Unveiling The Remarkable Discovery Of Pi By A Genius - Prepare To Be Amazed!

Summary

In this fun and educational video, the host explains how Archimedes discovered the value of pi using a simple method with a wheel. The video demonstrates how to measure the circumference of a circle and its relationship to the diameter using a homemade wheel from a cereal box. By rolling the wheel and marking its rotation, the presenter shows that the ratio of the circumference to the diameter is approximately 3.14, which is pi. The process highlights how Archimedes made this groundbreaking discovery with basic tools and ingenuity.

Takeaways

• 🌀 Archimedes discovered that the circumference of a circle equals 3.14 times the diameter, which is now known as Pi (π).
• 🎨 The video demonstrates how to visually calculate Pi using a wheel and a straight path.
• ✂️ The creator uses a cardboard cutout from a cereal box to replicate a wheel for the experiment.
• 📏 Archimedes used a simple cartwheel in his experiment, but modern tools like rulers and cutting tools make it easier.
• 🔴 The creator marks an arrow on the wheel to track one complete rotation, allowing them to measure the circumference.
• 🧮 The experiment shows that it takes about 3.14 diameters for the wheel to complete one full rotation, visually explaining Pi.
• 📐 The formula for circumference is confirmed as 2πr (2 times Pi times the radius).
• 📊 The calculated circumference using Pi and the radius matches the measured circumference, confirming the accuracy of the relationship.
• 📕 The creator refers to a book about Archimedes, highlighting his contributions beyond Pi, including the invention of the death ray.
• ✏️ The video encourages viewers to keep practicing math and drawing, with a call to action to subscribe and explore more educational content.

Q & A

Who was the first person to work out the value of pi?

Archimedes was the first person to work out the value of pi by analyzing the relationship between a circle's circumference and its diameter.

How did Archimedes calculate the value of pi?

Archimedes used a wheel, much like a cartwheel, and rolled it along a surface to measure how many times its diameter fit into its circumference. He found that it took about 3.14 diameters to complete one full rotation.

What is the mathematical formula involving pi to calculate the circumference of a circle?

The formula is C = 2πr, where C is the circumference and r is the radius of the circle.

Why is the number pi approximately 3.14?

Pi represents the ratio of a circle’s circumference to its diameter, which is approximately 3.14. This relationship was first observed by Archimedes and later refined through more precise calculations.

What simple materials did the presenter use to demonstrate the concept of pi?

The presenter used a piece of cardboard, scissors, glue, and a circular object like a glass or jar to create a simple wheel for the demonstration.

How did the presenter use the wheel to demonstrate the value of pi?

The presenter marked a point on the wheel, rolled it along a flat surface, and measured how many times the wheel’s diameter fit into its full rotation. The distance was approximately 3.14 times the diameter.

How can we apply the formula 2πr to find the circumference of a circle?

First, measure the radius of the circle (r). Then multiply it by 2 and by pi (3.14) to find the circumference. For example, if the radius is 34mm, the circumference would be 213.52mm.

What tools did the presenter use to ensure accuracy in the demonstration?

The presenter used a compass to draw a precise circle and a calculator to verify the result of the circumference formula.

Why is it important to understand where the value of pi comes from?

Understanding the origin of pi helps clarify its practical applications in mathematics and geometry, showing that it’s not just an arbitrary number but derived from real-world observations.

How did the presenter connect the demonstration to Archimedes' original method?

The presenter highlighted how Archimedes used a wheel in a similar manner, rolling it along a surface to measure the relationship between the circumference and the diameter, a method mirrored in the cardboard demonstration.

Outlines

00:00

🔍 Understanding Pi: The Origins of 3.14

This section introduces the origin of the number Pi (3.14) and how Archimedes discovered that the circumference of a circle equals 3.14 times its diameter. The narrator highlights how math teachers often assume students know this, but rarely explain it. Archimedes, using simple tools like an old wooden cartwheel, made this discovery. The video promises to walk through the process of how he worked it out with a demonstration using modern tools like a cereal box and glue.

05:02

🛠️ Building a Wheel to Calculate Pi

The narrator prepares to recreate Archimedes’ experiment by crafting a wheel from a cereal box. Step-by-step, they demonstrate how to cut and shape the cardboard, followed by marking and highlighting the wheel’s edges for visibility. The process mimics the tools available to Archimedes, showing that even basic items can demonstrate profound mathematical principles. The narrator also encourages viewers to subscribe to the channel for more educational content.

📏 Rolling the Wheel: Discovering the Circumference

In this segment, the narrator uses the cardboard wheel to roll along a flat surface, marking the point where it completes one full rotation. By doing so, they demonstrate how the length of the circumference relates to the diameter, and how this process led to the calculation of Pi. The narrator measures the distance and concludes that the circumference is about 3.14 times the diameter, explaining that this relationship is the basis of the value of Pi.

