Today is a free exploration day. I will share the details in class. The HW besides commenting about the lessons and what your learned and commenting on other people (this happens every week) is going to be given in class. Stay tuned....
In my outside explorations this weekend, I considered the existence of fractals in nature, the 1=2 proof, and the number 23. I reflected for quite some time on what we had learned about fractals appearing in leaves and other natural places. I also showed my roomate the 2=1 proof, eventually helping him to see what was wrong with it. It is fascinating to me what happens when you divide by zero, which is the reason it is something we are told not to do in algebra. I also reflected on the number 23. You may or may not be familiar with the recent film of the same name which details a long list of interesting coincidences surrounding the number. For example, Shakespeare was both born and died on the 23rd of february. Human beings have 23 pair of chromosomes. Blood circulates completely through the body (on average) every 23 seconds. So maybe these are all coincidence, but at the same time, with a little bit of "creative math" you can derive the number 23 from almost anything. For example, driving down the road awhile ago, I saw a sign saying "Exit 34, 1/2 mile away". No 23's, right? Well, if we divide 23 in half (the 1/2 coming from the exit being 1/2 a mile away) we get 11.5. 5 is 2+3, so it can be removed from 11.5, leaving just 11. so subtract this from the exit number, and you get 23. The speed limit at the time was 65, which happens to be 2*3 (6) and 2+3 (5). For you skeptics out there, no I don't believe there's some mystical property surrounding 23, but I do find it fun to figure out ways to derive it. It only proves in the end that you can find anything anywhere if you want to find it badly enough.
I discussed certain classes concerning math with another person during Friday's exploration period. We were trying to figure out why math classes seem so terrifying and overwhelming. When I first walked into the classroom I saw a formula and a triangle up on the board and I nearly had a heart attack. It bothers me that I am not more comfortable with math, because it is such a fundamental part of life.
I enjoy doing math when I understand it, but all of my previous teachers have just told me to do it without answering the big question, "Why?". I would like to study the origins of math, and how Pythagoras came around to discovering his theorm. I want to know what drove these men to come to such remarkable studies because I feel that they hold the answer to "Why?" which has so long been neglected in all of my classes.
I really liked the idea of discovering math by exploring our surroundings at IC, but experience was a bit distressing. When we left the classroom, I was excited to go out and find patterns of math outside, naturally existing and growing. I wanted to see my school in a new way and I thought it'd be great to be able to tie math into nature. However, I found that while there were plenty of patterns, most of them were not left to flourish and develop on their own. Everything seemed to be forced into some other, perhaps more "attractive" formation. Outside of the campus center I noticed that every tree along the walkway has been carefully planted in between each bench. Even in a set of two benches, there was a tree stuck right in between. Outside of park was the same thing, tree, pillar, tree, pillar. This is not to say that those patterns aren't interesting or valuable and they certainly are aesthetically pleasing, it just wasn't exactly what I was hoping for. I find it kind of unfortunate that we are conditioned to find a bland pattern like that prettier than wildly growing and intertwining plant life- which i believe is much more interesting and exciting in it's naturally functioning and beautiful chaos.
I just read 3 comments Sunday night. Chuck Hannah and Ashton. I understand that this is what is. Most of us may not be ready to put a continuous effort into expanding the mind but everything happens in its own time and I am not going to distress about it or to take it as my own personal failure, but at least these three entries did rejuvenate me and quality is more important than quality. Each one of them expressed a different idea and yet all three were somehow connected. In my own mind what Chuck wrote is that we create our own reality and give meaning to things (did you read the book man's search for meaning? What Ashton express was a sincere desire to go beyond the fear of Math and she feels intuitively that there is immense beauty and creativity in Math which is waiting to be discovered. And Hannah expressed the idea that the nature has beauty that is hidden within the seeming chaos...
