Bharatiya Ganitam - Episode 2 - ORIGINS OF GEOMETRY || Project SHIVOHAM

Summary

In this enlightening episode of Bharatiya Ganitam, we're taken on a journey to explore the origins of geometry in ancient Bharat. The episode delves into the Sulba Sutras, ancient texts detailing the geometric principles used in the construction of Vedic fire altars. These texts reveal the sophisticated understanding and application of geometry by ancient Indians, showcasing techniques like geometric transformations and the use of ropes for precision. This episode is a fascinating dive into how geometry was intertwined with cultural and religious practices, providing a unique perspective on ancient Indian mathematics.

Highlights

• Geometry was integral to Vedic rituals in ancient Bharat, especially in constructing fire altars. 🔥
• The Sulba Sutras are over 3,000 years old and showcase advanced geometric knowledge. 📚
• Ancient Indians used ropes to construct geometric shapes, allowing flexibility and precision. 🧵
• The episode explains geometric transformations like converting squares to circles and more. 🔄
• The importance of geometry in the Sindhu Saraswati civilization offers insights into their architectural prowess. 🏺

Key Takeaways

• Geometry has deep roots in ancient Bharat, specifically intertwined with cultural and religious practices. 🏛️
• The Sulba Sutras are ancient texts that laid the foundation of applied geometry in India. 📜
• Geometric principles were integral in constructing Vedic fire altars with precise dimensions. 🔥
• Ancient Indians used ropes for constructing geometric shapes, demonstrating advanced understanding for the time. 🧵
• The knowledge documented in Sulba Sutras continues to be relevant and inspiring today. 🕰️

Overview

Episode 2 of Bharatiya Ganitam dives into the ancient origins of geometry in Bharat, focusing on how this knowledge was immortalized in the Sulba Sutras. These ancient texts serve as some of the world's oldest documents on applied geometry, showcasing the precision and sophistication of early Indian mathematicians in constructing Vedic fire altars.

The episode highlights the crucial role of ropes in ancient geometric practices. These ropes allowed the creation of complex shapes that were essential for religious rituals, demonstrating a deep understanding of geometric transformations. This knowledge was not only applicable in religious contexts but also inspired practical innovations that are still relevant today.

Furthermore, connections are drawn between the Sulba Sutras and the advanced architectural practices of the Sindhu Saraswati civilization. This reveals a fascinating aspect of ancient Indian history, where geometry was not just a mathematical endeavor but a cultural and spiritual one, weaving through the fabric of everyday life in early Bharat.

Chapters

• 00:00 - 03:00: Introduction to Origins of Geometry This chapter introduces the origins of geometry, highlighting its significance as one of the most popular fields of mathematics. It is part of the web series 'Bharatiya Ganetham', which focuses on the rich history of mathematical research and innovation in ancient India. The episode discusses how geometry began and evolved in ancient Bharat.
• 03:00 - 06:00: Trikagni Kalaya and Fire Altars The chapter explores the origins of geometry in ancient Bharat, emphasizing its development in various fields such as Vedic rituals, Jyotisha Shastra, Shilpa Sastra, and Srividya. It references a related documentary made earlier on the same topic, suggesting that this chapter primarily delves into the same content with a focus on the origins of geometry. Those familiar with the previous work, 'The Vedic Geometry,' might find this chapter repetitive, though it provides a concentrated look at the foundational aspects of geometry.
• 06:00 - 10:00: Sulbasutras and Ancient Indian Geometry The chapter explores the origins of geometry in ancient India, particularly focusing on the contributions of Sulbasutras and other Vedic texts. It emphasizes how every ancient civilization, including India, developed geometry based on their unique needs and cultural context.
• 10:00 - 13:00: Units of Measure and Types of Chitis The chapter titled 'Units of Measure and Types of Chitis' explores the historical context of geometry in ancient Bharata (India). It begins with an invocation from a sacred text or a prayer, specifically referencing a term 'trikagni kalaya', which translates to 'the lord of'. The chapter seems to set the ground for discussing the units of measure and the early understanding and categorization of spatial concepts in ancient times. It suggests a blend of cultural, religious, and mathematical insights as part of the narrative.
• 13:00 - 18:00: Geometric Transformations in Sulbasutras The chapter titled 'Geometric Transformations in Sulbasutras' explores the significance of three fires, known as Trikagni or Traitagni, in ancient Bharat (India) and their connection to the genesis of geometry in Sanatana Dharma. The text highlights the reverence for Rudra as the lord of these three fires and discusses the perpetual presence and necessity of maintaining these fires in every home during ancient times. The importance of Agni (fire) in the spiritual and daily lives of people is emphasized.
• 18:00 - 22:00: Sulbasutras and Cultural Connections The chapter titled 'Sulbasutras and Cultural Connections' discusses the significance of different types of fire altars used in Vedic rituals. It explains the role of the ahavaniya, which is square-shaped and used for Vedic rituals, the graha patia, which is circular and used for household purposes such as cooking, and the dakshin agni, which is semi-circular and serves as a token of respect towards ancestors or pitru devatas. These three fires are collectively known as threat agni, and Rudra is worshipped as the lord of these three fires.
• 22:00 - 27:00: Sindhu Saraswati Civilization and Geometry The chapter discusses the origins of geometry in ancient Bharat through the construction of three fire altars in different geometric shapes, all of which must have the same area. This reflects the intricate understanding and application of geometry by the Sindhu Saraswati civilization.
• 27:00 - 32:00: Conclusion and Invitation to Research The chapter concludes by emphasizing the sophistication of ancient Bharat's geometric knowledge. It suggests that both man-made creations and natural patterns, like those of honeybees, exhibit intrinsic geometric understanding. The text reflects on how ancient Indian temples demonstrate advanced geometry, inviting readers to explore and research further into the origins and development of geometric concepts across history.

