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so this is the second part of a lecture on
vedas and sulbasutras yesterday we discussed
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what are sulvasutra text so what are the characteristics
of sulbakara which are defined in this text
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then we introduced the sulba theorem which
is more popularly known as pythagorean theorem
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so then we came to the applications of this
sulba theorem so we also saw the kind of rational
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that can be seen behind the triplets that
are given in the baudhayana
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sulbasutra and so on in todays talk we will
start with the transformation of geometrical
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objects for instance so we will start with
supposed there are 2 square if u have to construct
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a square so whose area will be this sum of
these 2 square or u can think of 2 square
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and i want to find out a square so which will
be the difference of these two squares and
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if you have to construct a circle whose area
is more or less the same as that
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of the square and so on so forth so these
are the kinds of problems which will discuss
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today and we also see so in connection with
this so the expression for some of the search
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see this is the very common problem which
one will be able to encounter suppose i construct
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a has been constructed so of a certain area
and i want to construct another so which will
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have twice the area of this so then we should
be able to find a way by which you will be
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find out
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the value of root 2 so if it 3 times then
root 3 and so on so these are common things
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so one way is of course geometrical find out
the value of root 2 so they have given certain
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expressions for route 2 so which is in the
form of a sum of rational numbers so all those
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things will be able to see today how this
sulbasutra kara arrive at the value approximation
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for root 2 then to at the end of the talk
so i will be discussing what are known as
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citis so citi as
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they was mentioning is basically collecting
things together putting things together so
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we have several citis which are listed and
so on so these names are derived from the
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shape of the altar in which is constructed
so so this is how ahh the name of various
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types of citis and the purpose of citis are
also stated so we will discuss all these topics
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today this is where i stopped yesterday so
as i said is square means desire of putting
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together
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means putting together so refer to smaller
one and refers to the larger one so what he
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says is if you have 2 squares say a b c d
and then c g h i so you want to construct
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a square so which will be the sum of these
2 squares basically the area of the largest
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square so this is a simple ahh instruction
which tells you how to go about so without
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even thinking of the ahh arithmetic which
is involved in that so you have a square you
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have another smallest square
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you just do a certain trick here and you should
be able to get the value of the largest square
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without doing any calculation numerical calculation
so all that it says is so you think of this
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smaller square c g here refers to the side
cg for instance so so you just think of placing
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this square there or marking c g in the largest
square b e can be understood to be a sort
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of rectangle here so this rectangle is b e
f a so then it says is a e so the diagram
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all that
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sutra says is the will give you this side
of the square that you desire so this all
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the sutra is so fine so now if you look at
the a e square is basically a b square+c g
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square ok a b square+c g square so there is
something which is interesting that emerges
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out of it so i wanted to spend a couple of
minutes on that so generally ahh all the text
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just state the role so this is how the structure
go so somewhere scholars are actually puzzles
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whether these
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people knew the truth or they do not knew
the truth this has seen a question which has
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been discussed at great length and what we
can easily is the sulbakara though they did
