What Is Pythagoras Theorem? | PYTHAGORAS THEOREM | The Dr Binocs Show | Peekaboo Kidz
Summary
TLDRThis video script explores the Pythagorean theorem, a fundamental principle in geometry with real-world applications. It traces the theorem's history, noting its use in ancient civilizations like Babylon and India, predating Pythagoras. The script explains the theorem's statement—that in a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides—and illustrates it with a practical example involving a cat rescue scenario. It demonstrates how to apply the theorem to find the correct ladder length, emphasizing the theorem's relevance and utility in everyday situations.
Takeaways
- 📚 The Pythagorean theorem is named after Pythagoras of Samos, a Greek mathematician and philosopher, but he was not the actual founder of the theorem.
- 🌟 The theorem predates Pythagoras and was used by ancient Babylonians and Indians, as well as in Egyptian constructions.
- 📐 The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
- 🔢 The Pythagorean equation is expressed as \( a^2 + b^2 = c^2 \), where \( a \) and \( b \) are the legs of the triangle, and \( c \) is the hypotenuse.
- 📏 The theorem can be applied to real-world problems, such as determining the length of a ladder needed to reach a cat stuck on a wall.
- 🐱 An example in the script illustrates using the theorem to find the correct ladder size by measuring the lengths of the wall and the ground, and then calculating the hypotenuse.
- 🧮 To find the ladder's length, one must square the measurements of the wall and the ground, add them together, and then take the square root of the result to get the length of the hypotenuse in meters.
- 🛠️ The script demonstrates how to apply the theorem step by step, including the calculation of squares and the use of the square root to find the practical solution.
- 📈 The script also touches on the historical and cultural significance of the theorem, mentioning the Pythagorean society and their contributions to science and philosophy.
- 🌱 The Pythagoreans believed in the equal rights of animals, which led to their prohibition of eating animals, showing a connection between their mathematical pursuits and ethical beliefs.
- 🎓 The episode concludes with an invitation to learn more in future episodes, emphasizing the educational purpose of the content.
Q & A
Who is the Pythagorean Theorem named after?
-The Pythagorean Theorem is named after the Greek mathematician and philosopher Pythagoras of Samos.
Did Pythagoras invent the Pythagorean Theorem?
-No, Pythagoras did not invent the Pythagorean Theorem. He is credited with proving it, but the theorem existed even before him.
In which ancient civilizations was the Pythagorean Theorem used?
-The Pythagorean Theorem was used in ancient Babylon, India, and Egypt.
What does the Pythagorean Theorem state?
-The Pythagorean Theorem states that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares of the other two sides.
How is the Pythagorean Theorem expressed mathematically?
-The Pythagorean Theorem is expressed as a^2 + b^2 = c^2, where a and b are the legs of the triangle and c is the hypotenuse.
What are the legs and hypotenuse of a right-angled triangle?
-In a right-angled triangle, the legs are the two sides that form the right angle, and the hypotenuse is the side opposite the right angle and the longest side of the triangle.
How can the Pythagorean Theorem be applied in a real-life scenario?
-The Pythagorean Theorem can be used to determine the length of a ladder needed to reach a certain height on a wall when the distance from the wall to the base of the ladder is known.
How do you calculate the hypotenuse using the Pythagorean Theorem?
-To calculate the hypotenuse c, you take the square root of the sum of the squares of the other two sides, c = sqrt(a^2 + b^2).
What was the length of the wall and the land in the provided example?
-In the provided example, the length of the wall was 3 meters, and the length of the land was 4 meters.
What is the significance of the Pythagorean Theorem in construction?
-The Pythagorean Theorem is significant in construction as it helps in determining accurate measurements and ensuring structures are built correctly, such as in the construction of the pyramids in ancient Egypt.
What values did the example provide for a^2 and b^2?
-In the example, a = 3 meters and b = 4 meters. Therefore, a^2 = 9 and b^2 = 16.
What is the final step to find the length of the hypotenuse in the example?
-The final step is to take the square root of c^2, which in the example is sqrt(25) = 5 meters.
Outlines
🎉 Winning and the Introduction of the Pythagorean Theorem
The script opens with a celebratory exclamation of winning and a brief conversation about reading quickly, attributed humorously to the Pythagorean theorem. The narrator introduces the topic of the Pythagorean theorem and its applications in real life. The historical context is provided, noting that although the theorem is named after Pythagoras, it was known and used long before him, particularly in ancient Babylon, India, and Egypt. The theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
🐱 Saving a Cat with the Pythagorean Theorem
The narrator presents an example to explain the Pythagorean theorem. A cat is stuck on a wall, and the narrator needs to find the right-sized ladder to rescue it. The lengths of the wall and the ground are measured as 3 meters and 4 meters, respectively. Using the Pythagorean theorem formula \(a^2 + b^2 = c^2\), the narrator calculates that the ladder (hypotenuse) should be 5 meters. The process involves squaring the lengths, summing them, and then taking the square root of the result. The successful rescue of the cat with the correctly sized ladder demonstrates the theorem's practical application. The script concludes with a fun fact about the Pythagorean society's beliefs and compassion towards animals.