Bharatiya Ganitam - Episode 2 - ORIGINS OF GEOMETRY || Project SHIVOHAM Transcription

• 00:00 - 00:30 [Music] [Music] geometry one of the most popular fields of mathematics and as part of this web series bharatiya ganetham a series that is completely dedicated to bring forward every spec of research and innovation that has gone into the field of mathematics in ancient parith in the episode number two we are going to see the origins of geometry how geometry originated in ancient bharat just in
• 00:30 - 01:00 case the title sounds familiar to you the vedic geometry something that i made almost an year ago a detailed doc film on how geometry originated and thrived in ancient bharat in four fields the vedic rituals jyotisha shastra shilpa sastra and srividya but this dark film where i'm going to focus only and only on the very origins of geometry and just in case if you have already watched the vedic geometry then you might as well skip this one because mostly it would be the similar content but the difference
• 01:00 - 01:30 is here i would like to focus only and only on the origins of geometry and for those of you who have not seen the dark film of the vedic geometry yet and if the subject is of interest to you i would suggest you watch that doc film as well the link would be below now coming to the actual topic how did geometry originated in ancient bharat let's get started first of all every civilization in the history of humanity had their own ways of dealing with geometry for their own needs this story is only and only about
• 01:30 - 02:00 how ancient bharata dealt with geometry and here is the genesis of geometry namaste bhagavan vahadeva often recited as part of surirudram our story begins with this specific word trikagni kalaya it means the lord of
• 02:00 - 02:30 three fires rudra is revered as the lord of three fires trikagni kalaya and what are those three fires that is where the genesis of the geometry begins in ancient bharat throughout the history of ancient bharata and by extension to the entirety of sanatana dharma agni has an incredibly important role during the ancient times in bharat there are always these three fires that have to be maintained in every home and these are called as trait agni and there are three
• 02:30 - 03:00 ahavaniya grahamatiya and dakshin agni ahavani yagni which is in the square-shaped fire altar as shown here is used for vedic rituals and graha patia which is in the circular shape is used for household purposes like cooking and dakshin agni which is in the semi-circle shape is used as a token of respect towards the ancestors or pitru devatas so these three fires together is called as threat agni and rudra is worshipped as the lord of three fires
• 03:00 - 03:30 trikagni kalaya and the genesis of geometry in ancient bharat began with constructing these three fire altars which are in three distinct geometrical shapes yet one strong constraint has to be respected all the time all these three fire altars should have exactly same area the choice of words is very crucial in any statement here i am saying the genesis of geometry by that what i mean
• 03:30 - 04:00 is the well-codified knowledge from ancient bharat as far as geometry is concerned i'm referring to that as the genesis of geometry look if we take a look around ourselves we can always find an intrinsic sense of geometry in everything that is man-made or for that matter anything that originated from nature in fact a honey bee might have a better sense of geometry than you and me and definitely when you would have walked into an ancient temple in bharat for sure our ancestors excelled in the art of geometry but if one really want
• 04:00 - 04:30 to understand what was the ancient knowledge like then the primordial source of such kind of mathematics those ancient scriptures where geometry is well codified and detailed out is called as sulbah sutras sulbah sutras are the primordial treatise on geometry not just in bharat but in the whole world how to construct these three fire altars of graha pathya aahaniya and dakshinagni in these respective shapes of square circle and semicircle all the geometric
• 04:30 - 05:00 principles involved behind the construction of these fire altars are detailed out in sulphur sutras the most distinct feature of ancient indian geometry is people back then used rope for any of these geometric constructions which provided incredible flexibility no matter which shape you're dealing with and this made sulba sutras very powerful by the standards of those times or maybe even by today's standards the sulba means rope and hence the name sulbah
• 05:00 - 05:30 sutras that means the principles of rope that's what the literal translation is the purpose of this doc film is to briefly introduce what are sul basutras and most importantly motivate those of you who are very interested in the subject to further do your own research on sul vasutras because these are the world's oldest written records about an applied geometry that is still active in bharat yet a vast majority of us might not be aware of it thanks to our education system
