Ancient temples Geometry - conference paper prepared on 28th Feb. 2021

National Conference on Ancient Indian Science, Technology, Engineering and Mathematics (AISTEM-2021), 19-20
March, 2021, NITTTR Kolkata, India.
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GEOMETRICAL DESIGN PHILOSOPHY
OF ANCIENT INDIAN TEMPLE AND ITS CONSTRUCTION METHOD
Samirsinh P Parmar
Department of Civil Engineering
Research Scholar, Ph.D. Geotechnical Engineering
Email: samirddu@gmail.com
Prof. Debi Prasad Mishra
Director, NITTTR, Kolkata
ABSTRACT
Each era has a distinctive construction practice which is unique and represents the ideology,
development, art and architecture of particular culture. In this context, the Hindu Temples are
epitome of knowledge, art, architecture, culture and represents the advancement of building science
of the ancient Indian subcontinent. The ideology and tradition of Indian Temple exists not only in
history but also in the present era which provides a sense of flow to traditional Indian values and
also creates a profound impact on the socio-economic life of the people. This paper deals with the
styles, design and geometry, structural system and construction technology of the Indian temples.
The distinctive architectural styles and elements of Hindu Temple are also presented in this paper.
The geometrical design concept which was prevalent in the Indian temple construction are explained
in this paper. The construction technology starting from the selection of the team to planning,
carving and assembling of individual pieces are also detailed in this paper. The relationship between
structure stability and symmetry and proportion of Indian Temples is also presented in this paper
which explains the resistance of Indian Temples against Seismic forces and other environmental
effects.
Keywords: Ancient Indian Temple, Geometry.
1. INTRODUCTION
The Hindu temples known as Mandir in Hindi. The word Mandir was derived from Sanskrit
word “Mandira”. Although the architecture of the Indian temple varies across the India, its basic
element remains the same. The temple in India as an architectural entity, emerged with certain
concepts about God and gods (human beings). They started to develop somewhere around 4500
years ago during the mature phase of Indus-Saraswati or Harappan Civilization (2600-2000 BCE).
The temples in these periods were open air shrines kept under sacred trees or near water bodies
which changed with the onset of Mahajanapada period (700 BCE). In this period, the concept of
temple as closed structure gained prominence with the ordinary thatched huts of the villages of
Northern India in the period between 700 to 500 BCE providing an early model for the temple
builders. The multistoried temples began to be constructed in the Sunga- Kusana period (200 BCE-
200 CE). In 320 CE, the Gupta empire was established and the concept of Duality in Bhakti- the god
and the devotee, the former being the most sacred entity, gained prominence. And due to this
concept, two spaces were provided in the temple, one for the God (garbha-griha) and one for the
devotees (Mandapa). An early example of such an arrangement is Sanchi Buddhist temple. The
limitation to vertical monumentality and height was broken in late fifth and early sixth century in
Gupta period with a second story as well as shikhara or vimana becoming a common feature in
Indian temples. Also, one of the most interesting features of these temples is that they were raised
without the use of mortars. The development of temple architecture or iconography took place
prominently in this period as mythologies and deities were translated in stone and became orating
the entities of the temple structure. Up to the fifth century, there was a unilinear development in the
temple architecture but with the onset of seventh century, the temple construction took a turn for

