Please post a brief abstract and title of your talk here. This would help others to know beforehand what you will be talking about. Also, if you have some comments to make after you listen to a talk, this is the place to share those comments.
I was at the Borders book store (near college St and Veterans intersection) yesterday and found some really beautiful books on the bargain section. These are very cheap. One of the books that I bought was "The story of Mathematics" by Anne Rooney. It was only $3.99. I thought some of you maybe interested in this beautiful and inexpensive book. It has lots of beautiful coloured pictures. So it makes reading fun. It is mind blowing to think how much mathematics one can learn with just $3.99
Abstract Non-Euclidean geometry can be defined as any type of geometry that is different from Euclidean geometry and developed all because of the unproved, different, and questionable fifth postulate from Euclid. The two most common types of non-Euclidean geometries are spherical and hyperbolic geometry. Non-Euclidean geometry is sometimes called Lobachevsky-Bolyai-Gauss geometry because those three men along with Riemann made some great contributions to the development of non-Euclidean geometry. Other mathematicians that also spent time working with the fifth postulate and toward the progress of non-Euclidean geometry were Proclus, Playfair, Saccheri, Lambert, Legendre, Beltrami, and Klein. Some of the mathematicians made developments on their own while others finished ideas that had already been started. All of this work that has been done by mathematicians from different countries have led to what we lean and know today as non-Euclidean geometry. When one compares and contrasts Euclidean geometry and non-Euclidean geometry there are differences when looking at parallelism or the fifth postulate, distance between lines, and the angle sums of triangles.
Religions influence on the mathematical world: In depth look on ancient India and Greece
Religion can significantly affect one’s life or it can be greatly insignificant. In the development of mathematics, it is easy to see religion intertwined. This holds true for nearly all cultures. The Greeks were able to discover the true beauty of music and astronomy, they were also able to discover the true beauty of both mathematics and religion. The Greeks created a view of the world in which math and religion were entirely linked. Never before or since has math played such a large role in life and religion. India has always had a rich connection with the religions of the land that includes Hinduism, Buddhism, and Islam. Since religion plays a vital role in society, the religious thinkers of India have brought vast change to the land. Indian mathematics can be traced back to around 600 BC, when a number of Vedic manuscripts were found. They continued their advancements in the mathematical world by the sulbasutras, astronomical findings, and geometric findings.
The Pythagorean Theorem in different Civilizations:
we are all familiar with the theorem and what is says but each civilization had their own approach and motivations behind the discovery of this proof. Just like math builds on itself, some ideas blend together that also give these civilizations something in common. We are all familiar with maybe one of two proofs that we learned when we were taught this theorem but throughout the course of history some 84 proofs of the Pythagorean Theorem have been recorded. This theorem may seem trivial and straightforward ever since it's discovery.
Christine and I will be discussing the Pythagorean Theorem throughout the ancient cultures of the Greeks, China, and India. We will talk about different reasons for the discovery and the applications used and focus heavily on the various approaches taken. Although all cultures derived the same theorem the way in which they found the theorem varies greatly but also shows some similarities.
Archimedes was without a doubt one of the most influential mathematicians in history. In many was he was a pioneer of various branches of science and applied mathematics. He will probably mostly always be remembered for "Archimedes' Principle" because of its popular use today, but there are many other lesser known works that deserve to be talked about. Being one of the first mathematicians to accurately calculate the value of pi, Archimedes was able to make many advancements relating to circles that are very applicable today. Archimedes was an amazing figure in the history of mathematics, and it is a shame that so much of his work was lost because with his ideas future mathematicians and scientists may have been able to accomplish so much more.
I will be talking about the History of Logarithms today... ABSTRACT: Most of the students in high school and in college have a difficult time with logarithms. In many cases, they memorize formulas and rules without actually understanding what a logarithm is. They even solve complicated problems, they learn how to integrate or differentiate then not knowing what they’re actually doing. Logarithms are an integral part of many forms of technology, and their history and development help us to see their importance and relevance. This paper surveys the origins of logarithms and their usefulness both in ancient and modern times. A brief introduction of the concept of logarithm, some properties and examples are also given.
The Approximations of Pi Abstract: looking at the history of the calculations to the number pi. Starting with the Babylonians and ending with the computers of today.
Using a picture of the sun setting on Lake Michigan, I can find a pretty good approximation of the radius of the earth. It involves the length of the reflection of the sun on the lake, some basic geometry and a little bit higher level of math that I probably wont get into during class.