• 05:30 - 06:00 so here are the five most important things that you should know about sulbasutra starting with the first one who authored these sulba sutras and what is the intended purpose fundamentally these sulbah sutras are considered as an integral part of yeservatham and they define direct and drive the principles of construction of all these fire altars and the yagna vedicas that are involved in a vedic ritual
• 06:00 - 06:30 varaha all these are the great rishis who authored sulbasutras and each of them had their own way of dealing with the geometrical principles that are needed for construction of these vedic fire altars of all these sulba sutras often bowdhy nasul bhasutras written by bhagti namahashi is considered to be one of the oldest which is more than 3000 years old anyways as far as the dating is concerned regarding the vedic scriptures i will refrain from it because it is always debatable because we could find these vedic practices in
• 06:30 - 07:00 much more older scriptures like the vedas and the puranas or ramayana in mahabharata so you cannot just go with 800 bce timeline but anyways getting back to our concept so these are different scriptures written by different mahashi's on the geometrical principles involved in the construction of the vedic firealters moving next to the second most important thing about the sulbasutras alignment with the cardinal directions of the earth and the sun we all know that the solstices and the equinoxes
• 07:00 - 07:30 significantly impact the direction in which sun rises and sets from any given fixed location on earth and also you might have gone through certain specific temples in bharat where sun enters into the garbage or into the interior parts of a temple on specific days in a year so how are those calculations made with regards to sun's position and how are those constructions executed this is what you are seeing on the screen survivors explains about how do we track the
• 07:30 - 08:00 position of a sun and eventually pin down the cardinal directions of earth with respect to sun's position on that given day in any year as you can see in the screen plant a stick vertically and then draw a circle with the help of a thread around it and right from sunrise up until sunset the shadow of the stick protrudes out of that circle two times one at sunrise and the other one at sunset and these two points when joined gives the east west line and sulphur sutras gives a clear algorithm a step by step one as to how do we construct a
• 08:00 - 08:30 square with its sides aligned to the cardinal directions of earth this i have already covered in detail in the vedic geometry documentary so i'll skip it for now but very important thing is how do we calculate sun's positions so perfectly is detailed allowed in sulva sutras third most important thing about sulbasutras is the units of measure what's geometry without a unit of measure there are different units of measure defined in different sulbasutras here is an example of one standard unit
• 08:30 - 09:00 of measurement angular 34 sesame seeds stacked up face to face gives one unit of measurement a basic unit of measurement called angular 120 such angulars is considered as the height of one human being at that time which is called as one purusa like this there are many other units of measurement in sulbasutras up next in number four is types of chitis or fire altars in sulbasutras this is the most complex
• 09:00 - 09:30 aspect about sulbasutras initially what we saw the treth agni which are in square circle and semicircle the relatively very simple geometrical shapes but for other vedic rituals there are much complex fire altars that needs to be constructed and they are not monoliths it is an arrangement of bricks which has to be cut to precession like you're seeing in on the screen the blueprint of shayna chitty rather and there are many more as you can see the shape of the bricks or the tiles
• 09:30 - 10:00 what you're seeing here you have square rectangle trapezium again in triangle we have isosceles and equilateral so the essence of sulphur sutras is all about making these bricks and constructing these fire altars here is where the complexity kicks in here is a prototype of sheenachiti sheena means garuda or a falcon and just observe the shapes of this tiles there are right angle triangles isosceles triangles squares and rectangles and lot of other geometric shapes this is a
• 10:00 - 10:30 miniature or a kind of a prototype of shenachiti each of this style will be actually to the size of a real brick i've explained this in detail in the vedic geometry doc film already so i'll keep it very short here to the context how about a little fun fact shayna in means falcon king of birds in that sense and this infamous place called shaheen bhag where there were a lot of protests regarding the caa so that word shaheen is actually a samskrutam word derived
• 10:30 - 11:00 from shayna shaheen shah or bad shah all these words sounds to be like arabic or muslim names or words these names are derivatives from the samskritam word sheena pretty interesting how deep are the cultural connects so these are the real size of the bricks of this shayna chitty which is in the shape of a falcon you can see how big are these triangular bricks all well stacked up in five layers to form the