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not explicitly give proof of this various
procedures it is quite interested in the the
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procedure itself for instance in the previous
thing so if you look at the sum of these two
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areas can be consumed like this a b e it can
be consumed of various triangles a b e a e
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f+ and so on now if
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you look at this so this triangle a b e if
it is sort of stopped off and rotated so that
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a d k it turns into a d k so you have to just
rotate it at a and then think of this triangle
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h e g and if you rotate it round h so this
will go and occupt the space h k i so this
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is essentially the proof of pythagoras theorem
this was called pythagoras theorem in fact
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this proof has been discussed
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in part 2 so the procedure which has been
given in sulbasutra so announce to the proof
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or rather i would say the proof is implicit
in the procedure that has been described refer
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time: 07:55) otherwise i am in that used to
that inspire with this i will proceed further
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to discuss the other interesting things so
before proceeding to that i will introduce
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you 2 certain terms which will be frequently
occurring in sulbasutras which have slightly
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different conversations
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in different context so that should be clarified
to the coming to the latest model of sulbasutra
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these become quite clear to you the term karani
has been used in different sensors in different
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contexts so you suppose it is a compound word
it is likely means different things here i
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wanted to clarify taking a sutra itself from
the katyayana sulbasutra in katyayana sulbasutra
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we have kanani so all the sutras says these
these are 5 names which have assigned to the
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god that you keep you thing in different context
ok so karani sometimes so all that refers
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to sutras so in fact the commentary to mahindra
clarifies so what do these terms mean so you
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will find in various places the terms like
actually means route 2 means root 3 the term
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has been defined as the it is different see
if you want to find out twice the area of
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this so size how root 2 obviously so we call
the term similarly root 3 and so on
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suppose you consider line so the perpendicular
line so that is called so that is how even
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baudhayana sulbasutra one is called interesting
presented for the word action yeah so this
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is a interesting ahh derivation which has
been presented for the word so suppose you
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think of a rectangle and the diagonal is referred
to as so these diagonals split this into 2
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halfs so means eye so splits the geometrical
object into 2 half like 2 eyes and of
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derivation that has been presented for the
world basically 2 opposite corners that connects
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2 opposite corners so karani as i was mentioning
is very frequently encountered so refers to
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the side so area is a obviously karani will
be the root a ok so it is in datsun so similarly
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kanari is a square root means root n ok it
is used in this sense so this root 10 will
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produce a square which has an area 10 so that
is the so it is
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in
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this
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sense
in this is used karani is also used in the
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sense of a certain measure for instance in
this sutra which we will discuss one more
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little later in greater detail this is the
sutra which present to the value of root 2
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ok so there the work karani is used in sense
of a certain unit of measurement ok now i
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move on to discuss the sutra which gives you
the procedure by which you will be able to
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find out the side of a square with you going
to
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be the difference of two squares and square
so earlier we saw sutra to clear the the procedure
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for finding the sum of 2 square feet here
is a difference so so this is how the word
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is derived so one who is desirous of removing
see you have a square you want to remove square
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from it so then he says
whatever be the measure that you want to remove
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the measure of the square you want to remove
from this so measure the measure of that you