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regionalization. The North Indian or the Nagara style adopted a curvilinear shikhara ending with a
pointed finial at the top whereas the south Indian or Dravida style developed stepped vimana ending
in a round stupi. In modern times, the temple construction in North India became more confused
whereas the temples of South, Gujrat and Orissa continued following the traditional temple
construction practices.
The Indian temple is a depiction of macrocosm (universe) as well as the microcosm (the inner
space). The idea behind the development of Hindu temple is to link man with the god. Hence, the
temple with all its architecture and decoration and rituals, is a place to get ultimate liberation which
is the guiding philosophy of Hinduism. The Indian temples also act as a place for more intellectual
and artistic development. The temple complex housed schools, hospitals and courts for general
citizen and its spacious halls were used for the recitation of Mahabharata and Ramayana. The
temple maintained its sustenance through the income generated from the cultivable land which was
assigned to it by the king. It also provided livelihood for large number of persons and greatly
influenced the economic life of the community.
The main objective of this paper is to give a comprehensive view on the style, design and geometry,
structural system and construction technology of the Indian temples. The relationship between
structure stability and symmetry and proportion of Indian Temples is also given here which explains
the resistance of Indian Temples against Seismic forces.
2. STEPS IN TEMPLE CONSTRUCTION
1. Bhu pariksha: Examining and choosing location and soil for temple and town. The land should
be fertile and soil suitable.
2. Sila pariksha: Examining and choosing material for image
3. Karshana: Corn or some other crop is grown in the place first and is fed to cows. Then the
location is fit for town/temple construction.
4. Vastu puja: Ritual to propitiate Vaastu devata.
5. Salyodhara: Undesired things like bones are dug out.
6. Adyestaka: Laying down the first stone
7. Nirmana: Then foundation is laid and land is purified by sprinkling water. A pit is dug, water
mixed with navaratnas, navadhanyas, navakhanijas is then put in and pit is filled. Then the
temple is constructed.
8. Murdhestaka sthapana: Placing the top stone over the prakara, gopura etc. This again
involves creating cavities filled with gems minerals seeds etc. and then the pinnacles are placed.
9. Garbhanyasa: A pot made of five metals (pancaloha kalasa sthapana) is installed at the place
of main deity.
10. Sthapana: Then the main deity is installed.
11. Pratistha: The main deity is then charged with life/god-ness.
3. ELEMENTS OF HINDU TEMPLE
The Hindu temples adopted a definite structure in the later half of the 7th century. The common
elements of the Hindu templesin their original Sanskrit terms are as followed :
The main compound of the temple is known as Vimana which comprises of two parts. The top
portion of the Vimana is known as Sikhara and the lower portion which lies inside the Vimana is
called Garbhagriha (cella or inner chamber), see also (Figure 1 (a) & (b))

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1. “Sikhara”refers to the spire or the tower. It is shaped as pyramidical and tapering representing
the mythological
2. “Meru” or the highest mountain peak.
3. “Garbhagriha” refers to the womb chamber which is the innermost chamber of any temple
where the deity resides. It is mainly square in layout and is entered through eastern side.
4. “Pradakshina Patha” refers to the ambulatory passageway for circumambulation and
comprises of enclosed corridor outside the garbhagriha. The devotees walk around the deity
in clockwise direction, paying their respect to the deity.
5. “Mandapa”, is the pillared hall in front of the garbhagriha, used as assembling point by
devotees for chant; rituals meditate or observe the priests perform the rituals.
6. Sometimes, “Natamandira” is also provided in some temples which mean the hall for dancing.
In some early temple structures, the mandapa was isolated and separate structure from the
sanctuary.
7. “Antarala”, refers to the intermediate chamber which joins the main sanctuary and the pillared
hall of the temple premises.
8. “Ardhamandapa”refers to the front porch in the main entrance of the temple which leads to
the main temple Some other essential structural elements found in the Hindu temples are
Mainly found in the south Indian temples.
9. “ Gopurams” are the monumental and ornate entrance to the temple premises.
10. “ Pitha”or the plinths of the main temple.
11. The gateways typical to north Indian temples are,”Toranas”.
Figure-1: Typical Component parts of Hindu temples.
5. ARCHITECTURAL STYLE:
The distinctive architectural styles of the Hindu temples have developed as a result of the wide
geographical, climatic, cultural, racial, historical and linguistic differences between the northern
plains and the southern peninsula of India. Broadly based on geography, the Hindu temples were
divided into three different orders; the Nagara or 'northern' style, the Dravidian or 'southern' style,
and the Vesara or hybrid style that is seen in the Deccan between the other two. Other distinct styles
exist in peripheral areas such as Bengal, Kerala and the Himalayan valleys.

