The Fibonacci Sequence
When I started to explore the history of mathematics I kept coming across the Fibonacci Sequence. I looked more into who this man Fibonacci was and how he developed the sequence. I came across a radio broadcast where the interviewer had a guest speaker on the show who was a mathematician at Stanford University. Keith Devlin is the author of: The Man of Numbers: Fibonacci's Arithmetic Revolution. The article delves into the origin of the basic arithmetic methods and how a man named Leonardo came to discover the need for the everyday man.
The Fibonacci Sequence is seen as a turning point in the history of mathematics. Through reading and exploring Leonardo Fibonacci, I discovered that Fibonacci did not find or create the arithmetic behind the sequence. I had just assumed that when something is named after someone it means that they created that piece of work. For example, Thomas Edison- Edison Screw Lightbulb.
Finger counting and the use of an abacus board proved to be an inefficient method of trading and the method of doing arithmetic was developed in India. It was then Arabic mathemticisions that developed modern algebra or at least the beginning of modern algebra.
It was this new method of algebra that found it's way to North America where Leonardo Fibonacci joined his father who was a businessman who represented Italian traders. Leonardo was considered a mathematical genius and realised that this algebra method had enormous potential to change commerce for everybody. He saw that if he could package and present this material to ordinary people in a way that ordinary people can understand it, then ordinary people could take charge and do their own arithmetic. It was seen as a personal computing revolution and with Leonardo Fibonacci paving the way with his mathematically gifted brain he created the sequence in which we know today.
When I started to explore the history of mathematics I kept coming across the Fibonacci Sequence. I looked more into who this man Fibonacci was and how he developed the sequence. I came across a radio broadcast where the interviewer had a guest speaker on the show who was a mathematician at Stanford University. Keith Devlin is the author of: The Man of Numbers: Fibonacci's Arithmetic Revolution. The article delves into the origin of the basic arithmetic methods and how a man named Leonardo came to discover the need for the everyday man.
The Fibonacci Sequence is seen as a turning point in the history of mathematics. Through reading and exploring Leonardo Fibonacci, I discovered that Fibonacci did not find or create the arithmetic behind the sequence. I had just assumed that when something is named after someone it means that they created that piece of work. For example, Thomas Edison- Edison Screw Lightbulb.
Finger counting and the use of an abacus board proved to be an inefficient method of trading and the method of doing arithmetic was developed in India. It was then Arabic mathemticisions that developed modern algebra or at least the beginning of modern algebra.
It was this new method of algebra that found it's way to North America where Leonardo Fibonacci joined his father who was a businessman who represented Italian traders. Leonardo was considered a mathematical genius and realised that this algebra method had enormous potential to change commerce for everybody. He saw that if he could package and present this material to ordinary people in a way that ordinary people can understand it, then ordinary people could take charge and do their own arithmetic. It was seen as a personal computing revolution and with Leonardo Fibonacci paving the way with his mathematically gifted brain he created the sequence in which we know today.
fibonacci_reference.docx | |
File Size: | 37 kb |
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Pythagoras
Pythagoras of Samos is seen as a Ionian Greek philosopher as well as a mathematician. But most of his information was written down centuries after he lived, therefore this information is seen as unreliable and many wonder if Pythagoras really contributed to mathematics at all. I have heard of the Pythagoreanism theorem and know that it relates to equations with triangles. However, my knowledge on the theory does not extend that and I hope to learn more about this and Pythagoras himself in my extended research.
Pythagoras of Samos is seen as a Ionian Greek philosopher as well as a mathematician. But most of his information was written down centuries after he lived, therefore this information is seen as unreliable and many wonder if Pythagoras really contributed to mathematics at all. I have heard of the Pythagoreanism theorem and know that it relates to equations with triangles. However, my knowledge on the theory does not extend that and I hope to learn more about this and Pythagoras himself in my extended research.
pythagoras_reference.docx | |
File Size: | 34 kb |
File Type: | docx |
Ancient Egypt
In ancient Egypt, many mathematical applications are scribed on the walls of tombs, however there was one roll of paper called a papyrus that was found in the grave of someone from the royal establishment. The papyrus showed writing and numerals and although much of the papyrus had been damaged and most was missing it showed mathematical applications about the bookwork in the Royal Court of Egypt. The papyrus was a balance sheet for income and expenditures. It also contained receipts and surplus for the court. I look forward to being able to understand further applications from ancient Egypt. The most relevant thing to me when I hear the word Egypt is the pyramids. I have also found in my research so far that Egyptian builders used horizontal and vertical lines as guidelines for building and also hanging art. There was even an Egyptian architects plan that showed number for co-ordinates. This application of mathematics is extremely interesting to me and through more exploration I aim to uncover more applications in Egypt, such as counting and the use of angles.
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Chinese Mathematics
Around 220 BC, the Great Wall of China was built and seen to be a great triumph of engineering skill and mathematical calculation. The Chinese were seen to use a form of counting board, which contained separate compartments for units, tens and hundreds. I as a practicing educator, have used such a 'table' before in a mathematics lesson with earlier years. From my research so far, it is this mathematical application discovered in ancient history that I can relate to through familiarity. It is known that the abacus soon became popular and became the preferred computing device. However, through research I have come to discover that the abacus may have led to the decline of Chinese mathematics. I aim to explore this finding more.
Around 220 BC, the Great Wall of China was built and seen to be a great triumph of engineering skill and mathematical calculation. The Chinese were seen to use a form of counting board, which contained separate compartments for units, tens and hundreds. I as a practicing educator, have used such a 'table' before in a mathematics lesson with earlier years. From my research so far, it is this mathematical application discovered in ancient history that I can relate to through familiarity. It is known that the abacus soon became popular and became the preferred computing device. However, through research I have come to discover that the abacus may have led to the decline of Chinese mathematics. I aim to explore this finding more.
chinese_mathematics reference.docx | |
File Size: | 29 kb |
File Type: | docx |
Pascal's Triangle
Pascal's Triangle is an algebraic construction of numbers. A French scientist named Blaise Pascal is now associated with one of the most interesting number patterns ever known. Despite the triangle being named after the French scientist, the pattern was known long before Pascal wrote about it. It has became apparent through my research so far that many creations in history that were named after famous philosophers or scientists, are not actually the individuals who discovered them. However, they may have taken something previously known and either published it for the common man, or manipulated it in a way that has made it more popular. With Blaise Pascal, he was the first to write about the properties and applications of the triangle. As you can see in this image on the right, these are the first eleven rows of Pascal's triangle. Each entry in the triangle is the sum of the two numbers above it. This interesting pattern of numbers plays an important role in probability theory, algebra and number theory.
Pascal's Triangle is an algebraic construction of numbers. A French scientist named Blaise Pascal is now associated with one of the most interesting number patterns ever known. Despite the triangle being named after the French scientist, the pattern was known long before Pascal wrote about it. It has became apparent through my research so far that many creations in history that were named after famous philosophers or scientists, are not actually the individuals who discovered them. However, they may have taken something previously known and either published it for the common man, or manipulated it in a way that has made it more popular. With Blaise Pascal, he was the first to write about the properties and applications of the triangle. As you can see in this image on the right, these are the first eleven rows of Pascal's triangle. Each entry in the triangle is the sum of the two numbers above it. This interesting pattern of numbers plays an important role in probability theory, algebra and number theory.
So far my thoughts on the history of mathematics has definitely changed before I started exploring research. I admit that I did not know much about the history of mathematical applications. I certainly did not think that evidence of these applications stemmed from such early on in history. As a future educator I feel that I should know the basic origins of mathematics in order to teach more relevant applications to students.
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