## Wednesday, November 14, 2007

### Cultural Contributions to Geometry

Choose ONE specific culture and follow the history of their contribution to the field of Geometry or Mathematics in general. Again, your response must be at least 3 paragraphs and you must respond to one other person.

Anonymous said...

Sometimes we wonder, “What cultures contributed to geometry”? Well, there are so many different cultures around the world and they all contributed to math in a different way. Geometry has to do with shapes, theorems, postulates, proofs, and equations. As I researched what cultures contributed to geometry, I came across the Ancient Indians. The Ancient Indians are one of the many cultures that contributed to geometry.

The Ancient Indians contributed to math in many ways. There were many great mathematicians. A few of them were Aryabhata, Brahmagupta, Bhaskara I, Mahavira, Sridhara, Bhaskara II, and Nilakantha. Aryabhata contributed to math by coming up with the formula for the area a triangle. In addition, he was the first one in Indian mathematics to come up with the formula. This formula is often used in math. The Indians also contributed to the math equations that we solve. The other things they contributed to math were the place-value notation and Pythagorean theorem. The Ancient Indians have contributed to math in many ways. Their contributions are greatly used in math now.

Now I know that the Ancient Indians contributed to math and that other cultures have contributed too. This research was very interesting to find that the Indians have so many intelligent mathematicians. There are many other cultures that have contributed to math in a variety of ways, but as for me I chose the Ancient Indians and researched what they have contributed to math. There’s so many to learn in mathematics, but we can only learn them one at a time.
-Patricia R. (Period 4)

patricia_pink31 said...

Sometimes we wonder, “What cultures contributed to geometry”? Well, there are so many different cultures around the world and they all contributed to math in a different way. Geometry has to do with shapes, theorems, postulates, proofs, and equations. As I researched what cultures contributed to geometry, I came across the Ancient Indians. The Ancient Indians are one of the many cultures that contributed to geometry.

The Ancient Indians contributed to math in many ways. There were many great mathematicians. A few of them were Aryabhata, Brahmagupta, Bhaskara I, Mahavira, Sridhara, Bhaskara II, and Nilakantha. Aryabhata contributed to math by coming up with the formula for the area a triangle. In addition, he was the first one in Indian mathematics to come up with the formula. This formula is often used in math. The Indians also contributed to the math equations that we solve. The other things they contributed to math were the place-value notation and Pythagorean theorem. The Ancient Indians have contributed to math in many ways. Their contributions are greatly used in math now.

Now I know that the Ancient Indians contributed to math and that other cultures have contributed too. This research was very interesting to find that the Indians have so many intelligent mathematicians. There are many other cultures that have contributed to math in a variety of ways, but as for me I chose the Ancient Indians and researched what they have contributed to math. There’s so many to learn in mathematics, but we can only learn them one at a time.
-Patricia R. (Period 4)

http://www.geocities.com/kvforp/VK1/History_Maths_Indian_contribution.html

Anonymous said...

Mathematics has evolved greatly throughout the ages. There have been dozens of mathematicians that helped contribute thoughts and ideas that made mathematics, or math, what it is today. However some cultures as a whole made major advances in math, and the Chinese people themselves are one of those important cultures. The Chinese made many key progresses in the numerous fields of mathematics, but the early focus on math in general was just to focus on astronomy to create an accurate calendar. Though, their progress has gotten much father than that.

The Nine Chapters on the Mathematical Art is an ancient Chinese book that was written as early as around 200 B.C.E. It contained over 200 different problems that included the use of architecture, agriculture, surveying, business, and even the deduction of pi (π). The Nine Chapters on the Mathematical Art influenced many of Chinese mathematicians, but it also greatly influenced much of the Eastern World as well. A man named Liu Hiu gave a commentary on this book, and he provided various instructions on how to complete a few problems in the book. One of the problems he tested was one that was very similar to Cavalieri's principle, which was on how to find the volume of a cylinder. Hiu found a relationship between finding the volume of a sphere with finding the volume of a solid that lied within the sphere. Liu Hiu also developed two estimates to discover the true value of π. He rounded the first to about 3.14, and his second was 3.1416. The Chinese are also said to have been one of the first to create and use linear and quadratic equations. Ironically, however, the Chinese rarely used fractions in early times. They often used the decimal system to represent parts of whole numbers. A man by the name of Shao Yong also created a list of binary numbers from 0 – 63, while a German man named Gottfried Leibniz discovered a similar technique in finding binary numbers centuries later.