I was thinking about Andrew's presentation on Vedic Mathematics, originally when we had learned it in class I thought of it as a potentially interesting way for kids to learn arithmetic. After I thought about this longer and thought it could be potentially more harmful than helpful because students would not see the methods behind the calculations they were doing. After Andrew's presentation today in class I realize that actually Vedic Mathematics is a great way to introduce proofs like Andrew had suggested, and rather than provide a shortcut they provide an example that is easy for a student to check their answers.
Yes, I totally agree. I also think that kids would really enjoy this Vedic stuff. On the one hand they would learn some really cool arithmetic tricks which they can use to entertain their friends at a party. But also, on the other and more serious side, it is a great way to introduce them to proofs which they are often scared of.
I am very glad that Andrew has chosen this topic because this was very much on my mind and I could not get to it in the interest of time.
I was very curious about the 13 Archimedean solids which Nick mentioned in his talk. I found more information about this on Wikipedia. There is a precise mathematical definition of these solids. An Archimedean solid is a convex polyhedron composed of two or more types of regular polygons meeting in identical vertices. So what Archimedes gave is a complete classification of these solids (13 types).
I also found some interesting history on the Cattle Problem on Wikipedea.
I had lots of comments to make after Rachel's presentation because I passionately love the number Pi. This is a number which has been very dear to my heart since I was a child. Since Pi seems such a fundamental number, it is natural to find this number in nature. Could it be that God used this number in designing the universe? Answer: YES, in all probability. There is a way to compute the digits of Pi using data that is given by God, namely the configuration of the stars. Here is how you do it. This idea is due to Robert Matthews who wrote this in the scientific journal "Nature" in 1995. It uses basic probability theory and a relies on a result of Euler (1 + 1/2^2 + 1/3^2 + 1/4^2 ... = pi^2/6). The idea is to find the angular distances (theta) between lots of stars and convert them into large integers by applying [1 + cos(theta)]*million. From this set of numbers pick random pairs and find the proportion (p) of these pairs with no common factor. It can be shown that pi is approximately equal to square root of 6/p. This approximation can be made as close as possible to the actual value of Pi by taking more and more stars in the data. By choosing just the top 100 brightest stars in the sky you can get an approximation of Pi as 3.12772 using this method! Note that the error is less than 0.4% for 100 stars. What is you use 1000 stars? 10000 stars? you can diminish this error as much as you please by taking more and more stars.
Conclusion: Pi is is the Sky which is God's creation without human intervention. Or you may equally well conclude that God is a mathematician! Aha!
Everyone had very interesting presentations yesterday. Thank you all for sharing.
I thought Rachel's presentation as very interesting. It is amazing that Pi has been studied for so long, I mean up to ten years ago. I also think it is so interesting that it is such a long number, and that some people actually found 707 digits by hand. Of course I love that Pi is 3.14 because that is my birthday too! haha
Good job to everyone on the presentations yesterday. I also thought the Vedic Mathematics presentation by Andrew was interesting. I love using shortcuts in math if it makes a problem easier but I enjoyed learning the set up behind the shortcuts. I'm excited to see what others will be presenting today; we all have selected diverse topics that are informational and intriguing!
A brief history of the voting possibilities and the electoral college. How can the appropriation of votes change the outcome of an election? How does the electoral college work.
Caitlin and myself will be talking about Navigational History. We will be talking about map making during the Renaissance and how it correlates to the longitude problem. We will also talk of John Harrison as well as the Lunar Distance Method of determining longitude.
We are really excited and have been talking about previous presentations. We think everyone is doing a really impressive job and find this as being a fun way of learning.
Yes, I am also excited about the presentations. I very much enjoyed the diversity of the presentations: full of interesting history, beautiful ideas, surprising facts and lots of culture. Good job everyone!
Today's 3 talks will also be very interesting. They can be put together under the theme "history of applied mathematics." I am sure you will enjoy these talks. They will focus more on the renaissance and modern mathematics.
Pell's Equation: I will review a little of the historical development of Pell's Equation, who the major contributors were, and an example of how each contributor solved the equation x^2 = Ny^2 + 1.
