model
for the married life of the couple.

VII
Historical Development of Astronomy in India:

Astronomy in India has deep roots, evolving as a vital discipline driven by practical, spiritual,
and economic needs. Vedic rituals required precise timekeeping and knowledge of cardinal
directions for altar placements. Agriculture, the backbone of the economy, depended on accurate
seasonal predictions, while maritime trade required understanding of celestial navigation using
constellations.

These needs led to the development of the Pañcāṅga (Indian calendar system), a sophisticated
and accurate timekeeping method still in use today. References to stars, planets, and comets
appear as early as the Atharvaveda-samhita. Texts like Parāśara-tantra (2nd millennium BCE)
provide detailed planetary observations, showcasing India’s long-standing tradition of systematic
astronomical study.

Indian astronomy evolved further with the Vedāṅga Jyotiṣa, which introduced the concept of
Yuga to align solar and lunar calendars. Ancient texts also documented planetary motions and
comets. Modern simulations suggest Vedic references to celestial events, like the Kṛttikā
(Pleiades), date back to around 3000 BCE.

The Ṛgveda and Atharvaveda list constellations and explore cosmology, including theories on
the origin of the universe (Nāsadīya-sūkta). Epics like the Rāmāyaṇa and Mahābhārata reflect
deep knowledge of celestial movements.

Jain literature also contributed, with texts like Tattvārthādhigama-sūtra discussing cosmology
and astronomy. Jain scholar Jyotiṣīsāgara authored a detailed four-chapter work on the subject in
238 CE.

No. Vedic Reference Statement Date

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 1 Śatapatha-brāhmaṇa Kṛttikā (Pleiades) never swerve from the east. 2950
(2.1.2.3) BCE

2 Maitrāyaṇīya-brāhmaṇa Winter solstice at the mid-point of the Śraviṣṭhā 1660

Upaniṣad (6.14) segment and the summer solstice at the beginning of BCE
Māgha.

3 Vedāṅga-jyotiṣa Winter solstice at the beginning of Śraviṣṭhā and the 1300

summer solstice at the mid-point of Āśleṣā. BCE

4 Taittirīya-āraṇyaka Abhaya Dhruva (currently identified as alpha-Draconis) 2800

(II.19.1) in the Śiṁśumāra Constellation is the pole star. BCE*

Fig: Astronomy References in Vedic Texts and Their Dating

By the 5th century CE, Indian astronomy saw a significant shift with the development of
Siddhānta texts. These works adopted advanced mathematical methods and incorporated
planetary systems and coordinate-based models.

Āryabhaṭa’s Āryabhaṭīya (499 CE) is the earliest comprehensive text on mathematical astronomy
in India. Varāhamihira (~530 CE), in his Pañca-siddhāntikā, described five major schools of
astronomy, including the Romaka and Sāura Siddhāntas, which tackled lunar and solar motions
and planetary movements.

Later, in 1504 CE, Nilakaṇṭha Somayāji’s Jyotirmīmāṁsā emphasized observational accuracy

and introduced a planetary model where planets orbited the Sun, which itself moved around the
Earth—a geocentric-heliocentric hybrid model close to modern frameworks.

IX
Indian Astronomers and Their Seminal Contributions:

Sl. Details of the Work / Period, Location Salient Contributions

No. Mathematician

1 Author not known – Prior to 6th Several versions exist. An ancient version
Sūrya-siddhānta century CE is summarized in Varāhamihira’s
Pañcasiddhāntikā. A modern version is
still used by traditional scholars and
calendar makers.

2 Varāhamihira – 6th century CE Presents an updated summary of five

Pañca-siddhāntikā ancient siddhāntas.

3 Āryabhaṭa – Born 476 CE; Includes mathematics, trigonometry (sine

Āryabhaṭīya Kusumapura, function), Earth’s rotation, and precise
near Pataliputra, planetary algorithms; discusses Earth's
Bihar position in cosmos and eclipses.

4 Bhāskara I – 7th century CE Commentaries on Āryabhaṭīya with

Āryabhaṭīya-bhāṣya, detailed explanations; developed the
Mahā-bhāskarīya Āryabhaṭan system further.

5 Brahmagupta – 7th century CE Comprehensive system for solar and

Brāhmasphuṭa- lunar calculations; introduced major
siddhānta, mathematical breakthroughs such as
Khaṇḍakhādyaka vargaprakṛti (quadratic indeterminate
equations) and cyclic quadrilaterals;
Khaṇḍakhādyaka was a manual.

6 Lalla – 8th–9th century Expanded on Āryabhaṭan system with

Śiṣyadhīvṛddhida- CE new algorithms.
tantra

X
7 Mañjūlācārya – 10th century CE Provided formulas for the second
Laghumañjasa correction of the Moon’s longitude;
derivatives for instantaneous velocities of
the Sun and Moon.