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Table-1. Comparison between Nagara and Dravidian Architecture
Feature Nagara architecture Dravidian architecture
Main temple spire (tower) Sikhara above sanctum
Vimana that may be multistorey
(talas), the top of which is called
the sikhara
Mandapa spire (tower) Yes No
Curvature of the spire
Curvilinear centred over the sanctum, also
straight-edged pyramidal
Straight-edged pyramidal,
sometimes curvilinear centred
over the sanctum[note 2]
Sanctum Single or multi-storey
Typically, single (Vimana may be
multi-storey)
Plan
Mandapa, sanctum and tower plans are
predominantly Chaturasra (square);
uncommon: Ashtasra, Vritta, Ayatasra, Ayata
Ashtasra, Ayata Vritta, Hasti
Prishta, Dwayasra Vrita
same, plus Prana Vikara
Gopuram Not a prominent feature
Characteristic, but not essential;
after 10th century often higher
than the vimana. May be several,
on all sides of the compound,
serving as landmarks for pilgrims
Other features
sacred pools, fewer pillared mandapas in
temple grounds (separate dharmashala),
prakara walls rare (e.g., Odisha after 14th
century), single or multiple entrances into
temple
sacred pools, many pillared
mandapas in temple grounds
(used for rites of passage
ceremonies,temple rituals),
prakara walls became common
after 14th century, single or
multiple entrances into temple
Major sub-styles Latina, Phamsana, Sekhari, Valabhi
Tamil (upper and lower
Dravidadesa), Karnata, Andhra
Geography
northern, western and central of the Indian
subcontinent
southern parts of the Indian
subcontinent, southeast Asia
Chronology of surviving
stone-masonry monuments
Late Kushana era, early Gupta: rudimentary
archaic; 6th-10th century: zenith
Late Gupta era: rudimentary; 6th-
10th century: zenith
*Reproduced after: Madhusudan A. Dhaky, Vinayak Bharne & Krupali Krusche 2014.
7. THE GEOMETRY OF HINDU TEMPLE
The geometry of Vastupurashamandala in which the form of Purasha was made to fit the abstract
idea of square as the highest geometric form. The basic form of Vastupurashamandala is the square
which represents the earth and the circle represents the universe suggesting timelessness and infinity
(see Figure-8). The mandala is actually a square divided into smaller squares arranged in the form of
a grid. Each smaller square depicts the area of the respective Gods. The most commonly used
mandala is the square subdivided into 64 and 81 squares. Thus, the Vastupurashamandala was the
basis of the ground floor plan for all Hindu temples. The basic shape of the temple plan was: the
outermost ring of square of the mandala from thickness of walls of main shrine, the central 4 squares
was reserved for the main deity, the inner ring of 12 square form the walls of the garbhagriha and
the next 16 to 28 forms the “pradkshina patha”. These simple divisions of square with permutation
and combination became the base for the development of more complex temple compound.

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Figure-2: The image of Vastupurushamandala with 64 blocks for different deities
8. FRACTLE GEOMETRY OF TEMPLES:
The sanatana Vedanta philosophy was described in ancient shani mantra, which is depicted below:
This Purnam Shanti mantra (पूर्णं शान्ति मंत्र) is from Isha Upanishad and is one of the main beliefs of
the Sanatana dharma.
ॐ पूर्णणमदः पूर्णणममदं पूर्णाणत्पुर्णणमुदच्यते
पूर्णणस्य पूर्णणमादाय पूर्णणमेवावमशष्यते ॥
ॐ शान्तिः शान्तिः शान्तिः ॥
The meaning of shloka is, “Supreme Being (Parmatma) is complete. It doesn’t depend on any
external agency for anything. Our Atman is a fragment of this infinite Supreme Being; hence our
Atman is also complete and has the same characteristics as those of Parmatma. Our Atman is a
replica of the Parmatma. The Supreme Being is infinite (अनंत). Hence, when a small fragment is
taken out of it, it still remains complete.”
According to the ancient Indian Sankhya School of Philosophy, the cosmos is holonomical. This
means that the structure of the cosmos replicates (self-similar) itself at ever-decreasing scales. Like a
hologram, every fragment of the cosmos is complete in itself and contains all the information of the
whole. The whole cosmos can be visualized in a microcosmic capsule called Pinda-Brahmanda.
The fractal architecture observed in every part of temple such as, shikhara (Plan and elevation),
temple plan, mandapa ceiling design, column design, etc.

