Today we are going to have a ball on Michaels toys.
We're gonna make a pi tape today also known as a diameter tape. Now as we know
every circle has a diameter some length that goes all the way across between two
points on opposite sides and the diameter times pi will give us the
distance around the circle the circumference or to put it another way
the circumference of a circle divided by pi will give us the diameter. If you know
one you know the other so if you wrap a measuring tape around a circular object
and you look at its circumference you can be safe knowing that here's zero for
every pi units 3.14 boy it's like a tenth of an inch I really really wish
that I had a decimal Imperial measuring tape but I don't so just bear with my
inaccuracies here. Let's say that pi is like here okay there's pi inches. Now two
pi is 6.28. That's about six and a third eyeballing there's two
pi. 3 pi is 9.42 so we'll just go a little shy of nine and a half.
There's 3 pi. If I wrap a measuring tape around a circular object and it's
circumference is pi units well that means it's diameter is one of those
units. If two pi units go around its diameter is two. If three pi units go all
the way around its diameter is 3 and so on. Now what this means is that you need
to take the circumference of the circle and then divide it by pi which is an
irrational number. It's got a lot of digits in it and you need to use a lot
of them to be precise but wait what if we didn't want to do any mathematical
figurine. What if we just had a measuring tape like this and rather than having
units listed this way it instead counted off pi units of length so we started at
0 and then one was here and 2 was here and 3 was here and so on well then we
could wrap the tape around the object read the number and although the tape
was around the circumference what we saw would be the diameter.
Such a thing is called a pi tape or diameter tape and what do you know this
measuring tape happens to be one.
if I flip it over to the other side you will
see that it has whoa okay first of all look how close I was. The integers you
see on the tape on the other side are pi inches and my guesses almost line up
perfectly. This is totally I'm not even joking
that's well it's really just luck but anyway the other side of this tape is
measured off in chunks of Pi inches so when you put the other side of the tape
around an object like say this cylinder I will see that its diameter is about
6.1 inches. Let's use the other side of the tape to
see what its diameter is when measured as an actual diameter oh look at that
we're just over six inches but why buy a diameter tape when you could make one?
Let's do that today. First things first we need to make ourselves a template so
what I'm gonna do is take this sheet of paper and I'm going to measure out PI
centimeters. The PI tape that I own is in imperial units but no one wants to
use those. Now for metric here's a nice shot of my bald spot
you know let's uh let's cut to a better angle. Perfect. Okay so here is our
beginning our zero point and PI centimeters will be 3.1
millimeter just a little shy of half a millimeter over that mark so I'll put it
here. Obviously if you want more precision you
can just well buy a mechanically made Pi tape but what's the fun in that? There we
go. So now we're gonna use this template to mark off every PI centimeters on our
tape you can use anything you want for a tape last year I made a PI tape using
actual masking tape I pulled out a long piece and then stuck another long piece
underneath it and precisely closed them and stuck them together so that no
sticky parts were left exposed it was not easy. Today I'm going to use
something a little easier I'm going to be using drywall tape which isn't sticky
all by itself but I think it's a little bit too wide I want to cut this in
half come with me
okay now that you have the physical tape that you're going to be putting your PI
centimeter marks on let's put them on. Luckily we already have a template that
shows us how far PI centimeters is. We just want to line up our tape with that
line and Mark off equal sections but I'm not gonna start at the very end of the
tape I'm gonna give myself a little bit of room and you'll see why later. Let me
grab a pen oh here we go. This is where we start and this is PI centimeters
further away now from that mark PI centimeters away is here and I will
continue making these marks until I run out of tape which will be very
monotonous for me but extremely exciting and time lapse for you.
Alright so I have made a mark every PI centimeters
along this tape. The next step is to label them so I'm gonna go ahead and
give myself a zero there and then a one here and then a two three four five six
seven and so on. The point being that when I put this pi
tape around an object the number that I see in this case six will tell me not
the circumference but the circumference divided by pi so the diameter. That is a
circle with a diameter of six centimeters. I will put these numbers on
now while you watch another montage.
How lucky is that that this tape will allow me to measure things of a diameter
up to 60 centimeters. That's great this is the longest PI tape I've ever made so
let's have some fun and test out how it works. I have here a metal ring that is
15 centimeters in diameter I measured earlier. What I'm gonna do is put this
ring right on the zero of the tape. Let's roll our ring without slipping and boom
15. 15 centimeter diameter. Thanks PI tape actually I take that thanks back because
we just rolled the shape but what if we can't roll it. If I wrap the tape around
look what happens. I know that this ring is 15 centimeters in diameter. It's
precision made it's a physics teaching tool for rotational inertia but my PI
tape is telling me that it's more than 15 centimeters in diameter. It's
somewhere around maybe I don't know 15 and a fifth or a sixth or something
what's going on? What went wrong? Well the problem is that by putting this tape
around the ring we're no longer measuring the diameter of the ring we
are now measuring the diameter of the ring plus the width of the very tape
we're using to measure it and that might seem like it wouldn't put us off by as
much as we are but we have added the thickness of our tape twice once to the
top and once to the bottom and the circumference the distance around is
that thickness times pi so we're actually noticing a circumference larger
by a factor of twice the thickness of our tape times pi so more than three
What that means is that when we wrap the tape around something we need a
different zero point that subtracts out the extra circumference added by putting
a PI tape around it because this ring is very well
made I'm gonna go ahead and use the ring as our template so the zero for wrapping
is right there. Let's make this clear to ourselves this is the zero for wrapping
and this one is for rolling. Now the moment of truth let's put our PI tape to
work on the cylinder we used earlier. Now in centimeters using a meter stick its
diameter is 15.4. Now let's take our PI tape wrap it around and see what
we get. Look at that beauty. I've wrapped the
tape around. Our wrapping zero is right there and sure enough it's a little
short of halfway between the 15 and the 16. 15.4 centimeter diameter. Great
work PI tape. So now you are equipped to be well bit of a superhero. The next time
someone says oh I just really wish I knew what the diameter of this thing was
you can say hey chill out I got you and you know that's really what friendship
is about. That's really what life is about and that's really what love is all
about. And as always