8 Śrīpati – Siddhānta-śekhara 11th century CE An important text

quoted by later
astronomers.

9 Bhāskarācārya II – Siddhānta-śiromaṇi, Born 1114 CE Standardized many

Vāsanābhāṣya, Karaṇakutūhala calculations and
algorithms in Indian
astronomy; rectified
mistakes, made
generalizations;
provided a
calculation manual
with ready-made
tables and
arithmetical
simplifications.

10 Kerala SchoolMādhava of Saṅgamag rāma 14th–19th Major contributions

– Veṇvāroha, Century1340– in mathematical
SphuṭacandrapātiParameśvara of 1425 CE1360– analysis, including
Vaṭasseri – Dṛgganita, Bhaṭadīpikā, 1455 CE1444– infinite series for π,
Siddhānta-dīpikāNilakaṇṭha Somayājī or 1550 CE1500– sine and cosine
Somasutvan of Trikkantiyur – Tantra- 1610 CE16th functions (ahead of
saṅgraha, Āryabhaṭīya-bhāṣyaJyeṣṭhadeva century CE19th Europe); major
– Gaṇita-yuktibhāṣāAcyuta Pisaroti – century CE revisions of planetary
SphuṭanirṇayatantraŚaṅkaravarman – theories around 1500
Sadratnamālā CE; innovations in
astronomical
computations;
systematic

XI
 application of
spherical
trigonometry;
improved eclipse
theory.

11 Gaṇeśa Daivajña – Grahalāghava Born 1507 CE Developed simplified

procedures for
calculating planetary
positions; his work is
still used in almanac
and Pañcāṅga
preparation.

12 Kamalākara – Siddhānta-tattva-viveka Born 1616 CE Produced elaborate

works on Indian
astronomical
concepts and
parameters, while
also incorporating
elements from
Ptolemy’s system.

13 Candraśekhara Sāmanta – Siddhānta- Born 1835 CE Introduced key

darpaṇa modifications in
planetary parameters;
revised lunar theory;
created simple
instruments;
reformed Odisha's
traditional calendar.

14 Raja Sawai Jai Singh – Yantrarāja-racanā, 1688–1743 CE Built famous

Zīj Muhammad Shahi astronomical
observatories across
North India.

Fig: Indian Astronomers and Their Seminal Contributions

XII
Pictures:

XIII
Module 3: Traditional Knowledge in Professional Domains

XIV
 1CR22EC018[Anjaneya Basavaraj Guggari]

Q7) Discuss the principles of sustainable architecture in

ancient Indian town planning. Provide examples of
structures that embody these principles.

Introduction:
Ancient Indian town planning exemplifies a profound understanding of sustainable architecture,
reflecting a harmonious relationship with nature, climate, and community. Rooted in principles
like Vaastu Shastra, climate responsiveness, and resource efficiency, these urban designs
were not merely functional but also ecologically attuned. This report delves into the core
principles of sustainable architecture in ancient Indian town planning, highlighting exemplary
structures that embody these ideals.

Sustainable architecture is not a modern invention—it has deep historical roots, especially in
civilizations that thrived through a deep understanding of natural systems and human needs. One
of the most profound examples of this synergy between architecture and sustainability can be
found in ancient Indian town planning. Long before the advent of industrialization, ancient
Indian architects and urban planners developed cities that were environmentally conscious,
culturally responsive, and functionally efficient.

Ancient Indian cities—ranging from the meticulously laid-out Indus Valley settlements to the
sacred temple towns of South India—were designed based on a set of ecological, spiritual, and
social principles. These included the use of local materials, climate-sensitive design, water
conservation techniques, waste management, and community-centric spaces. Central to this
was the ancient science of Vaastu Shastra, which guided everything from the orientation of
buildings to the layout of streets and the placement of water bodies.

Core Principles of Sustainable Architecture

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1. Integration with Nature and Climate Responsiveness

Ancient Indian cities were meticulously planned to align with natural elements and climatic
conditions. The application of Vaastu Shastra guided the orientation and layout of structures,
ensuring optimal sunlight, ventilation, and energy efficiency. For instance, the use of thick walls
and high ceilings facilitated passive cooling, reducing the need for artificial temperature control.

2. Water Management and Conservation

Given the diverse climatic zones across India, ancient urban planners developed sophisticated
water management systems. Structures like stepwells, reservoirs, and canals were integral to
urban planning, ensuring a sustainable water supply. These systems not only provided water but
also contributed to the cooling of the environment.

3. Use of Local and Natural Materials

Construction materials were sourced locally, minimizing transportation energy and costs.
Materials like mud, stone, and timber were commonly used, which were not only abundant but
also had low embodied energy. This approach ensured that buildings were in harmony with their
surroundings and climate.