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Figure-3. Fractal architecture of the shikhara.
The above figure was derived from comparative elevations and plans of: (a) Shikhara of Adinatha
temple (900 AD); (b) Shikhara of Paraswanatha temple (950 AD); and (c) Shikhara of Kandariya
Mahadev temple (1050 AD). As the degree of complication in geometry increases, the number of
self similar design increases, indirectly represents the fractal geometry.
Figure-4. Plan of Garbh Griha.
Growing complexity of components on both the interior and exterior wall of the various types of
garbhagrihas. On the inner wall the plans are with the components called: (1) Bhadra (2), Subhadra
(3), and (4)Pratibhadra (4), while on the exterior walls with (1)Arya, (2) Hastangula, (3) Bhagava,
and (4)Samadala.
Figure 5, below represents Plans of 8 types of Mandapas as described in Shilpa texts namely 1.
Vardharnan; 2. Swastika; 3. Garuda;4. Suranandan; 5. Sarvatobhadra;6. Kailash; 7. Indranila; 8.
Ratnasambhava. The external and internal wall geometry and elevation changes and becomes more
artistic and complex in geometry as there is a move from stage-1 to stage-8 of the mandapa
geometry. Here the design maintains symmetry with respect to x and y axis, and in some of the

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Figure-5. Fractal geometry of Mandapa in increasing order of fratal iteration.
9. HUMAN BODY AND TEMPLE GEOMETRY : According to the ancient scriptures
or agamas, the temple is a body. Hence a temple cannot be constructed as we wish. It has to follow
certain rules based on Tantra, Agama and Shilpa Śastra. Kśetra (area of the temple) is our sthūla
śarīra (gross body), deity the sūkshma śarīra (subtle body), and its prāña our kāraña śarīra (causal
body). The prāña of the deity is same as ours. The structure of a temple from feet to head consists
of six ćakras. So, each part of the temple such as garbhagriham, dhwajasthambham, etc. possesses
its significance in Tantra Śastra.
Figure-6. Human body and temple geometry represented as self similarity.
10. VINYASASUTRA (LAYOUT & ORIENTATION OF TEMPLE COMPLEXES)
The design lays out a Hindu temple in a symmetrical, self-repeating structure derived from central
beliefs, myths, cardinality and mathematical principles. The 8x8 (64) grid Manduka Hindu Temple
Floor Plan, according to Vastupurusamandala. The 64 grid is the most sacred and common Hindu
temple template. The bright saffron center, where diagonals intersect above, represents the Purusha
of Hindu philosophy.

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The four cardinal directions help create the axis of a Hindu temple, around which is formed a perfect
square in the space available. The circle of mandala circumscribes the square. The square is
considered divine for its perfection and as a symbolic product of knowledge and human thought,
while circle is considered earthly, human and observed in everyday life (moon, sun, horizon, water
drop, rainbow). Each supports the other.The square is divided into perfect square grids. In large
temples, this is often a 8x8 or 64 grid structure. In ceremonial temple superstructures, this is an 81
sub-square grid. The squares are called ‘‘padas’’. The square is symbolic and has Vedic origins from
fire altar, Agni. The alignment along cardinal direction, similarly is an extension of Vedic rituals of
three fires. This symbolism is also found among Greek and other ancient civilizations, through the
gnomon. In Hindu temple manuals, design plans are described with 1, 4, 9, 16, 25, 36, 49, 64, 81 up
to 1024 squares; 1 pada is considered the simplest plan, as a seat for a hermit or devotee to sit and
meditate on, do yoga, or make offerings with Vedic fire in front. The second design of 4 padas has a
symbolic central core at the diagonal intersection, and is also a meditative layout. The 9 pada design
has a sacred surrounded center, and is the template for the smallest temple. Older Hindu temple
vastumandalas may use the 9 through 49 pada series, but 64 is considered the most sacred geometric
grid in Hindu temples. It is also called Manduka, Bhekapada or Ajira in various ancient Sanskrit
texts. Each pada is conceptually assigned to a symbolic element, sometimes in the form of a deity or
to a spirit or apasara. The central square(s) of the 64 is dedicated to the Brahman called Brahma
padas.
Figure-7. Typical Temple Plan (a)Shrine alone (b)Shrine with porch (c)Shrine with Antarala and porch
(d)Sarvatobhadra shrine with four entrances (Source: Hardy, Adam. The Temple Architecture of India)
Figure-8. Typical Temple plan of temple : temple of Tanjavur
11. The Construction Technology of Ancient Hindu Temples
The available information of temple construction was collected from stone slabs, metal plates, palm
leaves and manuscripts. Primarily, both Dravidian and Nagara temple construction followed same