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mark something in the largest square for instance
in this diagram suppose you have the square
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a b c d you want to remove a certain area
so which is given by a e g h y axis that x
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is refers to us karani mark that a e and then
draw a line ok
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it is a very clear prescription so all that
i say is so from here you just make an arch
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so this other side ok from one side you just
drag it and take it to the other side so where
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every it fall so once you do that
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so what you will get is basically the area
of the square which is the difference of the
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two square if you construct so a p is the
measure so which gives the side of the difference
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of two squares so how does it work out we
can easily see this see a p square so in this
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just consider this triangle a e p so a p square
is epsquare-a e square now this ep is same
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as a a d by construction right all that you
see here is just an application of this sulva
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theorem right so this
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ap is directly gives you the side of the difference
of two squares so this is the prescription
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for baudhayana sulvasutra for constructing
a square which is the difference of two squares
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so this is a very important thing in fact
this principle is invoke in doing certain
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another kind of transformation which i will
be showing in the next slide so this will
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be quite clear all that we need to do is we
had just mark the largest square so whatever
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be the ahh side of the smaller
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square and then take and then do then we will
be able to get the other square transforming
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a rectangle into a square so this is the next
problem so
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the sutra goes like this you want to transform
into a square
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you want to do that ok
as i mention earlier one is called parshwamani
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the other is called priyamani ok so perpendicular
to that so all that he says is take priyamani
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as a karani and then so let us consider this
diagram and
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understand the sutra so we have a b c d is
rectangle now we want to transform this rectangle
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into a square so there is a certain prescription
which is given in sutra so it says so this
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has 2 side which are unequal so one is ab
and the other is bc so ab is all the sutra
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says is so take the measure of which is ad
and then mark it ok so this will be the xy
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line so you take this ab so ab and then you
mark y axis and fy so the remaining portion
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xy bc so that
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should be split into 2 half the side of the
2 space so all that we do is take one of them
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and then place it here ok so so there is a
small portion which is remaining here
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so this seen in previous sutra yeah you saw
that right so it is basically so how is it
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is to be done is something which has been
stated before so far is a look at the sutra
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number so this is 2 2 so 2 5 has been stated
before so basically the procedure which was
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adopted before has to be
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understood and so you have to apply that procedure
here in order to get this so what was the
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procedure adopted there ok if you look at
so we basically took this and then so he said
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you have to draw this line and then take it
to the other side say so that is all we need
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to here so we have to just take this line
and then take it there and then drop it so
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what we will get is basically this dp ok so
that is going to be the side of this and that
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is what the square is
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so by simply taking this you just hit at this
point and the script which is found here is
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basically occupied area so that is the procedure
for that is what is referred to as see this
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problem can visualise other way also so if
you think of this square all that i need is
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so this is what is extra here so we construct
the square you can think of removing this
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so removing this what is the square that is
going to obtain by me where is essentially
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this so that is what is
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refer to the procedure to get that so this
is the procedure for transforming a rectangle