4. Zoning and Urban Layout

Ancient Indian towns often followed a grid-based layout, dividing the city into distinct zones for
residential, commercial, and religious purposes. This zoning minimized congestion and
facilitated efficient movement and resource distribution.Exotic India Art

5. Community-Centric Design

Public spaces like temples, markets, and communal wells were central to town planning,
fostering social interaction and community cohesion. These spaces were designed to be
accessible and served multiple purposes, enhancing the quality of urban life.

Exemplary Structures Embodying Sustainable Principles

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1. Mohenjo-daro (Indus Valley Civilization)

Mohenjo-daro, one of the prominent cities of the Indus Valley Civilization, showcases advanced
urban planning. The city featured a grid layout with well-planned drainage systems and public
baths, indicating a high level of sanitation and water management. Buildings were constructed
using fired bricks, ensuring durability and thermal efficiency.

2. Dholavira (Gujarat)

Dholavira is renowned for its sophisticated water conservation systems, including reservoirs and
channels that harnessed seasonal rains. The city's layout comprised three divisions—citadel,
middle town, and lower town—each equipped with wells and open spaces. This strategic
planning facilitated efficient water distribution and community interaction.

3. Rani ki Vav (Patan, Gujarat)

Rani ki Vav is an intricately designed stepwell that served as a water reservoir and a community
gathering space. Its architectural design, with multiple levels and ornate carvings, not only
provided water but also offered passive cooling and aesthetic value. Deming Certification

4. Jaipur (Rajasthan)

Founded in the 18th century, Jaipur was meticulously planned according to Vaastu Shastra. The
city's grid layout, wide streets, and distinct zoning for different activities exemplify sustainable
urban planning. Structures like the Hawa Mahal utilized architectural features to facilitate natural
ventilation and cooling.

5. Khajuraho Temples (Madhya Pradesh)

The Khajuraho temples are architectural marvels that embody sustainable design principles.
Constructed using locally sourced sandstone, the temples' intricate carvings and open courtyards
facilitate natural light and air circulation, reducing the need for artificial lighting and ventilation.

XVII
1. Mohenjo-daro (Indus Valley Civilization)
 Location: Sindh, Pakistan
 Era: Circa 2500 BCE
 Key Features:
o Grid-based city layout with well-planned streets and drainage systems.
o Advanced drainage systems with covered drains and soak pits.
o Use of fired bricks for durable construction.
o Private wells and public baths, indicating sophisticated water management.
 Sustainability Aspects:
o Efficient water management and sanitation systems.
o Climate-responsive design with thick walls for thermal insulation.
o Resource-efficient construction using locally available materials.

2. Dholavira (Gujarat)
 Location: Kutch, Gujarat, India
 Era: Circa 3000 BCE
 Key Features:
o Zoned city layout with distinct sectors for residential, administrative, and
ceremonial purposes.
o Sophisticated water management systems, including reservoirs and channels.
o Use of sun-dried bricks and lime mortar for construction.
 Sustainability Aspects:

XVIII
 o Rainwater harvesting through reservoirs and channels.
o Efficient water distribution to different city sectors.
o Use of local materials minimizing transportation energy.

Conclusion

Sustainable architecture in ancient Indian town planning showcases a profound understanding of

ecological harmony, resource efficiency, and community-centric design—long before modern
sustainability became a global concern. Ancient Indian towns were not only built to last but also
to coexist seamlessly with their natural surroundings. The principles of orientation, ventilation,
water conservation, and the use of local materials reveal a deep-rooted ethos of environmental
consciousness and cultural continuity.

Ancient planners meticulously considered climatic conditions, topography, and socio-cultural

needs while designing cities, ensuring minimal ecological disruption. Cities like Mohenjo-Daro
and Dholavira demonstrate advanced urban planning with effective drainage, water harvesting,
and grid-based layouts, reflecting a high degree of sustainable thinking. The Vastu Shastra and
other traditional texts offered frameworks that aligned human habitation with cosmic and natural
forces—further underscoring the holistic sustainability approach.

Today, revisiting these traditional practices offers valuable insights for contemporary urban
design, especially in the context of climate change, resource scarcity, and the need for resilient
communities.

Sustainable architecture in ancient Indian town planning is a testament to the ingenuity,

foresight, and ecological wisdom of early Indian civilizations. Unlike modern development
trends that often lead to environmental degradation, ancient Indian towns were designed to work
in harmony with nature—not against it. Their design principles were deeply rooted in local
climate responsiveness, resource efficiency, and spiritual-philosophical alignment, as guided by
treatises such as Vastu Shastra, Arthashastra, and Manasara.

These towns were planned with long-term habitability in mind. Techniques like passive cooling,
natural lighting, rainwater harvesting, waste management, and the use of local, renewable
materials (such as stone, lime, mud, and wood) demonstrate a mature understanding of
ecological cycles and sustainable practices. The integration of community spaces, temples, water
bodies, and green belts fostered not just environmental sustainability, but also social and cultural
well-being.

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