• 11:00 - 11:30 shayanachiti sul vasudras very well defined the guidelines and the geometric principles behind baking these bricks so well that it even takes into account the losses that would occur in the shape of the brick once it gets dried up and how to cover those losses so when you make a brick it would be wet when you bake it the shape could slightly alter so the actual dimensions of the brick when you make it freshly and when it is wet when it goes into the oven and comes out of
• 11:30 - 12:00 it well hardened the dimensions could be different so how do we make up for that loss sulbasutras even take into account at that specifics as well coming to the fifth and last and the most important and relevant subject of the geometric transformations how do you transform one shape into another shape restricting within the same area and this is the most scientific reason why you should research about sulbasutras if
• 12:00 - 12:30 the subject is of interest to you how do you construct a square of certain dimensions and then transform that square into a rectangle of exact same area or vice versa that is one example another example is how do you construct a square and then construct another square which is three times the area of the initial square and same way another geometric transformation is construct a square and then constructed another square which is one third of the area of the given square like this there are many geometric transformations of
• 12:30 - 13:00 transforming a circle into a square a square into a circle a square into a rectangle a triangle into a square a square into a triangle so on and so forth so let's take one or two examples to understand the essence of this geometric transformations as part of sul vasudras here is an axiomatic principle from the sul sulbasutras to construct a right angle triangle bujakoti karani nyayam we know this as pythagoras theorem but in samskrutam it is called as bhujakoti
• 13:00 - 13:30 karaninyayam bhuja and koti are the base and height of the triangle and currently is the diagonal so you can in simple and literal translation you could call it as the principle of the diagonal that runs between the base and the height of a triangle translation is given here and in simply put the rope stretched along the length of the diagonal of a rectangle makes an
• 13:30 - 14:00 area which the vertical and the horizontal sides make together this is what we call today as pythagoras theorem but as i said in my previous documentary on the vedic geometry pythagoras was not the original inventor of this as at the very least babylonians or egyptians knew it much before pythagoras did but coming to the ancient bharat this bujakoti karaninyayam is very much an integral part of yazuru we all know that the main purpose or one of the main purpose of this theorem is to construct right angled geometric
• 14:00 - 14:30 shapes but how was it used in ancient bharat let us try to find an example from the sula basutras itself here is an example of a geometric transformation where we need to triple a square that means we start with a square and then construct another square which is three times the area of the initial square now how are we going to solve this problem using bhakti-karaninyam or pythagoras theorem let's try and see that briefly this is
• 14:30 - 15:00 from the sul bhajutras written by katya namahashi and here is what the sulbasutra says the diagonal made between the diagonal of initial square and a length equal to its side gives an area three times of the initial square sounds like a bit of tongue twisting but it's pretty simple just look at the diagram we first start with a square of side a which is shown here as a b c d of side a for that using the bujakoti karaninyam we can calculate what is the length of the diagonal of ac going by
• 15:00 - 15:30 the bujakoti karaninyam aka pythagoras theorem a b square plus bc square is equal to ac square and by that we have ac is equal to a root 2. now we take ac as a length and a breadth of the rectangle with side a so then we construct a rectangle a c f e of length a ro2 and breadth a so in the rectangle a c f e if we apply the bujakoti
• 15:30 - 16:00 karaninayam then we will get the diagonal of this rectangle as a root 3. so this length between a and f which is a root 3 a square which is formed with side af with a root 3 is 3 times the area of the square abcde of side a so this is how you can triple the area of a square using bujakoti karaninyam aka pythagoras
• 16:00 - 16:30 theorem but why are these kind of transformations needed here it is these kind of transformations are needed to cut the bricks proportionally to construct the yagna vedis or the fire altars imagine that you want a brick of area x to construct any kind of a yagna vedhi and then you need another brick which is three times the area of this brick now how are you going to calculate these kind of principles will help you to calculate by doing this geometric transformations and this is
• 16:30 - 17:00 the reason why bujakoti karaninyayam was constituted as part of azerbaijan now a simple logical question that i should ask myself is what is the intention of pythagoras behind quote unquote inventing the so-called pythagoras theorem that we are studying today why was it used for for what purpose these questions have to be asked then you'll get to know the real truth same way here are a couple of other
