This
week we will be learning about Pythagoras, one of the first Greek mathematical
thinkers.
His famous
Pythagorean Theorem(Pythagoras theorem)
found out something amazing to do with right angled triangles. Can you find out
what it was? Write it on the blog!
Over 2000 years ago there was an amazing discovery about When the triangle has a right angle (90°) and squares are made on each of the three sides, then the biggest square has the exact same area as the other two squares put together! It is called "Pythagoras' Theorem" and can be written in one short equation:a2 + b2 = c2
•c is the longest side of the triangle •a and b are the other two side
The Pythagoras theorem is applicable to the right angled triangles.The longest side of the triangle is called a "hypotenuse" , so the formal definition is the square of the hypotenuse is equal to the sum of the squares of the other two sides.
(Example:)
In a right angle triagle, Base=3 cm Height=4 cm
To find out the hypotenuse, We can apply Pythagoras theorem: Hypotenuse square = Base square + Height square = 3 square + 4 square = (3x3) + (4x4) = (9) + (16) = 9 + 16 = 25 = 5X5 hypotenuse = 5cm
Pythagoras, the first Greek mathematician created the Pythagorean Theorem. It can be also written as an equation which is related to the lengths of right angled triangle A B C. The sum of areas of squares formed on side A and B equals the area of square formed on side C.
What is a Hypotenuse? According to Pythagoras the Hypotenuse is the opposite side of the right angle. It is also the longest side of the triangle. According to Pythagoras, in a right angled triangle let the sides be A, B and C. The total of both of the areas of squares which are formed by sides A and B is equal to area of square formed on side C which is the Hypotenuse. As a square is Equally sided, the square with side A will have Area = AxA= A2. Similarly, we get BxB = B2 AND CxC = C2. ∴ A2 + B2 = C2 For example: If the sides making the right angle were 4 cm and 3 cm, then we can find out the size of the hypotenuse. [4x4] + [3x3] = C2 16 + 9 = 25 C2 = 25 Square root of 25 is = 5 ∴ C = 5
Pythagoras theorem He discovered that if you have a right angeled triangle and squared each side of the triangle. By adding together the the two squares formed on the right angle they are equal to the square on the diagonal. Pythagoras theorem is times tables and adding.
Pythagorean Right-Angled Triangles Right-angled triangles with whole number sides have fascinated mathematicians and number enthusiasts since well before 300 BC when Pythagoras wrote about his famous "theorem". The oldest mathematical document in the world, a little slab of clay that would fit in your hand, is a list of such triangles.
The first nine years of the war consisted of both war in Troy and war against the neighboring regions. The Greeks realized that Troy was being supplied by its neighboring kingdoms, so Greeks were sent to defeat these areas.
As well as destroying Trojan economy, these battles let the Greeks gather a large amount of resources and other spoils of war, including women (e.g., Briseis, Tecmessa and Chryseis).
The Greeks won many important battles and the Trojan hero Hector fell, as did the Trojan ally Penthesilea. However, the Greeks could not break down the walls of Troy.
Patroclus was killed and, soonafter, Achilles was felled by Paris.
Helenus, son of Priam, had been captured by Odysseus. A prophet, Helenus told the Greeks that Troy would not fall unless:
a) Pyrrhus, Achilles' son, fought in the war, b) The bow and arrows of Hercules were used by the Greeks against the Trojans, c) The remains of Pelops, the famous Eleian hero, were brought to Troy, and d) The Palladium, a statue of Athena, was stolen from Troy (Tripp, 587).
Phoenix persuaded Pyrrhus to join the war. Philoctetes had the bow and arrows of Hercules, but had been left by the Greek fleet in Lemnos because he had been bitten by a snake and his wound had a horrendous smell. Philoctetes was bitter, but was finally persuaded to join the Greeks. The remains of Pelops were gotten, and Odysseus infiltrated Trojan defenses and stole the Palladium.
The Trojan Horse
Still seeking to gain entrance into Troy, clever Odysseus (some say with the aid of Athena) ordered a large wooden horse to be built. Its insides were to be hollow so that soldiers could hide within it.
Once the statue had been built by the artist Epeius, a number of the Greek warriors, along with Odysseus, climbed inside. The rest of the Greek fleet sailed away, so as to deceive the Trojans.
One man, Sinon, was left behind. When the Trojans came to marvel at the huge creation, Sinon pretended to be angry with the Greeks, stating that they had deserted him. He assured the Trojans that the wooden horse was safe and would bring luck to the Trojans.