🧠 Archimedes' Formula: Applying 2πr

Here, the narrator breaks down Archimedes’ famous formula, 2πr, which calculates the circumference of a circle. Using a radius of 34 mm, they demonstrate how multiplying 2, Pi, and the radius results in a circumference of 213.52 mm. A comparison is made between the calculated value and the experimental result, proving that the formula works accurately. The section ends with admiration for Archimedes' brilliance.

🎨 Conclusion: The Genius of Archimedes and the Value of Pi

The final paragraph emphasizes the genius of Archimedes in discovering the value of Pi using simple tools like a cartwheel. The narrator encourages viewers to learn more by purchasing a book on Archimedes and to stay tuned to the channel for more educational videos. They also highlight the importance of practice in mastering drawing, which the channel focuses on.

Keywords

💡Pi (π)

Pi (π) is a mathematical constant that represents the ratio of a circle's circumference to its diameter, approximately equal to 3.14. In the video, it explains how Archimedes worked out that this ratio holds true for any circle, illustrating this using a cartwheel as a practical example.

💡Archimedes

Archimedes was an ancient Greek mathematician and physicist who is credited with discovering the value of pi. The video emphasizes his ingenuity in determining pi using simple tools, like a wooden cartwheel, demonstrating his process through an interactive experiment.

💡Circumference

The circumference is the total distance around the edge of a circle. In the video, the presenter calculates the circumference by rolling a wheel along a straight line and measuring how far it travels in one full revolution. This experiment visually demonstrates the relationship between the circumference and pi.

💡Diameter

The diameter of a circle is the straight-line distance across its center, from one edge to the other. The video explains that pi represents how many diameters fit into the circumference of a circle, with the practical example showing that about 3.14 diameters fit along the wheel’s circumference.

💡Radius

The radius is the distance from the center of a circle to any point on its edge. In the video, the presenter uses the radius to apply the formula for the circumference, 2πr, where 'r' is the radius. This formula is critical in understanding how the value of pi helps in calculating the circumference.

💡Cartwheel

A cartwheel is used as a practical tool in the video to demonstrate the concept of pi. By rolling the wheel along a straight path and marking its progress, the presenter shows how many diameters fit into the circumference, connecting this to Archimedes' discovery.

💡2πr (Circumference Formula)

2πr is the formula used to calculate the circumference of a circle, where 'r' stands for the radius and π is approximately 3.14. The video demonstrates how this formula applies to a real-life scenario, measuring a circle’s radius and multiplying it by 2π to find the circumference.

💡Measuring Tools

Measuring tools, such as a ruler, compass, and calculator, are used in the video to replicate the process of calculating pi. Although Archimedes didn’t have sophisticated tools, the video presenter uses these modern instruments to verify the accuracy of the pi-based calculations.

💡Accuracy

Accuracy refers to the degree of closeness between the calculated value and the actual measurement. In the video, the presenter checks the accuracy of his calculated circumference by comparing it to the actual measurement of the wheel’s travel distance, finding that it closely matches.

💡Practical Experiment

The practical experiment in the video involves cutting out a cardboard wheel, drawing lines to simulate the circle, and rolling the wheel to calculate the circumference. This hands-on approach illustrates how ancient mathematicians like Archimedes might have tested their hypotheses in a simple, observable way.

Highlights

Archimedes discovered that the circumference of a circle equals 3.14 times its diameter.

Archimedes used simple tools like a wooden cartwheel to work out the value of pi.

The demonstration involves creating a cardboard wheel and road to simulate how Archimedes might have experimented.

The circumference of the wheel was measured by rolling it along a straight road.

It was found that the wheel's circumference is approximately 3.14 times the diameter.

The demonstration reveals that pi represents the number of diameters it takes to equal the circumference of a circle.

Archimedes' formula for the circumference of a circle is expressed as 2πr, where r is the radius.

A practical example is used with a radius of 34 millimeters, and the formula calculates the circumference as 213.52 millimeters.

The accuracy of the formula is demonstrated using a calculator and physical measurements.

Pi (π) is explained as the mathematical constant derived from the relationship between the circle’s diameter and its circumference.

The video emphasizes how basic geometric principles can be discovered through experimentation, without sophisticated tools.

The number pi (3.14) is intrinsic to every circle, no matter the size.

Archimedes' methods still form the basis of modern geometry and mathematics related to circles.

The use of cardboard and simple instruments in the demonstration helps visualize abstract mathematical concepts.

The video concludes with a reminder that Archimedes' discovery of pi was based on logical reasoning and observation, a major breakthrough in ancient mathematics.