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into square so to construct a square that
is n times a given square this is a very interesting
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problem so which has been discussed and which
incidentally gives you a certain way by which
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you can find out the value of root 10 and
the value of shirt so whatever n can be it
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is a very simple and very inspective procedure
so which one can find in the sulbasutra
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katyayana sulvasultra in fact yesterday i
refer to one of this i will recall that quickly
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now so the problem is this you want to basically
find out the value of root n how do you go
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about the sutra says slightly different way
suppose you have n squares as much as you
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want ok so so you want to find out the area
which will be given by these n squares so
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how do you construct a square which will have
the area of some of the n square which is
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the most general
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way of getting the problem as much so much
ok
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so means so remove one from that ok here ahh
we let us look at this diagram so he basically
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tells that you have to conceive of your certain
triangle wherein the side of the triangle
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one of the side so which we can consider the
base so is n-1 times ok so then the other
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2 sides so have to be of this measure n+1*a/2
and n+1*a /2 so what would be the perpendicular
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draw from a will be root n times a and you
put
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it in a form of algebraic equation so in this
figure bd=1/2 of bc that is n-1/2*a we consider
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this triangle a b d ok so then the equation
is this so ad square ok ad square is difference
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of these 2 and ab is n+1/2*a the whole square
and bd is n-1/2*a whole square so the difference
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of these two square basically is na square
which is ad square so from this what you get
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is basically the value of root n so the problem
has been posted as ahh problem of constructing
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a
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square so who area will be n times the area
of smaller square whatever be the dimension
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is what we are going to get see in al these
things what yesterday was mentioning ahh this
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sulva theorem or baudhayana theorem which
is generally referred to as pythagorean theorem
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so what is under operation we all these transformation
so if i did this whether you want to submit
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have whether you want to find the difference
so the underlying principle happens to
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be the baudhayana theorem ok now we would
move on to another problem which has been
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the most difficult problem for which many
scholars from all civilizations have been
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taking a head so how was you just say i want
to have a square whose area is same as that
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of a circle or i want to have a circle whose
area is a square so some kind of ahh prescription
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which is found in sulbasutra is what we are
going to discuss now so so this in
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every sutra we will find this ok so you want
to transform a square into a circle so what
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is to be done so he says
as i was repeatedly telling is the diagonal
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line means half of it let us look into this
diagram abcd so this is a square and i want
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to get a circle so whose area will be more
or less same as with this square ok
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so usually the conceive of the diagram constructed
with the direction mark on one edge so this
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is how we do in all the plans
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elevations whatever we do you mark with so
similarly we can think of ok so the sutra
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goes like this is half of the diagonal which
is od so this if says just take it this line
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so it you can think of it to be oe now so
i have rotated it and brought it there
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which is remaining above see when od become
oe so sometimes protruding out of it so that
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is what is referred to as here so whatever
you mean so here it is me that
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portion me one
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third of it ok so what does this prescription
amount to so let us look into the details
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which have been dotted down here see ab let
us say is 2a the side of the square is 2a
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so op is the radius of the circle whose area
is going to be square so od=root 2a obviously
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so then me is root 2a-a so that is the portion
that is which is exceeding so the sutra said
