What is Order of Rotational symmetry? Video Lecture | Mathematics (Maths) Class 7 (Old NCERT)

hello friends this video on symmetry
part 12 is brought to you by exam for
calm no more fear from exam so let us
look at this and see if it has a
rotational symmetry or not so we have
taken the English alphabet B and this
red dot shows the center of rotation so
we are going to rotate be around this
point perfect
now what would happen if I rotate it by
90 degrees in the clockwise direction if
I do that this is the next position that
I get is it identical to the original
position no okay let me further rotate
it by 90 degree that means basically
from the original position we are
rotating it by 180 degrees so what would
happen so from original position 180
degree so you get this shape is this
identical to the previous to the
original one no now let us rotate it
further by 90 degree that means 180
degree plus 90 degree which would be
nothing but 270 degrees so if you rotate
it by 270 degrees the shape is like this
again is this identical to the original
shape no now if you further rotate it by
270 degree plus 90 degree which is 360
degree so you are basically rotating the
original object by 360 degree so what
happens you get this is this the same as
the original image the original object
yes so what did we observe between 0
degree and 360 degree how many identical
positions do you find so how many
identical position did you see this is
the only identical position that you
found right so this is the common
scenario which happens with every object
that when you rotate an object by 360
degree it comes back to its original
position so do you think that this
object has rotational symmetry not
really because this is this this is
something which happens with every
object so we really can't say
you know this object has something
different but this object shows only one
identical position between zero Degree
about 360 degree now how do we know that
which object has how much of rotational
symmetry so for that we introduce a
concept of order of rotation now for
example in this case this object has
only one identical position right that
means between zero degree and 360 degree
how many identical position only one
identical position so now looking at the
number of identical positions between
zero degree and 360 degree we decide the
order of rotation of an object and this
order of rotation tells us how much
rotational symmetry an object possess so
order of rotational symmetry is the
number of positions in which the object
looks exactly the same in one complete
turn ok so when we say one complete turn
that means 360 degree so you rotate an
object for different different angles
till it is 360 degree and then in that
entire journey look for the number of
positions where the object looks the
same so let us understand in the example
let us take this example ok so here you
have three arrows inside this circle now
again let us mark a point a let us say
we mark this point as a just for our
reference now what do we do let us say
that we rotate this entire shape in the
clockwise direction by 120 degrees now
why am i rotating it by 120 degree that
is because if you look at this picture
very closely you have three different
arrows now if you assume it to be a
circle so how can you and if this is
your centre of rotation right if this is
your centre of rotation and you have
three different arrows now I want that
after one rotation this arrow should
shift here so if we want one arrow to
get shifted by one place in that case
since there are three arrows so each
good sub in an angle of how much at the
center so these are the three arrows so
each arrow will subtend and angle at the
center and the total angle is 360 degree
so each angle would be how much that it
would be 360 degree divided by three
which is equal to 120 degree so each of
this angle is 120 degree so that means
if we rotate it by 120 degree then only
the arrows will move by one one position
so what happens when we rotate it by 120
degree in the clockwise direction so
this is what we get so in this case what
happened basically this point a actually
moved somewhere here so you see the
point E has actually moved descent but
when you look at this image this image
is exactly the same as the original
image right forget about the point e
that that we have put just for our
reference but otherwise this image is
exactly the same as the original image
then it was do one thing let us rotate
it further in the clockwise direction by
120 degree so that is 120 plus 120 which
is 240 degrees so what do we see so when
you rotate it by 240 degrees here we see
that even though the point a has shifted
here but overall the image still looks
the same so when you look at all the
three images you see that all of them
are exactly identical now then you
repeat it further by one more 120 degree
that is 240 plus 120 that is 360 degree
what happens you see that you come back
to this original position where Point a
comes here again so this is like a cycle
but in this if I ask you that between 0
degree and 360 degrees because this is
one complete rotation right you started
from here 128 thank you for 120 again
120 then you reach the original position
this is one complete site one complete
rotation so in one complete rotation
between zero degree and 360 degree how
many identical positions did you come
across so you came across three
identical positions right so we see that
the order of rotational symmetry or the
order of symmetry for this image is
three so when we see that the order of
rotational symmetry for this particular
object is three that means if you rotate
that object there are three identical
positions which come in one complete
rotation rotation so that means by the
time you rotated by 360 degree you come
across three identical positions of that
object so the order of symmetry for this
particular object is three now all
objects you have seen that all objects
when rotated by 360 degree after 360
degree it comes back to its original
position so all objects have so the
number of identical positions between 0
and 360 degree minimum it should be one
right so all objects have a rotational
symmetry of order one so uniqueness is
when the order of rotational symmetry is
greater than one and that is when we say
that the object possess or tation and
symmetry that means if you talk about
the letter B so we had discussed about
the rotational symmetry of letter P in
the previous slide right so we saw that
there is just one identical position
between 0 and 360 degree so we see that
the order of rotational symmetry for B
is 1 and every object behaves the same
way as B even the peacock you remember
in the the peacock image also when you
rotate it by 360 degree it comes back to
its original position so the order of
rotational symmetry was 1 so the
uniqueness is when we talk about objects
with rotational symmetry great
because only then we are saying that
there are multiple instances when there
are identical positions even before
completing 360 degree so I think with
this example your concept of rotational
symmetry and order of rotational
symmetry must be clear even if it is not
clear please rewind in half and just try
to understand the concept thank you
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