I was at the Borders book store (near college St and Veterans intersection) yesterday and found some really beautiful books on the bargain section. These are very cheap. One of the books that I bought was "The story of Mathematics" by Anne Rooney. It was only $3.99. I thought some of you maybe interested in this beautiful and inexpensive book. It has lots of beautiful coloured pictures. So it makes reading fun. It is mind blowing to think how much mathematics one can learn with just $3.99
ReplyDeleteNon-Euclidean Geometry
ReplyDeleteAbstract
Non-Euclidean geometry can be defined as any type of geometry that is different from Euclidean geometry and developed all because of the unproved, different, and questionable fifth postulate from Euclid. The two most common types of non-Euclidean geometries are spherical and hyperbolic geometry. Non-Euclidean geometry is sometimes called Lobachevsky-Bolyai-Gauss geometry because those three men along with Riemann made some great contributions to the development of non-Euclidean geometry. Other mathematicians that also spent time working with the fifth postulate and toward the progress of non-Euclidean geometry were Proclus, Playfair, Saccheri, Lambert, Legendre, Beltrami, and Klein. Some of the mathematicians made developments on their own while others finished ideas that had already been started. All of this work that has been done by mathematicians from different countries have led to what we lean and know today as non-Euclidean geometry. When one compares and contrasts Euclidean geometry and non-Euclidean geometry there are differences when looking at parallelism or the fifth postulate, distance between lines, and the angle sums of triangles.
Religions influence on the mathematical world: In depth look on ancient India and Greece
ReplyDeleteReligion can significantly affect one’s life or it can be greatly insignificant. In the development of mathematics, it is easy to see religion intertwined. This holds true for nearly all cultures. The Greeks were able to discover the true beauty of music and astronomy, they were also able to discover the true beauty of both mathematics and religion. The Greeks created a view of the world in which math and religion were entirely linked. Never before or since has math played such a large role in life and religion. India has always had a rich connection with the religions of the land that includes Hinduism, Buddhism, and Islam. Since religion plays a vital role in society, the religious thinkers of India have brought vast change to the land. Indian mathematics can be traced back to around 600 BC, when a number of Vedic manuscripts were found. They continued their advancements in the mathematical world by the sulbasutras, astronomical findings, and geometric findings.
The Pythagorean Theorem in different Civilizations:
ReplyDeletewe are all familiar with the theorem and what is says but each civilization had their own approach and motivations behind the discovery of this proof. Just like math builds on itself, some ideas blend together that also give these civilizations something in common. We are all familiar with maybe one of two proofs that we learned when we were taught this theorem but throughout the course of history some 84 proofs of the Pythagorean Theorem have been recorded. This theorem may seem trivial and straightforward ever since it's discovery.
Pythagorean Theorem
ReplyDeleteChristine and I will be discussing the Pythagorean Theorem throughout the ancient cultures of the Greeks, China, and India.
We will talk about different reasons for the discovery and the applications used and focus heavily on the various approaches taken. Although all cultures derived the same theorem the way in which they found the theorem varies greatly but also shows some similarities.
This comment has been removed by the author.
ReplyDeleteThe Work of Archimedes
ReplyDeleteArchimedes was without a doubt one of the most influential mathematicians in history. In many was he was a pioneer of various branches of science and applied mathematics. He will probably mostly always be remembered for "Archimedes' Principle" because of its popular use today, but there are many other lesser known works that deserve to be talked about. Being one of the first mathematicians to accurately calculate the value of pi, Archimedes was able to make many advancements relating to circles that are very applicable today. Archimedes was an amazing figure in the history of mathematics, and it is a shame that so much of his work was lost because with his ideas future mathematicians and scientists may have been able to accomplish so much more.
I will be talking about the History of Logarithms today...
ReplyDeleteABSTRACT: Most of the students in high school and in college have a difficult time with logarithms. In many cases, they memorize formulas and rules without actually understanding what a logarithm is. They even solve complicated problems, they learn how to integrate or differentiate then not knowing what they’re actually doing. Logarithms are an integral part of many forms of technology, and their history and development help us to see their importance and relevance. This paper surveys the origins of logarithms and their usefulness both in ancient and modern times. A brief introduction of the concept of logarithm, some properties and examples are also given.
The Approximations of Pi
ReplyDeleteAbstract: looking at the history of the calculations to the number pi. Starting with the Babylonians and ending with the computers of today.
Finding the radius of the earth using a picture.
ReplyDeleteUsing a picture of the sun setting on Lake Michigan, I can find a pretty good approximation of the radius of the earth. It involves the length of the reflection of the sun on the lake, some basic geometry and a little bit higher level of math that I probably wont get into during class.