Mindmap
Keywords
💡Pythagoras Theorem
💡Hypotenuse
💡Right-Angled Triangle
💡Pythagorean Equation
💡Legs of a Triangle
💡Square
💡Square Root
💡Pythagorean Clan
💡Ancient Babylonians
💡Egyptian Constructions
💡Pythagorean Society
Highlights
Introduction to the Pythagorean theorem and its real-world applications.
Explanation of the historical origins of the Pythagorean theorem, including its use in ancient Babylon, India, and Egypt.
Clarification that Pythagoras did not invent the theorem but provided its proof.
Statement of the Pythagorean theorem: The square on the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides.
Introduction of the Pythagorean equation: a² + b² = c².
Visualization of a right-angled triangle with sides labeled as a, b, and hypotenuse c.
Example scenario: Using the Pythagorean theorem to find the correct ladder size to rescue a cat.
Measurement of the wall (3 meters) and the land surface (4 meters) as the sides a and b of the triangle.
Substitution of the measured values into the Pythagorean equation: 3² + 4² = c².
Calculation of the squares of the sides: 3² = 9 and 4² = 16.
Summing the squares of the sides: 9 + 16 = 25.
Conversion of c² into c by taking the square root: √25 = 5.
Finding the correct ladder size to be 5 meters.
Verification of the theorem with the calculated values.
Mention of the Pythagorean society's contribution to scientific progress in Greece and their belief in animal rights.
Transcripts
oh
[Music]
yay
i won i won kitty oh doctor how do you
read so fast
it's simple the pythagoras theorem
helped me to get the fastest way home
from the market
the pythagoras theorem kitty
hey friends we often hear people asking
if math formulas could be applied in the
real world
so in today's episode let us explore the
formula which can be used in many
circumstances and learn how to solve the
pythagoras theorem
zoom in
so what is the pythagoras theorem
let us begin from the beginning
the phytogas theorem is said to get its
name from a greek mathematician and
philosopher pythagoras of samos who is
believed to be a pioneer of this theorem
but that's not true as he is not the
actual founder of this theorem but was
one of the pythagorean clan members who
devoted their lives to the subject and
never revealed who its real founder was
however in reality this theorem existed
even before pythagoras and was useful
even then
whereas pythagoras only gave us the
proof of this existing right angled
triangle theory
yes the traces of pythagoras theorem
could be found in the construction of
ancient babylonians which existed even
thousands years before pythagoras
not only that but it marks its presence
in ancient india as well
which is believed to have a rich culture
of mathematics
the mathematical miracle was also used
in egyptian constructions where they
used pythagoras theorem to build the
pyramid and other structures
but the crucial question is what does
the pythagoras theorem actually say
the pythagoras theorem says that the
square on the hypotenuse of a right
angled triangle is equal in area to the
sum of the squares of the other two
sides
this theorem can be written as an
equation relating the length of the
sides a b and c
often called the pythagorean equation
that is denoted with the formula
a square plus b square is equal to c
square
confused no worries let us look at each
of its terms with the help of an example
but before we start with our example we
need to learn a few terms first which
are essential to understand
now visualize a right angled triangle
which has a b and c sides
in this diagram a and b are the legs of
this triangle and the side opposite to
the right angled triangle which is c is
called the hypotenuse
and is the longest side of the triangle
[Music]
moving further to our example
imagine a cat stuck on the surface of a
wall screaming for help
and the only way to save the cat is by
climbing over the wall
so you'll look around and find a few
ladders lying beside
but you have less time in hand and the
cat is hanging between life and fall
so we need to choose the correct sized
ladder as quickly as possible
fortunately you remember the pythagoras
theorem that says
a square plus b square equals c square
so let us assume the wall as a
the surface of land as b
and the ladder you need to find
as c
which is also your
hypotenuse then you quickly take out the
measurement tape and measure the length
of the wall that comes to three meters
then you measure the surface of the land
that comes down to four meters
now as a equals 3 meters
and b equals 4 meters
then we know c will be equal to the sum
of the square of the length of the other
two sides
and to prove that
you need to substitute these values into
the formula which is a square plus b
square equals c
which will also give you the correct
size of the ladder
hence proving this theorem
now as you have the value of a and b
you are required to find their square to
move further
so the first thing you do is substitute
a as 3
and b as 4
and the values you get after
substitution are
9 and 16 respectively
which are their squares
then you put these square values into
the formula which adds up to 25 square
meters
which is the value of c square
but let me tell you that this is not the
end because the ladder size could never
be in square meters as the other two
sides are in meters
so our next task is to convert this c
square into c
and its value square meter into meters
and to do so we apply square root on
both sides which converts c square into
c
and 25 square meters into 5 meters
and hence the value of the hypotenuse
and the correct size of the required
ladder
is
5 meters
and along with that two things happen
here
one is you prove the formula right as
that the square on the hypotenuse of a
right angled triangle which is c square
whose value is 25 square meters is equal
in area to the sum of the squares of the
other two sides
which are a square and b square
that is
9 plus 16
is also 25
and the second thing we found is the
correct size of the ladder which is five
meters
and hence you can save the cute little
kitty cat easily
trip your time
did you know the pythagorean society
later progressed as the main scientific
school of greece
also pythogrians think that animals have
the same rights to live as mankind hence
they held the prohibition of eating
animals
so kind of them
hope you learned something new in
today's episode until next time it's me
dr bynox zooming out
[Music]
oh
never mind
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