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procedures up to construction of the temple. The slight variation occurred due to the variability of
materials used for construction, the climate or theavailability of manual labors for construction.
It started with the selection of team headed by chief architect (sompuras in the west, mahapatras in
the east and sthpatis in the south). The construction team consisted of four classes:
1) Sthapati (Main architect versed in traditional science, mathematics and Shilpashastras)
2.) Sutragrahin who did the work assigned by sthapati
3.) Taksaka who did the carving and cutting of stone
4.) Vardhakin is the mason or carpenter who assembled all the pieces.
The construction of temple was a long and tremendous process which sometimes used to last for
years. The first stage was the planning of the temple where the sthpati with the team did the
selection of site, inspection of site, orientation and layout of the site, selection of materials,
quarrying and transportation of materials. The layout was done on the basis of Indian Circle Method
and with the help of instrument known as “shanku yantra”. The nature of main deity played a major
role in determining the orientation of temple. The stone which was to be used for construction must
have some quality features such as even color, hard and perfect and pleasing to touch. The second
stage was the craving of different parts of the temples in which the takshaka directed the sculptors
and shilpis to carve parts according to the drawings and specification. The cutting and carving the
stone was done according to pre defined shape. The joining was also pre decided and rough joinery
was created while cutting. The tools required such as hammers, chisel were locally made and
sharpened regulary. The sketching was done either by charcoal piece or sharpened bamboo pieces.
The polishing was done using stone bars. The third and the final stage consisted of tassembling of
the parts of temple which consisted of the actual construction of the temple. Ramps were constructed
for the easy placement of heavy materials. The major joinery system used during the assembling of
temple were mortise and tenon joint ( peg is fixed between the two mortise cut out in two different
stones and was used primarily used between two courses of masonry to avoid movement due to
lateral forces) and lap joint. The usual thickness of stone used for wall varied form 800 mm to 1200
mm. The column consisted of 5 parts as two parts of base, one part as shaft and two as the capital of
column. Also, columns and beams were monolithic structure.
Hindu temples were found on diverse locations, each situated in unique geography, topography,
materiology, etc. of the area, hence it incorporats different construction styles and materials. Some
of the examples of such locations are depicted below:
 Mountain temples: such as Mansa Devi, Vaishnow devi etc.
 Cave temples: Chandrabhaga, Chalukya land Ellora
 Step well temples: Mata Bhavani Vav, Khodiyar mata ni vav (Both are in Ahmedabad,
Gujarat)
 Forest temples: Kasaun and Kusama
 River bank and sea shore temples: Jagannath Puri, Somnath.Kashi, Haridwar, Rameshwaram
etc.
12. Art and Cultural representation in Temples:
A typical, ancient Hindu temple has a wealth of art – from paintings to sculpture, from symbolic
icons to engravings, from thoughtful layout of space to the fusion of mathematical principles with
the Hindu sense of time and cardinality. Ancient Sanskrit texts categorize idols and images in a
number of ways. For example, the dimensionality of completion is one of the classification methods:

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 Chitra: images that are three-dimensional and fully formed
 Chitrardha: images engraved in half relief
 Chitrabhasa: two-dimensional images, such as paintings on walls and cloth.
Concluding Remarks
The temple architecture portrays the advancement of ancient Indian building sciences. This paper
discussed the styles, design and geometry, philosophies, construction technology, self-similarity of
human body with temple elements geometry of the Indian temples. The volume of work and area
covered by temples were dependent on various factors like location, budget and type of building
stones available for temple construction. Depending on the time scale and geographical locations the
temple geometry changes in terms of materials and design over a period of time. The use of fractal
architecture is dominant for almost all styles of architecture for all parts of temples and even today it
is in practice. It seems that, the art work in stone on every part of temples was intended to maintain
and transfer the information purpose. The fractal geometry of shikhara provides it an ambient look
in complete balance of mass and symmetry. The zigzag vertical offsets in increasing number with
each side recess, creates vertical rhythm. The horizontal abutments spreading towards ground and its
horizontal carvings increases stability of temple structure. The geometry of temple architecture was
prepared in such a manner that they can sustain moderate earthquakes. The temples are not only just
structures, but it simulates the human body symbolically and the seven chakras of kundalini shakti to
be awakened step by step from feet to head respectively.
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Ancient temples Geometry - conference paper prepared on 28th Feb. 2021