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one third of this see one third of it has
to be added to that say one third which is
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basically pm so pm is one
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third of this so what it amounts to is the
radius is a/3 so half the side is a so a/3r
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or 2+root so this what is the prescription
which has been given in baudhayana sulbasutra
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00:28:07,879 --> 00:28:15,159
for transforming a square into a circle so
accurate this so let us see little later ok
199
00:28:15,159 --> 00:28:24,951
so in this we find root 2 of it so you know
the value of a so that you do not know what
200
00:28:24,951 --> 00:28:33,109
root 2 is rupees have you been find out who
so then you will be immediately able to compute
201
00:28:33,109 --> 00:28:34,469
this see if you
202
00:28:34,469 --> 00:28:39,960
look so this sutra is 2 9 the couple of sutras
later baudhayana presents another sutra so
203
00:28:39,960 --> 00:28:59,039
which gives the value of root 2 so
204
00:28:59,039 --> 00:29:18,779
is basically some unit some unit measure so
means one third of it you have to add which
205
00:29:18,779 --> 00:29:39,809
is immediately preceding one fourth of that
so one fourth or one third then it says subtraction
206
00:29:39,809 --> 00:29:53,029
okay negative kind of so you have to subtract
134 of that ok here refers to 1/3*4 so ok
207
00:29:53,029 --> 00:29:57,779
you have to substract this and the
208
00:29:57,779 --> 00:30:09,489
word as i was mentioning so it means it is
not exact value so approximate value ok so
209
00:30:09,489 --> 00:30:19,869
this amounts to 1 414215 and this i think
is correct to 6 decimal places ok this is
210
00:30:19,869 --> 00:30:29,609
what ahh is the sutra which gives the value
of root 2 in baudhayana sulbasutra we see
211
00:30:29,609 --> 00:30:39,899
soon how baudhayana might have arrived at
this expression for root 2 so i mention this
212
00:30:39,899 --> 00:30:46,219
has been studied in the more greater detail
and further requirements have been presented
213
00:30:46,219 --> 00:30:47,580
in one of the
214
00:30:47,580 --> 00:30:52,120
commentaries so there are several explanations
which have been offered by various scholars
215
00:30:52,120 --> 00:31:00,029
to study this sutra and what we will be presenting
here is certain geometrical way of arriving
216
00:31:00,029 --> 00:31:06,619
at this expression for root 2 which we find
in baudhayana sulbasutra in fact later mr
217
00:31:06,619 --> 00:31:12,401
srinivas may be ahh telling you how this can
we obtain so from different kind of a problem
218
00:31:12,401 --> 00:31:20,909
which is called ok so that we touch up on
later as you go through the course so
219
00:31:20,909 --> 00:31:29,509
this geometrical construction is quite instructive
and in fact recently one of the article i
220
00:31:29,509 --> 00:31:37,529
think henderson i think from the columbia
university also he studied this problem when
221
00:31:37,529 --> 00:31:43,229
he visited india and he came up with a very
interesting paper so wherein he mentioned
222
00:31:43,229 --> 00:31:49,219
he also points out it is not that others have
not he also points out in his own way as to
223
00:31:49,219 --> 00:31:56,219
how this expression for instance so this meaning
of the word as i said is only approximate
224
00:31:56,219 --> 00:31:57,219
so with me some
225
00:31:57,219 --> 00:32:01,629
other term which can be added so it is never
going to end so it is never going to end so
226
00:32:01,629 --> 00:32:07,649
even from geometry can see that so to just
keep on doing this process so you will be
227
00:32:07,649 --> 00:32:17,419
ending up with the smaller and smaller square
let me describe this first so we want to find
228
00:32:17,419 --> 00:32:25,479
the side of the square which will be the sum
of two squares so abcd and bef are the two
229
00:32:25,479 --> 00:32:35,009
squares we consider so the second square befc
is first split into three parts that is what
230
00:32:35,009 --> 00:32:37,729
one third to understand and
231
00:32:37,729 --> 00:32:49,960
the third part you further divided into 3
ok so you this is further divided into 4 parts
232
00:32:49,960 --> 00:32:59,220
1/3*4 ok so you just place all this in 4 and
these 4 you just place here so this goes there
233
00:32:59,220 --> 00:33:11,159
and occupies so in this square apqr this is
void here at this point so if you say that
234
00:33:11,159 --> 00:33:19,739
the side of the square is going to be so 1+1/3+1/3*4
so there is a certain void and that has to
235
00:33:19,739 --> 00:33:29,249
be sort of subtracted and how is this value
corresponding to the void here that i will
236
00:33:29,249 --> 00:33:32,009
show in the next slide this portion
237
00:33:32,009 --> 00:33:41,019
is 1/3*4 because one third of it and this
is divided into 4 that is going to be this
238
00:33:41,019 --> 00:33:51,529
distance so the area of this void is 1/3*4
square so i remove a small strip from this
239
00:33:51,529 --> 00:33:57,609
so that the small strip corresponds to this
area so this is how i post the problem suppose
240
00:33:57,609 --> 00:34:05,869
a strip of breath b is consider so two strips
basically one strip along the side and the
241
00:34:05,869 --> 00:34:14,540
another is this is this strip which i mark
here so 2b*1+1/23+this-bsquare so this will
242
00:34:14,540 --> 00:34:18,500
be the left hand side and if equate
243
00:34:18,500 --> 00:34:27,980
so if ignore these square so you can easily
see so b is 1/3*4*34 so this again an approximation
244
00:34:27,980 --> 00:34:34,840
because i have ignored b square so getting
this estimate and this can be extended at
245
00:34:34,840 --> 00:34:47,280
all levels ok so now this b happens to be
1/3*4 so at the next level it is 1/3*4*34
246
00:34:47,280 --> 00:34:53,630
square kind of thing and so on and so forth
so in this can be extended so the expression
247
00:34:53,630 --> 00:34:59,180
that is given in the sulbasutras so very interesting
expression in the sense that you will find
248
00:34:59,180 --> 00:35:00,490
3 hear
249
00:35:00,490 --> 00:35:07,640
the same 3 appearing added with 4 and then
3 4*34 and next term i think will be 3*4*34*1154