All in all, the Chinese people made many advances in the history of mathematics. Personally, I believe they made a huge contribution to the understanding of this topic, especially with the book The Nine Chapters on the Mathematical Art. Nevertheless, the Chinese aren’t the only ones who made developments in math. The Greek people, Arabic people, and so much more also supplied much information in the mathematical fields. Without all of the many cultures who study and continue to study math, we wouldn’t have many advances in science or everyday life. All their findings and discoveries are all significant.

http://www.newagequest.com/NAIC/shao.html
http://aleph0.clarku.edu/~djoyce/ma105/simultaneous.html
http://www.pps.k12.or.us/depts-c/mc-me/be-as-ma.pdf

- Krizelle C. Per. 2

Samantha P. per 6 said...

Samantha P. per. 6
Greek's Contributions

Mathematics is a big part of history and there are so many contributions. There are several countries,cultures,and people that have created the foundation of mathematics. There are several different types of mathematics that are in the world today, geometry is just one of them. Geometry has been a part of the Greek's culture since before Christ was born.
The word geometry actually comes from the greeks. According to History of Mathematics For Young Mathematicians geometry means "the measurment of earth". The greeks always tried to prove the reasons for equations by using geometry. They liked to understand geometry to its fullest. Without the greeks, people would not understand the elements of geometry.
There are so many greeks that contributed to geometry. People like Pythagoras of Samos, Theaetetus of Athens, and Hippocrates of Chios. Pythagoras came up with several theorems. Theaeteus founder of solid geometry,three dementional shapes. Hippocrates "wrote the first 'elements of geometry'"(Soft Suffer). The Greeks put so much into geometry. They have helped several other cultures understand the meanings of proofs, theorems, postulates, and the elements of geometry!

_http://www.historyforkids.org/learn/greeks/science/math/
_http://geometryalgorithms.com/history.htm#Greek
_http://www.mathsisgoodforyou.com/topicsPages/general/greeks.htm
_http://dictionary.reference.com/browse/solid%20geometry

Joanne R. said...

There are many people around the world that have shown their contribution to geometry and math in many ways. The French people of Europe have made their equal share of their contribution. For instance, a man named Blaise Pascal came up with the theory of probability. Pascal was 16 years old when he came up with this theory. We use his methods in basic geometry and mathematics. He also invented the first adding machine in the world, which is now called the calculator. We use calculators as an item in every day life and use it for simple things such as taxes.

Rene Descartes was also a man who contributed to mathematics. He found ways to use the alphabet in equations. Rene found ways and invented methods, such as, using exponents in an equation. He also came up with an easy method to see what numbers turned out to be positive, and what others were negative. This is also known as “Descartes’ Rule of Signs.” We also use this all around the world and in every day life.

There was also a man named Charles Hermite that made contribution to this world today. He was a teacher to most and inspired people. He came up with ways to make mathematics “easier” and way for people to understand. He also proved transcendental numbers and easier equations throughout people in France. All of these people from France have contributed many things for our world today.

-Joanne R. Period 6

http://warrensburg.k12.mo.us/math/pascal/jacob.html

http://library.thinkquest.org/3531/mathhist.html

http://en.wikipedia.org/wiki/Charles_Hermite

Anonymous said...

Historic Geometry Alex G per 6
There are many historic people and cultures that contributed to geometry. One of those cultures would be Egypt. Egypt was a very vast growing civilization at an early start because it was an oasis in the middle of a desert. Egypt had their Nile river that provided feral land for food to grow etc. The Egyptians knew how to find the areas of shapes and knew the Pythagorean theorem before the Greeks did. They also had types of numbers but written through hieroglyphics.
Another culture that contributed to geometry would be the ancient Greeks. Plato was one of the many ancient Greeks to contribute to geometry. He figured out that geometric shapes were perfect and that there were ways to prove them right. So Plato invented proofs, or a hypothesis or way of proving a shape of figure right. Another Greek man who contributed to geometry is Archimedes. He discovered how to measure volume and area.
One more culture that contributed to geometry would be ancient India. The Indians had to build sacrificial altars and their calculations had to be exact. Some things that India discovered would be Linier and Quadratic equations. They also knew about the Pythagorean theorem, and some fractions.

Anonymous said...

Sometimes we wonder, “What cultures contributed to geometry”? Well, there are so many different cultures around the world and they all contributed to math in a different way. Geometry has to do with shapes, theorems, postulates, proofs, and equations. As I researched what cultures contributed to geometry, I came across the Ancient Indians. The Ancient Indians are one of the many cultures that contributed to geometry.