I was thinking about Andrew's presentation on Vedic Mathematics, originally when we had learned it in class I thought of it as a potentially interesting way for kids to learn arithmetic. After I thought about this longer and thought it could be potentially more harmful than helpful because students would not see the methods behind the calculations they were doing. After Andrew's presentation today in class I realize that actually Vedic Mathematics is a great way to introduce proofs like Andrew had suggested, and rather than provide a shortcut they provide an example that is easy for a student to check their answers.
ReplyDeleteYes, I totally agree. I also think that kids would really enjoy this Vedic stuff. On the one hand they would learn some really cool arithmetic tricks which they can use to entertain their friends at a party. But also, on the other and more serious side, it is a great way to introduce them to proofs which they are often scared of.
ReplyDeleteI am very glad that Andrew has chosen this topic because this was very much on my mind and I could not get to it in the interest of time.
I was very curious about the 13 Archimedean solids which Nick mentioned in his talk. I found more information about this on Wikipedia. There is a precise mathematical definition of these solids. An Archimedean solid is a convex polyhedron composed of two or more types of regular polygons meeting in identical vertices. So what Archimedes gave is a complete classification of these solids (13 types).
ReplyDeleteI also found some interesting history on the Cattle Problem on Wikipedea.
I had lots of comments to make after Rachel's presentation because I passionately love the number Pi. This is a number which has been very dear to my heart since I was a child.
ReplyDeleteSince Pi seems such a fundamental number, it is natural to find this number in nature. Could it be that God used this number in designing the universe? Answer: YES, in all probability. There is a way to compute the digits of Pi using data that is given by God, namely the configuration of the stars. Here is how you do it. This idea is due to Robert
Matthews who wrote this in the scientific journal "Nature" in 1995. It uses basic probability theory and a relies on a result of Euler (1 + 1/2^2 + 1/3^2 + 1/4^2 ... = pi^2/6).
The idea is to find the angular distances (theta) between lots of stars and convert them into large integers by applying [1 + cos(theta)]*million. From this set of numbers pick random pairs and find the proportion (p) of these pairs with no common factor. It can be shown that pi is approximately equal to square root of 6/p. This approximation can be made as close as possible to the actual value of Pi by taking more and more stars in the data. By choosing just the top 100 brightest stars in the sky you can get an approximation of Pi as 3.12772 using this method! Note that the error is less than 0.4% for 100 stars. What is you use 1000 stars? 10000 stars? you can diminish this error as much as you please by taking more and more stars.
Conclusion: Pi is is the Sky which is God's creation without human intervention. Or you may equally well conclude that God is a mathematician! Aha!
Everyone had very interesting presentations yesterday. Thank you all for sharing.
ReplyDeleteI thought Rachel's presentation as very interesting. It is amazing that Pi has been studied for so long, I mean up to ten years ago. I also think it is so interesting that it is such a long number, and that some people actually found 707 digits by hand. Of course I love that Pi is 3.14 because that is my birthday too! haha
Good job to everyone on the presentations yesterday. I also thought the Vedic Mathematics presentation by Andrew was interesting. I love using shortcuts in math if it makes a problem easier but I enjoyed learning the set up behind the shortcuts. I'm excited to see what others will be presenting today; we all have selected diverse topics that are informational and intriguing!
ReplyDeleteMath and Elections (applied math)
ReplyDeleteA brief history of the voting possibilities and the electoral college. How can the appropriation of votes change the outcome of an election? How does the electoral college work.
How gravity effects geodesics, the study of catenary and cycloids
ReplyDeleteby Remi Mbah and Kevin Bugusky
Dive into the origins and evolution of 2 age old problems and their increasing effects on the world.
Caitlin and myself will be talking about Navigational History. We will be talking about map making during the Renaissance and how it correlates to the longitude problem. We will also talk of John Harrison as well as the Lunar Distance Method of determining longitude.
ReplyDeleteWe are really excited and have been talking about previous presentations. We think everyone is doing a really impressive job and find this as being a fun way of learning.
Yes, I am also excited about the presentations. I very much enjoyed the diversity of the presentations: full of interesting history, beautiful ideas, surprising facts and lots of culture. Good job everyone!
ReplyDeleteToday's 3 talks will also be very interesting. They can be put together under the theme "history of applied mathematics." I am sure you will enjoy these talks. They will focus more on the renaissance and modern mathematics.
Pell's Equation: I will review a little of the historical development of Pell's Equation, who the major contributors were, and an example of how each contributor solved the equation x^2 = Ny^2 + 1.
ReplyDelete