250
00:35:07,640 --> 00:35:18,320
or something like that and this can go on
and on ok so this is sort of rational ahh
251
00:35:18,320 --> 00:35:28,580
approximation for the shirt so which will
be recurring so we saw in the previous slides
252
00:35:28,580 --> 00:35:35,840
so when this problem of transforming a square
into a circle we had the expression for the
253
00:35:35,840 --> 00:35:43,160
radius to be radius is a/3*2+root2 and how
did they find out root 2 that
254
00:35:43,160 --> 00:35:50,060
also we saw so this is what we saw the radius
is this so if you sort of impose the constraint
255
00:35:50,060 --> 00:35:56,990
as mentioned earlier that this circle has
to have the same area of the square so which
256
00:35:56,990 --> 00:36:04,280
was transformed then we have the equation
pi r square=4a square right so we took the
257
00:36:04,280 --> 00:36:10,600
side to be 2a and that should be pir square
as we understand today so what has been given
258
00:36:10,600 --> 00:36:21,670
as r is this expression so if we use the value
of root 2 which has been shown by the himself
259
00:36:21,670 --> 00:36:22,670
then the
260
00:36:22,670 --> 00:36:28,060
value of pi do not have to be approximately
this ok in this prescription which has been
261
00:36:28,060 --> 00:36:40,910
given so i discussed about 2 root a similar
thing can be done for root 3 also so we can
262
00:36:40,910 --> 00:36:51,960
have a similar geometrical construction so
the expression will be something 1+2/3+1/3*5-1/3*5*52
263
00:36:51,960 --> 00:36:59,920
and so on so forth i think this should be
ahh quite clear from the description that
264
00:36:59,920 --> 00:37:06,690
was given for root 2 it is very similar ahh
diagram so where in you have three
265
00:37:06,690 --> 00:37:16,640
squares considered see abcd behc and then
efgh we have to add two thirds of that on
266
00:37:16,640 --> 00:37:23,680
both side and then that is why we have 2/4
and then one fifth of its so that this create
267
00:37:23,680 --> 00:37:28,080
such void and by formulating which is similar
to the equation because describe you will
268
00:37:28,080 --> 00:37:44,350
get 2 3 so this has been stated by in fact
so we have the inverse problem so earlier
269
00:37:44,350 --> 00:37:51,260
we discuss the problem of transforming a square
into circle if we invite the problem for you
270
00:37:51,260 --> 00:37:52,870
have a circle so that has
271
00:37:52,870 --> 00:37:58,920
been transformed into a square and for that
we have an express of this form which is given
272
00:37:58,920 --> 00:38:13,480
in
the sulbasutra all of them refer to diameter
273
00:38:13,480 --> 00:38:26,590
so
so make it into a divide by a so 29 so you
274
00:38:26,590 --> 00:38:38,030
divide further by 129 once can see that that
this is exactly the inverse of that and all
275
00:38:38,030 --> 00:38:43,870
the numbers will become evident so i will
just leave this and i will proceed to other
276
00:38:43,870 --> 00:38:47,860
topics so the form is something which is very
interesting that is what i want to tell once
277
00:38:47,860 --> 00:38:49,570
more 1/8 1/8
278
00:38:49,570 --> 00:38:54,970
and 29 and this very interesting form i think
you can see the rational perhaps once you
279
00:38:54,970 --> 00:39:03,680
study this one does not know whether they
but anyway one of the one of the ways is geometrical
280
00:39:03,680 --> 00:39:12,790
way the other is other way all that we find
is this interesting expression in this sulbasutras
281
00:39:12,790 --> 00:39:19,640
so now i move on to another topic for which
so all this mathematical rules have been invented
282
00:39:19,640 --> 00:39:23,860
by the sulbakara so this is what is called
citi as i was
283
00:39:23,860 --> 00:39:30,861
mentioning repeatedly so this citi is basically
a alter actually say altar ok so where in
284
00:39:30,861 --> 00:39:43,710
lot of bricks etc are put together and a certain
platform is created so cit so this is how
285
00:39:43,710 --> 00:39:52,950
the derivation the word citi goes in fact
for those who are more interested in knowing
286
00:39:52,950 --> 00:40:03,550
the details with citi word has been defined
in the ok so this sacrificial alter are primarily
287
00:40:03,550 --> 00:40:17,260
fro 2 purposes one is for the other is part
of ok both in where in you have various so
288
00:40:17,260 --> 00:40:21,260
one will be in the form of circle the other
is in the form of semicircle the other will
289
00:40:21,260 --> 00:40:25,740
be in the form of square so the area of all
the three has to be same and that is how it
290
00:40:25,740 --> 00:40:34,600
is sort of constructor any way and there are
various means that which is desired and action
291
00:40:34,600 --> 00:40:43,970
which is performed to fulfil a certain desire
so all these have been prescribed to be performed
292
00:40:43,970 --> 00:40:54,050
in citis of difference shapes the it will
be in the form of isosceles triangle of rhombus
293
00:40:54,050 --> 00:41:10,260
ciiti in the form of a certain kind of vessel
ok so in the form of water jar so that is
294
00:41:10,260 --> 00:41:17,780
one thing the other interesting part which
one finds even the vedas is so a particular
295
00:41:17,780 --> 00:41:23,580
person so this vedic please performs the certain
on a particular year suppose you want to performs
296
00:41:23,580 --> 00:41:30,490
in next year so then they say so the height
of the alter has to increase see we have this
297
00:41:30,490 --> 00:41:39,530
mantra so in this thithi basically how 5 layers
so the numbers of bricks in a particular layer
298
00:41:39,530 --> 00:41:40,530
will
299
00:41:40,530 --> 00:41:45,980
be 200 so this is one constrain which is set
the second constrain will be the area of this
300
00:41:45,980 --> 00:41:55,950
the whatever be whether it is so you have
a certain area and the area is basically measured
301
00:41:55,950 --> 00:42:01,750
the person height so that also will be fixed
so this si the one constrain of the area the
302
00:42:01,750 --> 00:42:09,520
second constrain is 200 bricks and the third
thing which is prescribed is so 1000 bricks
303
00:42:09,520 --> 00:42:10,520
have to be
304
00:42:10,520 --> 00:42:15,800
there so which means automatically there will
be 5 layers ok so 200 in each layers so far
305
00:42:15,800 --> 00:42:20,860
