The word "radical" comes from the Latin word "radix", that means "root",
from what we get not only the word "radical", but also "radish"! The
other use of "radical" means "by the roots" or "from the roots", such as a "radical" change in a person. A political"radical" is someone who wants radical change by radical means, like an extremist. Another word from the same source is "eradicate" originally, to "root out" or "pull out by the roots". And a square root is called a root in the first place because a root is the source of something. If you square a number, the number it came from is the root, as if the square grew from it.
Friday, December 3, 2010
History...
Babylonians:
The Babylonians were the first ones to talk about radical expressions or squares roots. They also were the ones who invented the sign for the square root and other things. And the Babylonian mathematics were more advanced than Egyptian maths. They could extract square and cube roots, work with Pythagorean triples 1200 years before Pythagoras, and they had a knowledge of pi , they could solve some quadratics and even polynomials of degree 8 (which I don’t even know what it is), but we know that they solved linear equations and could also deal with circular measurement. Babylonian mathematics was based much more on algebra and less on geometry, different from the Greeks.
The Babylonians existed from about 7000 to about 2500 years ago. They lived in the area of present day Iraq between the Tigris and Euphrates rivers where the two rivers join the Persian Gulf. The main concentration of the population was in and around the city of Babylon. The Babylonians were for the most part farmers; they created a very complicated system of irrigation between the two rivers to feed their production of gardens and cactus.
Even though they had very little raw materials, the Babylonians developed new construction techniques for the construction of buildings. the Babylonians had many very interesting and and very beautiful temples and buildings. The Babylonians left behind a lot of crafts and beautiful artifacts. Babylonians were really intelligent people who made large advances in the techniques of agriculture, math and science.
The Babylonians were the first ones to talk about radical expressions or squares roots. They also were the ones who invented the sign for the square root and other things. And the Babylonian mathematics were more advanced than Egyptian maths. They could extract square and cube roots, work with Pythagorean triples 1200 years before Pythagoras, and they had a knowledge of pi , they could solve some quadratics and even polynomials of degree 8 (which I don’t even know what it is), but we know that they solved linear equations and could also deal with circular measurement. Babylonian mathematics was based much more on algebra and less on geometry, different from the Greeks.
The Babylonians existed from about 7000 to about 2500 years ago. They lived in the area of present day Iraq between the Tigris and Euphrates rivers where the two rivers join the Persian Gulf. The main concentration of the population was in and around the city of Babylon. The Babylonians were for the most part farmers; they created a very complicated system of irrigation between the two rivers to feed their production of gardens and cactus.
Even though they had very little raw materials, the Babylonians developed new construction techniques for the construction of buildings. the Babylonians had many very interesting and and very beautiful temples and buildings. The Babylonians left behind a lot of crafts and beautiful artifacts. Babylonians were really intelligent people who made large advances in the techniques of agriculture, math and science.
More History...
Pythagoras:
Pythagoras studied odd and even numbers, triangular numbers, and perfect numbers. Pythagoreans contributed to our understanding of angles, triangles, areas, proportion, polygons, and polyhedral. He was part of the Pythagoreans group and they were the ones who invented the Pythagorean theorem. The Pythagoreans made a theorem that deals with the lengths of the sides of a right triangle. It is often written as an equation. It says 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 that is equals c.
Pythagoras, was born in Turkey in 500-580 BC. He was the son of Mnesarchos and met Thales, who was a scientist and is called “the father of science” that came up with the idea and was the first to see charges in effect. Pythagoras left Turkey and somehow went to Egypt, and there, he learned a lot from the Egyptians. Some say that he left because of the Pythagoreans, that didn’t like his ideas that banned him away from their society. And others, say that he left because his friends Thales told him that it would be a great experience for him to be there and learn from their culture and thoughts about math. Pythagoras thought that the numerical intelligence of the Universe was represented by the Tetractys - triangular arrangements of ten dots, with one on top, two on the second row, three on the third and four on the fourth. Ten was considered the perfect number and a magical sign. that is a symbol composed of ten dots in a pointing up in a triangular formation. It was a sacred symbol for the Pythagoreans. Because the Pytahoreans thought that each number had a magical thing. They also were the first ones to invent and talk about numerology. They believed that:
1. The number one: the number of reason.
2. The number two: the first even or female number, the number of opinion.
3. The number three: the first true male number, the number of harmony.
4. The number four: the number of justice or retribution.
5. The number five: the number of curiosity.
6. The number six: the number of creation.
7. The number seven: the number of magic and intelligence.
8. The number eight: the number of balance and authority.
9. The number nine: the number of forgiveness and compassion.
10. The number ten: the tetractys, the number of the universe
The Pythagorean school was the first school of math. They were very strict with the students and had many rules that involved tradition, thoughts about society and believes.
