hi welcome to math antics we've learned
a lot about geometry so far but there's
one really important geometric shape
that we still need to cover and that
shape is a surgery since the invention
of the wheel circles have been extremely
important to all humanity grogg make
wheel
thanks Grogg in fact you probably see
circles almost everywhere you turn but
mathematically what is a circle well in
geometry a circle is defined as the set
of all points that are equidistant or
the same distance from another single
point and the best way to understand
what that means is to see it in action
so here's a single point to start with
and now let's start drawing points that
are equidistant from it this point is a
foot away to the right now let's make
another point a foot away but in another
direction let's say up here now let's
make another one also a foot away but in
another direction right here now let's
make another right here whew I'm getting
tired but do you see what's happening
the more equidistant points we add the
more the pattern looks like a circle and
that's why a circle is defined as the
set of points that are equidistant from
a center point but of course we usually
don't see it as a set of points because
there's infinitely many of them so they
form a continuous circle okay
now let's learn about the parts that
make up a circle first of all we have
the original point that we started with
that's called the center or the origin
of the circle next we have the distance
that we use to draw all of the
equidistant points that form a circle
that distance is called the radius the
radius is important because it's the
distance from the center of a circle to
any other point on the perimeter of that
circle and even though a circle only has
one radius dimension you can draw as
many radius lines as you want to usually
you'll
only see one radius line drawn since
it's the same length no matter where you
draw it
another important circle dimension is
called the diameter the diameter is the
distance across the circle if you start
at one point on the circle and then draw
a line straight through the center to
the other side
that distance is the diameter as you can
see the diameter is really just the same
as two radius lines drawn in exactly
opposite directions so for any circle
the diameter is always exactly twice as
long as the radius all of the
equidistant points we drew combine to
form the perimeter of the circle
remember that perimeter is just the
distance all the way around a shape but
because a circle is a special shape the
perimeter of a circle gets a special
name it's called the circumference the
circumference is the distance all the
way around a circle we're going to learn
how to calculate the circumference of
any circle in the next video
we'll also learn how to calculate the
area of any circle but before we can
learn those things we first need to
learn about pi wrong mate pi
sorry grog not that kind of pun in math
the word pi which is spelled P I refers
to a very special number in fact it's so
special that it gets its own symbol this
Greek letter here is the symbol for the
number pi but if pi is just a number why
don't we write it like that why do we
need to use a special symbol for it it's
a good question and I'll get to that in
just a minute but first let's learn what
pi really is by seeing how it relates to
a circle it turns out that pi is really
a ratio now if you're not sure what a
ratio is you can watch our video about
them but basically a ratio is just a
relationship between two numbers that's
written like a fraction hi is the ratio
of two different distances on a circle
it's the ratio of the distance around a
circle to the distance across a circle
and what do we call those two distances
yep the circumference and the diameter
so pi is the relationship of the search
cumference to the diameter and as you'll
see in a minute because pi is a ratio
it's the same number for any circle no
matter how big or small okay but what
number is it what's the value of pi well
to figure that out
have a look at these two circles one big
and one small
we're going to imagine that our circles
diameters are flexible like a piece of
string and that we can wrap them around
the outside edges circumference --is of
the circles so for each circle if we
start at the top and wrap the diameter
around the circumference we see that one
diameter is not enough to go all the way
around so let's get another diameter and
keep going where the first diameter
stopped hmm two diameter still isn't
enough to go all the way around it looks
like we're gonna need to get a third
diameter and keep going oh so close
three diameters is almost enough but it
looks like we're gonna need just a
little bit more to form a full
circumference that little bit more turns
out to be about 0.14 diameters that
means that it takes 3.14 diameters to
equal one circumference for any circle
big or small so the value of pi is
always 3.14 well okay pi is a little
more complicated than that
3.14 is really just pi rounded off to
two decimal places and we actually have
to ram a PI off because it's a type of
number that's called irrational an
irrational number has decimal digits
that never end and never repeat grog
confused yes
irrational numbers are confusing but
seeing some more of PI's decimal digits
will help you understand what I mean to
be more precise pi is 3.14159 two six
five three five eight nine seven nine
three two three eight and the decimal
digits just keep on going forever
without repeating pretty amazing huh but
the good news is that saying PI as 3.14
is usually close enough for most math
problems
so that's all you really need to
memorize and that's why we use a symbol
for pi in equations we could write PI
with just two decimal places or we could
write it with five decimal places to be
more accurate or we could write it with
hundreds of decimal places to be super
accurate or we could just use the symbol
to represent the true value which is
infinitely accurate okay
turn on this video we learned what a
circle is and we've learned about the
important parts of the circle the center
the radius the diameter and the
circumference we've also learned about a
very special number called pi pi is the
ratio of a circles circumference to its
diameter and its value is about 3.14 no
matter what size the circle is in our
next video about circles we're going to
learn how we can use the number pi to
find the circumference and the area of
any circle and even though there's not
much math you can actually practice in
this section don't worry there'll be
lots of practice problems in the next
section to make up for it
thanks for watching math antics and I'll
see you next time mmm draw good at math
learn more at math antics calm