it have stability of these 3 should have bricks
are arranged in alternatively so the same
306
00:42:20,860 --> 00:42:24,770
kind of bricks which is arrange all of them
will collapse so therefore that we will see
307
00:42:24,770 --> 00:42:32,140
little later now what he says is means you
have to perform it with 1000 bricks in a first
308
00:42:32,140 --> 00:42:40,380
year so next time if you want to perform then
it says third time if you want so it
309
00:42:40,380 --> 00:42:48,220
goes like that this is also found in vedas
as 2 the purpose for which a particular citi
310
00:42:48,220 --> 00:42:53,770
has to be done for instance if you desire
a large number of cattles then you perform
311
00:42:53,770 --> 00:43:00,050
this you cannot conclude with that is a different
thing but this means enemy ok so not well
312
00:43:00,050 --> 00:43:01,970
wisher so these are these are various prescription
desirous of having so large area designing
313
00:43:01,970 --> 00:43:03,080
current position today for various purposes
then as i was
314
00:43:03,080 --> 00:43:06,970
mentioning earlier so this height of the citi
so they say perform it for the first time
315
00:43:06,970 --> 00:43:12,420
then it says third time so this is how the
prescription goes in vedas ok then it also
316
00:43:12,420 --> 00:43:16,730
says sort of shape image ok usually suppose
you have a certain ideal is called ok an image
317
00:43:16,730 --> 00:43:21,250
of something so means so you you create the
alter so this so does not refer to age
318
00:43:21,250 --> 00:43:26,620
means bird which fly ok so you have to construct
the alter in the form of a bird ahh so this
319
00:43:26,620 --> 00:43:31,160
is set of prescription which one finds in
this so what is this bird so there are other
320
00:43:31,160 --> 00:43:42,120
statement which are found in various brahmana
so i am just decide a couple of them and then
321
00:43:42,120 --> 00:43:47,560
proceed further if comes down quickly something
take up so which it wings spread ok so it
322
00:43:47,560 --> 00:43:52,760
comes down quickly bounds on something graph
and then proceed so it is a
323
00:43:52,760 --> 00:44:01,880
sort of metaphorical description so once you
perform the sacrifice so as it comes and takes
324
00:44:01,880 --> 00:44:07,760
it so to all your wishes will be fulfilled
and then that is kind of description so the
325
00:44:07,760 --> 00:44:09,600
one who hates you once you perform this so
this enemies will also be sort of finished
326
00:44:09,600 --> 00:44:15,280
something like that ok ahh in this connection
so various measures have been specified so
327
00:44:15,280 --> 00:44:18,620
from very small to purusa the angula is one
the small dimension and what is
328
00:44:18,620 --> 00:44:29,570
angula so it says constituted angula and you
can also specify in terms of tila so which
329
00:44:29,570 --> 00:44:34,880
is much smaller unit so this is 34 tila and
conclude angula and then this goes on this
330
00:44:34,880 --> 00:44:41,330
table if 10 angula makes see all that has
been very clearly stated so that will be in
331
00:44:41,330 --> 00:44:45,900
fact usually people say okay so that will
be roughly angula so this si how it goes and
332
00:44:45,900 --> 00:44:51,770
then it goes up to a purusa so it starts with
angula and then goes up to purusa purusa measn
333
00:44:51,770 --> 00:44:52,770
a human being the
334
00:44:52,770 --> 00:44:59,600
height of human being this measures so if
you just take this angula and then so if you
335
00:44:59,600 --> 00:45:06,110
see that so everything is with reference to
2 purusa ok so finally the measurements will
336
00:45:06,110 --> 00:45:15,260
be given in terms of purusa larger measurements
so how much should be the width and breadth
337
00:45:15,260 --> 00:45:21,280
of vedic the entire sacrificial place ground
so they will all be specified in terms of
338
00:45:21,280 --> 00:45:25,470
purusa so if you are the performer then your
height will be measured and the vedi will
339
00:45:25,470 --> 00:45:26,470
be
340
00:45:26,470 --> 00:45:27,640
constructed based on that it now i quickly
ran through a few slides wherein ahh the shapes
341
00:45:27,640 --> 00:45:30,060
of various bricks have been given in great
detail for all the measurements etc i states
342
00:45:30,060 --> 00:45:34,520
her i will not spend much time here this for
instance if you want to construct itself of
343
00:45:34,520 --> 00:45:42,120
various types so one particular have described
here in this slide so there are several types
344
00:45:42,120 --> 00:45:48,450
of bricks 1 2 3 bricks so we can see this
one half of it and therefore you have this
345
00:45:48,450 --> 00:45:50,740
root 2 times and one-
346
00:45:50,740 --> 00:45:55,510
half again ok so this is one set of bricks
if you put them together so you get another
347
00:45:55,510 --> 00:46:02,390
kind of a shape so this will b5 is called
hamsamukhi so now slowly you can see so this
348
00:46:02,390 --> 00:46:07,360
is the body of the syena and this is the head
of the syena so you can see so this picture
349
00:46:07,360 --> 00:46:17,860
this is what shown earlier so this is the
head so this is a body this is a wing
350
00:46:17,860 --> 00:46:24,600
and this is called the we can see that so
it is made up of basically 5 types of bricks
351
00:46:24,600 --> 00:46:30,640
total number of bricks as i was mentioning
should be 200 so this is a constraint so head
352
00:46:30,640 --> 00:46:38,580
will have 14 bricks body will have 46 bricks
wings 108 tail 32 the total so these are the
353
00:46:38,580 --> 00:46:43,360
5 types of bricks see all that has very very
clearly stated in the sutra so 32 times will
354
00:46:43,360 --> 00:46:50,060
go in creating the tail of this 108 so all
that has been stated so this is
355
00:46:50,060 --> 00:46:55,590
the second layer the second layer will be
such that no two tail will be exactly fitting
356
00:46:55,590 --> 00:46:59,330
see they will be so start of interest is will
be filled in second layer and this also has
357
00:46:59,330 --> 00:47:03,370
200 but there are 5 difference thing head
has only 10 here and body has 48 in the previous
358
00:47:03,370 --> 00:47:05,230
if you see it has 14 and 46 so this is made
up of only 4 types of bricks so these four
359
00:47:05,230 --> 00:47:06,620
types they constitute the second layer the