The Ancient Indians contributed to math in many ways. There were many great mathematicians. A few of them were Aryabhata, Brahmagupta, Bhaskara I, Mahavira, Sridhara, Bhaskara II, and Nilakantha. Aryabhata contributed to math by coming up with the formula for the area a triangle. In addition, he was the first one in Indian mathematics to come up with the formula. This formula is often used in math. The Indians also contributed to the math equations that we solve. The other things they contributed to math were the place-value notation and Pythagorean theorem. The Ancient Indians have contributed to math in many ways. Their contributions are greatly used in math now.

Now I know that the Ancient Indians contributed to math and that other cultures have contributed too. This research was very interesting to find that the Indians have so many intelligent mathematicians. There are many other cultures that have contributed to math in a variety of ways, but as for me I chose the Ancient Indians and researched what they have contributed to math. There’s so many to learn in mathematics, but we can only learn them one at a time.
-Patricia R. (Period 4)

http://www.geocities.com/kvforp/VK1/History_Maths_Indian_contribution.html

Anonymous said...

In response to Patricia R.'s comment:
I never realized how much Ancient Indians contributed to math. I never knew that they helped create formulas for math. That's really interesting.
- Krizelle C. Per. 2

Samantha P per. 6 said...

Samantha P per.6

comment to joanne r. per.6

Joanne i think that was a very interesting peice. I enjoyed learning about who made the first calculater. That is so appealing that Rene came up with positive and negetive numbers. I think that you proved the point that people of france contributed a plethera to mathematics. I enjoyed your peice, you did a great job!

Anonymous said...

Responding to Samantha P.

I really liked what you wrote. It was very informational and I learned a lot from it. I never knew that the greeks contributed to geometry in many ways. I really enjoyed reading your essay and I think you did a good job!

-Patricia R. (p.4)

Anonymous said...

In response to Joanne R.: Wow. I never really knew that the calculator was first used and invented in France. That is really cool! It also seems like Rene helped create algebra since you said that he figured out ways to use the alphabet in mathematics. That is all really interesting. I certainly learned a lot just by reading your work!

- Krizelle C. Per. 2

Arman P. said...

Well a culture that contributes to geometry is after thinking about it is Egyptians, well because geometry has allot to do with shapes and sizes and when all those egyptians made the pyramids there had to be a master mind to tell them the exact shapes and sizes and measures to cut and put together or else it would fall apart or it would be crooked and the pharos would not be to pleased with their had work on the pyramids. So for the egyptians there had to be a mathamatical genious to be able to solve such a thing as the pharos statue. There had to be some mathamatition to be able to realize how these people had to place and cut and measure these huge blocks so it would fit perfectly. If it was left to just eyeball it then it would be crooked or it would colapse on some of the builders and lives would be lost. So their was a mathamatition to tell the people or slaves as they may have called to build these pyramids. Its not too easy to just guess and and know how to build a pyramid. Espesially with all those secret compartments and the special rooms for the pharos to rest in piece or for example like treasure rooms. You have to know allot of Geometry to be able to consturct a huge pyramid with rooms and secrete doors and passages to wonders beyond. So geometry would come in handy when youll wanna create some thing and there are many more cultures with genious mathamatitions such as the ones who were Egyption. Now I know about all of these matamatitions and how these amaxing things wouldnt be accomplished if it wasnt for geometry. I never really thought of it like this that the pyramids would need a mathamatition to be build. -Arman P. (period 1)

Anonymous said...

The Alex Salas per . 1
well geometry is used in everday life or in our culture by shapes, theorems,postulates,proofs,and equations. mostly every culture uses geometry in the cultures.
im going to tell how you how and who uses them in my little story...

in the ancient greek cultures, Pythagoras were very awakened in finding of the new patterns they were gonna make and rules in mathematics and music, and came up with some ideas of a mathematical proof. Although the Greek women usually didnt take part in the work to the mathematics they were not allowed to study science, Pythagoras did have some not alot of women among their students. Socrates, a little after the concluded and developed logical methods for conclusive whether something was true or not true.

my brother ruben wanted me to put some of his culture in to this comment. while in construction you need to know your angles and degrees to get big things done. when your shopping for food or other supplies you have to know your math and other mathematics to help your figure out how much money you could spend? or even if you have enough money to pay for your convident stuff...

well i really didnt get what were suppose to do, hope this works out

bahhhbyyyee !