• 17:00 - 17:30 examples on the geometric transformations of transforming a circle to a square and a square to a circle for those of you who are a bit more savvy with mathematics you know that this has been a kind of a riddle for the mathematicians in ancient greek for well over 2000 years it pestered the minds of leonardo da vinci and likes of him and the solution to this problem is given as part of sulphur i did a separate documentary on the vedas and the vitruvian man where i explained about this geometric transformation should be interested to watch so like this there are many
• 17:30 - 18:00 geometric transformations detailed out as part of sulphur sutras and these geometric transformations are the reasons why we need to really delve deep into the sulphurs maybe today our level of maturity with respect to geometry is far more advanced than what it was in sulbasutras completely agree but at the very least it serves as an incredible inspiration to the youth of this bharat which is producing millions of stem graduates every year who don't have a single clue about the great
• 18:00 - 18:30 contributions that came in from bharath in the field of mathematics every time we get to hear that sick dumb and idiotic answer saying that indians invented zero indians did not invent zero rather it's a place value system but most importantly there are many many mathematical contributions that came in from bharat and that is the reason i've been doing this web series on bharatiya gandhitam from project shivoham another very important line of thought
• 18:30 - 19:00 and something that we should pay our attention towards is the sindhu saraswati civilization or the indus valley civilization a civilization that thrived almost more than 5 000 years from now in the region of harappa and mohenjodaro i don't want to go deep into it but just one very interesting fact that i would like to touch upon is the brick the harappan brick researchers have found that the bricks used in the sindhu sarasota civilization are of the dimensions 4 is to 2 is to 1 which is
• 19:00 - 19:30 one of the most optimal dimensions for the best structural integrity in whichever structure that we use this bricks in without a deep sense of geometry this is just impossible so what we need to think about and rather research more is what has been the maturity of sindhusar swathi civilization on the grounds of geometry another very important and interesting fact about the sindhu saraswati civilization's geometrical expertise is
• 19:30 - 20:00 that for constructing a right angled structure they have been very fond of using circles and as we know the line that passes through the centers of the circle and the vertical line which cuts through the points of intersection forms an exact right angle or 90 degrees now if you observe the pattern or the commonality here constructing a circle with a thread has been the practice in the vedic rituals and this specific fact that sindhu saraswati civilization people have also been using circles to
• 20:00 - 20:30 derive right angles kind of gives a sense of commonality between these two civilizations and we cannot jump to a conclusion saying that both are the same but definitely both originated from the same land bharath so without giving into any confirmation bias fact of the matter is we need to understand and research more about sindhu saraswati civilization's geometric expertise and as well try to understand its relevance or if there is any relationship with that of the vedic rituals which are in
• 20:30 - 21:00 practice even today rolling back all the way where we started in sri rama trikagni kalaya and the trethagni that is where the geometry in bharat originated in a well codified format and if you are more interested in the subject the next time when you go to a siwa ask the pujari over there what is the meaning of trikagnikalaya and listen for yourself how treth agni or the three fire altars
• 21:00 - 21:30 gave rise to the origins of geometry in ancient bharath so that is a brief account on how geometry originated in ancient bharath and there are tons of scriptures especially the sul vasudras on ancient indian mathematics what every person who has a deep interest in the contributions that came in from ancient bharat into the field of mathematics should be reading and researching about ancient advanced technology these are not synonyms for flying spaceships and
• 21:30 - 22:00 aliens and whatnot sulbah sutras are very basic practical and world's oldest applied geometry which can be definitely called as advanced technology of those times executing the entire geometry with rope and a bunch of nails the sul vasudras of the vedic culture also establishes that how dharma nurtured science in bharat while in other parts of the world religion opposed science in bharat dharma nurtured science and
• 22:00 - 22:30 dharma is not and never equal to a religion and for those of you who are interested do research about sulba sutras you will be amazed and enlightened at the same time and as always thanks for watching [Music] you