third layer will be again the first layer
360
00:47:06,620 --> 00:47:07,620
fourth and fifth
361
00:47:07,620 --> 00:47:10,950
layer so this is how this is constrain so
regarding this is fabrication of brick also
362
00:47:10,950 --> 00:47:14,390
there are some specifications in the sulvasutras
see these are all some interesting things
363
00:47:14,390 --> 00:47:20,900
so it says extraction created on various so
in that sense they uses so so in making this
364
00:47:20,900 --> 00:47:25,250
brick we have to add various extractions so
it is primarily to ahh add more strength to
365
00:47:25,250 --> 00:47:34,480
the bricks so then is he says something which
is repeated in every sutra so means to add
366
00:47:34,480 --> 00:47:35,530
more strength to that
367
00:47:35,530 --> 00:47:42,630
ok so the hair of goat so it is like today
this fibre reinforce know there are they are
368
00:47:42,630 --> 00:47:47,330
the fibre ok so various things which are added
and it also specifies that once you fabricate
369
00:47:47,330 --> 00:47:55,320
the brick and it gets dry so to the dimension
of the brick will be reduced ok so it says
370
00:47:55,320 --> 00:48:02,430
one thirty of the size will be reduced some
kind of prescription which has been given
371
00:48:02,430 --> 00:48:07,290
here and therefore in trying to create an
altar you have to consider the factor also
372
00:48:07,290 --> 00:48:08,590
in talking so this is
373
00:48:08,590 --> 00:48:16,780
was states and constructing so you have to
consider how much gap you have to create so
374
00:48:16,780 --> 00:48:23,970
that i mean you fill those gap together so
that the dimension is order met with venue
375
00:48:23,970 --> 00:48:30,260
constructed the whole alter ok then certain
other subscriptions see when you construct
376
00:48:30,260 --> 00:48:41,120
so you do not give much gaps otherwise the
area of criteria which has been stated for
377
00:48:41,120 --> 00:48:46,100
will not be fulfilled then so what is this
veda that i am talking about
378
00:48:46,100 --> 00:48:57,230
between the two layers whatever be the joint
so then he says say this is interesting in
379
00:48:57,230 --> 00:49:04,830
the sense that see when you create certain
structure so you should see to it that more
380
00:49:04,830 --> 00:49:10,490
or less the same kind of material used and
used a completely different material then
381
00:49:10,490 --> 00:49:15,640
this will not stick with that and therefore
he says is basically brick made out of clay
382
00:49:15,640 --> 00:49:21,530
so is not made out of clay would not be using
here so all these prescription are been here
383
00:49:21,530 --> 00:49:22,530
so
384
00:49:22,530 --> 00:49:25,780
with the few observations will end our task
on veda and sulbasutras as you would have
385
00:49:25,780 --> 00:49:33,110
seen the primary purpose for which the sulbasutra
text came with existence is to see that you
386
00:49:33,110 --> 00:49:38,940
have very clear rules which are stated which
will facilitate as in constructing all those
387
00:49:38,940 --> 00:49:45,130
constructing is fire places on altars of different
sizes and shapes so and in this connection
388
00:49:45,130 --> 00:49:49,060
both construction as well as transformation
ok so if you construct a certain and you will
389
00:49:49,060 --> 00:49:50,060
have
390
00:49:50,060 --> 00:49:57,600
another thing which will be of different shapes
we should have the same and therefore this
391
00:49:57,600 --> 00:50:09,730
is equivalent to transforming one into the
other so this is the primary purpose but this
392
00:50:09,730 --> 00:50:15,620
was not the purpose of geometry got developed
civilization and i also demonstrated that
393
00:50:15,620 --> 00:50:20,490
how baudhayana would have arrived at the different
triplets which has been mentioned by him and
394
00:50:20,490 --> 00:50:31,740
how the proof of these sutras are implicitly
involved in the procedures which have been
395
00:50:31,740 --> 00:50:44,680
delineated for various construction or transformation
of one figure to another figure so this was
396
00:50:44,680 --> 00:50:50,400
demonstrated and regarding the antiquity of
this baudhayana sulbasutra see this another
397
00:50:50,400 --> 00:51:03,000
thing you need to remember so in this tradition
we see that it has been an oral tradition
398
00:51:03,000 --> 00:51:11,230
and therefore any proof would have been combined
by the not explicitly available in the sutra
399
00:51:11,230 --> 00:52:37,050
systems and regarding antiquity so we find
various triplets in this babylonian tablets
400
00:52:37,050 --> 00:53:04,820
but
401
00:53:04,820 --> 00:55:56,200
there is no general statement like the baudhayana
theorem in any of these other conditions so
402
00:55:56,200 --> 00:56:02,360
regarding pythagoras so pythagorean theorem
so many careful people they use pythagorean
403
00:56:02,360 --> 00:56:07,050
the pythagoras or directly involve or not
we do not know and therefore they call it
404
00:56:07,050 --> 00:56:16,560
pythagorean and this sulbasutra text are primarily
meant for assisting the vedic please ok that
405
00:56:16,560 --> 00:56:25,720
is the purpose of this so let me reiterate
that and but looking at this we also are able
406
00:56:25,720 --> 00:56:26,720
to get a
407
00:56:26,720 --> 00:56:33,570
picture of the kind of the mathematics which
was involved and how it got developed so in
408
00:56:33,570 --> 00:56:40,540
the antiquity at least 2500 years from now
so much before that and we also see the use
409
00:56:40,540 --> 00:56:52,170
of fraction 1/3+1/3*4 so all that they are
all very interesting things without found
410
00:56:52,170 --> 00:57:00,040
and the value of root 2 is remarkable accuracy
and he also saw the use of algebra which is
411
00:57:00,040 --> 00:57:01,040
involve for instance
412
00:57:01,040 --> 00:57:05,760
suppose you wanted to find out the construction
in katyayana sulbasutra so it impossible for
413
00:57:05,760 --> 00:57:16,710
us to find out so without the alzebra involve
so this prescription cannot be given also
414
00:57:16,710 --> 00:57:26,140
getting into so we have various shape of alter
and so on as regards this citis so it has
415
00:57:26,140 --> 00:57:40,190
been found that around 200 bce so we find
construction so in the excavations found so
416
00:57:40,190 --> 00:57:42,710
these are the references thank you