Transcripts

why does the number pi equal 3.14 and

who first worked it out the answer will

astound you because math teachers assume

you know already but they never actually

explain

now this is archimedes and he worked out

that the circumference of a circle

equals 3.14 times the diameter but how

did he do it let's not talk about it

let's work it out archimedes didn't have

sophisticated tools all he had was an

old wooden cartwheel luckily we have

sophisticated tools like kellogg's

crunchy nut cornflakes

uh what are we gonna do with this we're

gonna

carefully

open it out

because we want the cardboard and i'm

going to draw a line across there

and cut very carefully along that line i

feel really sophisticated you can use a

scalpel and a ruler and a cutting mat

but scissors will do take your time

go all the way to the end try and keep

it as straight as you possibly can

i cut off the ends like that

and i'm going to quickly cut across

there just that good and you can just

see a bit of a line across the top then

we can cut out this big section of the

front of the cornflakes box

you can use any kind of cardboard you

like you want it to be thick enough to

be useful

and thin enough to be nice and easy to

cut out

and then i'm going to get some glue i'm

using prick stick you can use whatever

glue turn it upside down and i'm going

to glue right up

to the edge

like that and then i'm going to stick it

on there like that

and leave that alone and this line here

you can

see it's kind of there's a thickness

there

this is going to be the level of the

road okay so we're looking at the road

sideways along we're gonna get this

wheel

to roll along it like that

so let's make a wheel

now archimedes already had a wheel but

we need to make one and you can draw it

with a compass and you can have

the point right in the center of the

circle and draw it around like that or

if you haven't got a compass to hand you

can use a glass or a jam jaw or anything

round

and draw

all the way around it like that i'm

going to cut this out roughly first and

then i'm going to cut it out very

carefully following around the

circumference of the circle

and while i'm doing this

come down here you'll see a little

subscribe button and if you click that

you will be subscribed to the shoe in a

drawing channel and when you do there'll

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links in the description box below

here we go

and there is going to be our wheel i

think the center is about there maybe

about there

so i'm going to guess that that's the

center

i'm going to get a sharpie pen

and i'll draw a little circle around it

so that's like the axle where the the

axle goes through the wheel

uh through the hole in the wheel and we

put a shadow in there as well

and then we want this is the kind of a

joining timber that joins the whole

wheel together

and then ah behind it we've got these

planks of wood

like this and we'll have another one

there

and another one there

and we can make this look a bit more

realistic if you get a thinner pen you

can

then kind of make it look it's got like

a wooden

effect

we'll have a different kind of pattern

on each plank

to separate them out we can have

something like

that and

something like that and we want one

across the middle as well don't we yeah

that going across there like that and if

you want to be really fancy i happen to

have a gray pen here so i'm going to add

a little bit of shadow

across there if you haven't got a gray

pen you could use a pencil and do

something like that instead just to kind

of add a bit of shadow effect i think

i'm going to shape that in there as well

i think to make it easy and see what's

going on here i'm also going to

just kind of

rub my sharpie pen against the edge just

to kind of highlight the circumference

so that we can see it

as the wheel goes around i'm just kind

of

just marking it so these are all the

tools that archimedes had was a wheel

and a road and he thought let's start

there on the road and he thought what

i'm gonna do is i'm gonna draw

an arrow pointing down

like that and let's color it in red

just so it stands out a bit better he

said let's start right there put the

arrow at the beginning i'm going to use

the pin of my compass as the axle

and i'm gonna

and i'm gonna

and i'm gonna roll this all the way

along the road

until

the arrow points right down again which

is there

and then i'm going to make a mark

okay

so it's gone all the way around once so

that is the length of the circumference

and i wonder if there's any kind of

relationship going on here so let's have

a look let's see

that's one diameter

that's two diameters

that's three diameters and that's four

diameters

so we started at zero

that's one that's two

that's three

and that's four

let's have a look at what's going on

here so if that's four then that is

about three and a half isn't it maybe

there's more there that's 3.25

which means that at 3.25 so there's one

and two then that means that that

is 3.14

and that is where the number pi comes

from it's the number of diameters it

takes for the wheel to travel around one

full

cycle

no one ever told me that at school no

one if they'd have told me that i would

have understood how do i know all this i

wrote the book archimedes the man who

invented the death ray click the links

and go get a copy for yourself and find

out what a genius he really was

so how does this work out the famous

formula algorithm is two

pi

r

equals the circumference okay

so let's see what is the radius and i'm

measuring that and i would say that was

34 millimeters so here

the radius

equals 34

millimeters so

2 pi r means 2

times pi

times

34 millimeters equals the circumference

so let's see what we get here's a

calculator so we'll go 2

times

pi which is 3.14

3.14

times 34 millimeters 34

equals

213.52

millimeters

let's see what we get here we are

210 211 213.5

smack on

213.52 i mean this is not the most

accurate model but i think that kind of

proves

where this whole relationship comes from

so we can say here

that 2

times pi which is 3.14

times 34

millimeters that should be double m

there shouldn't it

equals circumference equals

two

one three point five two millimeters

and this here is two one

three point

five two

millimeters so that is how the

incredibly clever archimedes worked out

the value of pie using just

an old cartwheel brilliant thanks for

watching and make sure you're subscribed

to the shoe render drawing channel for

lots more drawing videos every week

in the meantime keep drawing drawing

drawing practice practice practice and

i'll see you next time you take care now

bye bye