Unveiling The Remarkable Discovery Of Pi By A Genius - Prepare To Be Amazed!
Summary
TLDRIn 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
🔍 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.
🛠️ 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.
Mindmap
Keywords
💡Pi (π)
💡Archimedes
💡Circumference
💡Diameter
💡Radius
💡Cartwheel
💡2πr (Circumference Formula)
💡Measuring Tools
💡Accuracy
💡Practical Experiment
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
be a little bell comes up and ring that
and you'll be notified every time i do
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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
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