Pythagoreans Rules:
• To abstain from beans.
• Not to pick up what has fallen.
• Not to touch a white chicken
• Not to mix the fire with iron.
• Do not look in a mirror beside a light.
They were also very fair” in many ways. For example, they believed that men and women are equal and should be treated equally. They shared a common way of life, everything was shared. And their mathematical discoveries were also shared. Pythagoreans were very knowledgeable. They had their own way of living and the way they thought worked perfectly to their way of lives.
For Pythagoras death, there are two theories. There was a war against the Pythagoreans and the city of Croton and it was burned. Pythagoras was caught and killed by the rebels when he refused to cross the field of beans or that when he took refuge in the Temple of the muses and died of hunger.
Conclusion:
I picked this topic on radical expressions and triangles because I really like them and they are things that I going to be seeing in the next years of my life in math. I also did because I wanted to know more about it and I knew that I also going to research for the Babylonians and I wanted to know more about them. I think it’s incredible that these people, that lived more than 5000 years BC had these thoughts and were starting the discoverers of math and science. I think its just awesome.
Pythagoras studied odd and even numbers, triangular numbers, and perfect numbers. Pythagoreans contributed to our understanding of angles, triangles, areas, proportion, polygons, and polyhedral. He was part of the Pythagoreans group and they were the ones who invented the Pythagorean theorem. The Pythagoreans made a theorem that deals with the lengths of the sides of a right triangle. It is often written as an equation. It says 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 that is equals c.
Pythagoras, was born in Turkey in 500-580 BC. He was the son of Mnesarchos and met Thales, who was a scientist and is called “the father of science” that came up with the idea and was the first to see charges in effect. Pythagoras left Turkey and somehow went to Egypt, and there, he learned a lot from the Egyptians. Some say that he left because of the Pythagoreans, that didn’t like his ideas that banned him away from their society. And others, say that he left because his friends Thales told him that it would be a great experience for him to be there and learn from their culture and thoughts about math. Pythagoras thought that the numerical intelligence of the Universe was represented by the Tetractys - triangular arrangements of ten dots, with one on top, two on the second row, three on the third and four on the fourth. Ten was considered the perfect number and a magical sign. that is a symbol composed of ten dots in a pointing up in a triangular formation. It was a sacred symbol for the Pythagoreans. Because the Pytahoreans thought that each number had a magical thing. They also were the first ones to invent and talk about numerology. They believed that:
1. The number one: the number of reason.
2. The number two: the first even or female number, the number of opinion.
3. The number three: the first true male number, the number of harmony.
4. The number four: the number of justice or retribution.
5. The number five: the number of curiosity.
6. The number six: the number of creation.
7. The number seven: the number of magic and intelligence.
8. The number eight: the number of balance and authority.
9. The number nine: the number of forgiveness and compassion.
10. The number ten: the tetractys, the number of the universe
The Pythagorean school was the first school of math. They were very strict with the students and had many rules that involved tradition, thoughts about society and believes.
Pythagoreans Rules:
• To abstain from beans.
• Not to pick up what has fallen.
• Not to touch a white chicken
• Not to mix the fire with iron.
• Do not look in a mirror beside a light.
They were also very fair” in many ways. For example, they believed that men and women are equal and should be treated equally. They shared a common way of life, everything was shared. And their mathematical discoveries were also shared. Pythagoreans were very knowledgeable. They had their own way of living and the way they thought worked perfectly to their way of lives.
For Pythagoras death, there are two theories. There was a war against the Pythagoreans and the city of Croton and it was burned. Pythagoras was caught and killed by the rebels when he refused to cross the field of beans or that when he took refuge in the Temple of the muses and died of hunger.
Conclusion:
I picked this topic on radical expressions and triangles because I really like them and they are things that I going to be seeing in the next years of my life in math. I also did because I wanted to know more about it and I knew that I also going to research for the Babylonians and I wanted to know more about them. I think it’s incredible that these people, that lived more than 5000 years BC had these thoughts and were starting the discoverers of math and science. I think its just awesome.
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