Only two people, Laocoon and Cassandra, spoke out against the horse, but they were ignored. The Trojans celebrated what they thought was their victory, and dragged the wooden horse into Troy.
That night, after most of Troy was asleep or in a drunken stupor, Sinon let the Greek warriors out from the horse, and they slaughtered the Trojans. Priam was killed as he huddled by Zeus' altar and Cassandra was pulled from the statue of Athena and raped.
After the War
After the war, Polyxena, daughter of Priam, was sacrificed at the tomb of Achilles and Astyanax, son of Hector, was also sacrificed, signifying the end of the war.
Aeneas, a Trojan prince, managed to escape the destruction of Troy, and Virgil's Aeneid tells of his flight from Troy. Many sources say that Aeneas was the only Trojan prince to survive, but this statement contradicts the common story that Andromache was married to Helenus, twin of Cassandra, after the war.
Menelaus, who had been determined to kill his faithless wife, was soon taken by Helen's beauty and seductiveness that he allowed her to live.
The surviving Trojan women were divided among the Greek men along with the other plunder. The Greeks then set sail for home, which, for some, proved as difficult and took as much time as the Trojan War itself
Over 200 years there was a discovery about triangles and it was called Pythagorean Theorem. It got its name from a famous Greek mathematician called Pythagoras. Formal proof shows that the theorem is not true for any triangle but only for right angled triangles.
Using the equation a2+b2=c2, different kinds of problems can be solved. The c stands for the length of the hypotenuse and a and b stand for the two other lengths which are perpendicular to each other. The theorem states that the sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse.
Over 2000 years ago there was a amazing discovery about triangles... When the triangle has a right angle (90 degrees) and the squares are made on each of the three sizes then the biggest square has the exact same area as the other two squares put together.
Over 2000 years ago there was an amazing discovery about When the triangle has a right angle (90°) and squares are made on each of the three sides, then the biggest square has the exact same area as the other two squares put together! It is called "Pythagoras' Theorem" and can be written in one short equation:a2 + b2 = c2
ReplyDelete•c is the longest side of the triangle
•a and b are the other two side
:-) *good info
Delete:-) *deep detaled
:-} needs some work * nothing realey
Gurpinder - try and be a little more specific about your wishes.
DeleteThe Pythagoras theorem is applicable to the right angled triangles.The longest side of the triangle is called a "hypotenuse" , so the formal definition is the square of the hypotenuse is equal to the sum of the squares of the other two sides.
ReplyDelete(Example:)
In a right angle triagle,
Base=3 cm
Height=4 cm
To find out the hypotenuse, We can apply Pythagoras theorem:
Hypotenuse square = Base square + Height square
= 3 square + 4 square
= (3x3) + (4x4)
= (9) + (16)
= 9 + 16
= 25
= 5X5
hypotenuse = 5cm
Pythagorean Theorem
ReplyDeletePythagoras, the first Greek mathematician created the Pythagorean Theorem. It can be also written as an equation which is related to the lengths of right angled triangle A B C. The sum of areas of squares formed on side A and B equals the area of square formed on side C.
What is a Hypotenuse?
According to Pythagoras the Hypotenuse is the opposite side of the right angle. It is also the longest side of the triangle.
According to Pythagoras, in a right angled triangle let the sides be A, B and C. The total of both of the areas of squares which are formed by sides A and B is equal to area of square formed on side C which is the Hypotenuse.
As a square is Equally sided, the square with side A will have Area = AxA= A2.
Similarly, we get BxB = B2 AND CxC = C2.
∴ A2 + B2 = C2
For example: If the sides making the right angle were 4 cm and 3 cm, then we can find out the size of the hypotenuse.
[4x4] + [3x3] = C2
16 + 9 = 25
C2 = 25
Square root of 25 is = 5
∴ C = 5
Pythogarus is a Greek mathematician who lived around 500 BC.
ReplyDeleteHe state that the square of the hypotenuse is equal to the sum of
squares of other two sides.
It can be written in short equation as a2 + b2 = c2 .
In the above given diagram a and b are right angle triangle and
c is the longest side of the triangle.
Pythagoras theorem
ReplyDeleteHe discovered that if you have a right angeled triangle and squared each side of the triangle. By adding together the the two squares formed on the right angle they are equal to the square on the diagonal. Pythagoras theorem is times tables and adding.
