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