Anonymous said...

in response to Krizelle C. Per. 2

i liked how she had well information to her comment, it was great in words and strong structure, it was GREAT !

i got my information from
http://www.historyforkids.org/

the alex Salas per 1

Anonymous said...

I like how you compare Eqyptians to Geometery. i like your Blog haha.. its true when you say that egyptians made the pyramids and there has to be a master mind to tell them the exact shapes and sizes and measures to cut and put together or else it would fall apart or it would be crooked and the pharos would not be to pleased...
-Brian R. Period 1

Anonymous said...

Katie Siciliano
Period 2

When asked what cultures contributed to Geometry, I didn't know off the top of my head. So in doing research, I noticed that it wasn't just one or two different cultures, but that there was a large variety that contributed in many different ways. The one
culture that I chose was that from the Greek. They technically did not invent geometry but they did expand on what the Egyptians, Babylonians, and other ancient cultures did. The Greek basically took the discoveries from the ancient cultures and also discovered new things of their own.

One of the most well known scholars in Ancient Greece was Euclid. He changed the way that he solved basic problems. He asked “why?” And throughout his life he studied all about different points, planes, lines, triangles, circles, squares, and spheres. He did proofs to explain the math problems that he faced.

The Greek did not just expand geometry for the sake of expansion, they also used it in some of their activities. One thing that geometry helped them with was understanding the stars. But not only the stars were understood, geometry helped surveying, navigation, and even building. When looking for the exact meaning of geometry and how it relates to the Greek I found that, "The word geometry is Greek for geos - meaning earth and metron - meaning measure."(-http://math.about.com/library/weekly/aa031503a.htm)

http://www.yale.edu/ynhti/curriculum/units/1984/2/84.02.05.x.html
http://mathforum.org/cgraph/history/greekgeometry.html

Anonymous said...

Theirs alot of different cultures that use/improve math from the Ancient indians to the Egyptians. A other example of a culture that uses math is the mayans.
Just like the Egyptians, Mayans built pyramids/temples too. The mayans used geometry when builting the pyramids as well as the other cultures. An example of geometry is making the archs on the top of the pyramid and cutting even pieces/shapes to fit the walls and stairways.The had to built smart because they didnt want the temples/pyramids to fall in front of their eyes.
if the mayans had secret rooms inside the pyramids they would have to add support to the walls so that if the walls break and hit the kings tomb, you would want the king to be disturbed in his after life...hahaha...
Other ways the mayans use math is by making a base 20 (vigesimal) and base 5 numbering system .Also, the preclassic Maya and their neighbors independently developed the concept of zero by 36 BC.
Who would of that they mayans would figure something like that..(im not saying the mayans are dumb..hah...it might og came out wrong)
-Brian R. Period 1

http://en.wikipedia.org/wiki/Maya_civilization#Mathematics

Bobbie S. said...

The Mayan Numbers have existed as far back as the early classic period 400 AD. The Mayans had a very different way of doing math. The Mayans made a very good math system with only using three symbols. Those symbols are a dot, a bar, and a zero. A dot stood for one and a bar stood fro five .Mayans used a base number of twenty instead of ten which is how we do today. The base number of twenty was also used as a big portion to the Mayan calendar.
The Mayans ritual calendar was called the, Tzolkin. The Tzolkin was composed of 260 days. The Tzolkin was soon with a 365 day calendar called the “Haab”. The calendar then consisted of 18 months with 20 day, numbered 0-19. As short month was only 5 days and was called a Wayeb which, was considered a very unlucky time. It took this calendar 52 years to move through a complete cycle. This calendar could not have been made without the help of Mayan mathematics.
The Mayans contributed to mathematics, it was very sophisticated, logic. And ahead of its time. They used many different symbols that made their mathematics very unique and different. The Mayan calendar also helped with the calendar today even though the Mayan calendar is different. That’s why the Mayan culture is important to the math we use today.

http://www.michielb.nl/maya/math.html
http://en.wikipedia.org/wiki/Maya_numerals

Bobbie S. said...

Responding to Patricia R.(Period 4)

I really liked your story. I learned so many new things. I never knew that the ancient Indians contributed to math by coming up with the formula of the area of a triangle. I also learned that they contributed to math by helping with the place-value notation and Pythagorean theorem. I think you did a greay Job!
- Bobbie S. per:6