Pythagorean Right-Angled Triangles
ReplyDeleteRight-angled triangles with whole number sides have fascinated mathematicians and number enthusiasts since well before 300 BC when Pythagoras wrote about his famous "theorem". The oldest mathematical document in the world, a little slab of clay that would fit in your hand, is a list of such triangles.
The War
ReplyDeleteThe first nine years of the war consisted of both war in Troy and war against the neighboring regions. The Greeks realized that Troy was being supplied by its neighboring kingdoms, so Greeks were sent to defeat these areas.
As well as destroying Trojan economy, these battles let the Greeks gather a large amount of resources and other spoils of war, including women (e.g., Briseis, Tecmessa and Chryseis).
The Greeks won many important battles and the Trojan hero Hector fell, as did the Trojan ally Penthesilea. However, the Greeks could not break down the walls of Troy.
Patroclus was killed and, soonafter, Achilles was felled by Paris.
Helenus, son of Priam, had been captured by Odysseus. A prophet, Helenus told the Greeks that Troy would not fall unless:
a) Pyrrhus, Achilles' son, fought in the war,
b) The bow and arrows of Hercules were used by the Greeks against the Trojans,
c) The remains of Pelops, the famous Eleian hero, were brought to Troy, and
d) The Palladium, a statue of Athena, was stolen from Troy (Tripp, 587).
Phoenix persuaded Pyrrhus to join the war. Philoctetes had the bow and arrows of Hercules, but had been left by the Greek fleet in Lemnos because he had been bitten by a snake and his wound had a horrendous smell. Philoctetes was bitter, but was finally persuaded to join the Greeks. The remains of Pelops were gotten, and Odysseus infiltrated Trojan defenses and stole the Palladium.
The Trojan Horse
Still seeking to gain entrance into Troy, clever Odysseus (some say with the aid of Athena) ordered a large wooden horse to be built. Its insides were to be hollow so that soldiers could hide within it.
Once the statue had been built by the artist Epeius, a number of the Greek warriors, along with Odysseus, climbed inside. The rest of the Greek fleet sailed away, so as to deceive the Trojans.
One man, Sinon, was left behind. When the Trojans came to marvel at the huge creation, Sinon pretended to be angry with the Greeks, stating that they had deserted him. He assured the Trojans that the wooden horse was safe and would bring luck to the Trojans.
Only two people, Laocoon and Cassandra, spoke out against the horse, but they were ignored. The Trojans celebrated what they thought was their victory, and dragged the wooden horse into Troy.
That night, after most of Troy was asleep or in a drunken stupor, Sinon let the Greek warriors out from the horse, and they slaughtered the Trojans. Priam was killed as he huddled by Zeus' altar and Cassandra was pulled from the statue of Athena and raped.
After the War
After the war, Polyxena, daughter of Priam, was sacrificed at the tomb of Achilles and Astyanax, son of Hector, was also sacrificed, signifying the end of the war.
Aeneas, a Trojan prince, managed to escape the destruction of Troy, and Virgil's Aeneid tells of his flight from Troy. Many sources say that Aeneas was the only Trojan prince to survive, but this statement contradicts the common story that Andromache was married to Helenus, twin of Cassandra, after the war.
Menelaus, who had been determined to kill his faithless wife, was soon taken by Helen's beauty and seductiveness that he allowed her to live.
The surviving Trojan women were divided among the Greek men along with the other plunder. The Greeks then set sail for home, which, for some, proved as difficult and took as much time as the Trojan War itself
Pythagorean Theorem
ReplyDeleteOver 200 years there was a discovery about triangles and it was called Pythagorean Theorem. It got its name from a famous Greek mathematician called Pythagoras. Formal proof shows that the theorem is not true for any triangle but only for right angled triangles.
Using the equation a2+b2=c2, different kinds of problems can be solved. The c stands for the length of the hypotenuse and a and b stand for the two other lengths which are perpendicular to each other. The theorem states that the sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse.
Pythagorean Theorem
ReplyDeleteOver 2000 years ago there was a amazing discovery about triangles... When the triangle has a right angle (90 degrees) and the squares are made on each of the three sizes then the biggest square has the exact same area as the other two squares put together.
This can be written as a short equation as below:
a2 + b2 = c2
Hello Alisha...
DeleteI really like your work and I actually learnt something.
FROM SRI THE BEAUTIFUL BLOGGER
he ripped triangles and it became a other shape he named a b and c the angle c was the biggest
ReplyDelete