In my weekend exploration i went 3 hours away to STate College Pennsylvania, where Penn State University is located. It seemed like the football game I was at on Saturday was all about numbers. The first numbers of the day were the 150 dollars i paid for my ticket to see this game. We then drove 3 hours to the stadium and parked in lot 3. After parking we walked toward the stadium to see thousands of people dressed all in white because this game was what penn state calls a white-out. Whenever a huge opponent like Notre Dame comes, everybody wears white, and this was the first ever FULL STADIUM white out. once we got to our seats i wondered how many people the stadium could hold. I was sitting in row 72 out of 400 in my section. I tried to add up how many sections and seats there could be but this stadium s one of the largest in the United states. After Penn state defeated Notre Dame 31-10, we were informed that the game had a record breaking crowd of 110,078 people in attendance. I think its truly amazing how one game can bring that many people together in one place at a time. Another fun fact is that State College registered a really small earthquake because of all the noise the stadium made on Saturday.
I'm not sure if I'm doing exactly what I'm supposed to, but I found it really interesting to keep math in the back of my head all weekend. It actually worked - I saw Math everywhere. I first began noticing it in architecture; how all the buildings were beautiful because of perfect symmetry, etc. I went to my boyfriend's nephew's 7th (lucky number!) birthday party and helped him count his money. I timed he and his friends in their big-wheel/bicycle race. When I was trying to show my boyfriend how to bake brownies, he asked me how he'd get 2/3 cup when the only measuring cups I had were 1, 1/2, 1/3, and 1/4. At first I thought he was joking but then I just told him to use the 1/3 cup twice. He felt kind of stupid. I can't even remember specifics right now but all weekend I was commenting on how Math really is everywhere, and everyone kind of thought I was crazy at first, but then they started noticing it too.
Being a fan of music, i looked into how music and math are related. I realized that Music is made up of sound. Sound is made from repeating sound waves. The musical pitch of each note has a corresponding frequency measured physically cycles per second. When i got home that night, i looked into it further on the Internet and found this site, http://members.cox.net/mathmistakes/music.htm which puts basically everything i do on the guitar and relates it to math. Going in, i knew that math was definitely in music, but after reading this website, i noticed that music really is math.
In our free exploration some friends and I explored 3 and its multiples. We discussed how you can find this number in many aspects of our lives. Our eating cycle for example is a form of three, so are the triangles that make up pyramids (which are a very important shape). Then to continue my research this last weekend I tried to build on this theory of math in our lives and universe. I googled math and the universe and came across a very interesting blog in which people were discussing this topic. The blog talked about how the universe is sort of a machine and that the rules which allow it to work are based on logical processes (i.e math). This also lead to mentioning the fact that the universe is multidimensional and so there must be math embedded inside it that we cannot even wrap our minds around. But this math in other dimensions holds our world together as well as all the other dimensions. The interesting thing about this is the question "Is math anything more than just something we created as humans to explain the universe?" and that by defining math we define the universe. For example to translate the world around us. This is a excerpt from the blog explaining how we use math to define things around us: "how many atoms there are = mass how many atoms it can pull toward itself and how fast those atoms move = gravity how many electron move in a given time period=current" This is something I found very interesting to think about, and will hopefully pursue it more in the future.
In our group, Chuck was talking about the number 23 and its presence in nature. We came to the conclusion that it is not necessarily that that particular number has a greater significance than other numbers, just that you can find what you are looking for if you really look. This concept surrounding the number 23 was based off of a movie, which also got me thinking about Darren Aronovsky's movie "Pi". In that movie, they briefly talk about Gematria, or finding the meaning in the numerical value of Hebrew words. In class, I figured out the numerical value of several of my classmates' names and see if I found any patterns. I also found the numerical value of other common words. For example, the numerical value of the word "ahava" (which means "love" in Hebrew) is 13. The number thirteen in the Jewish culture does not have such negative connotations, and rather is a more positive number. 13 is the age of Bar Mitzvah, or the age of taking on new responsibility. I also have tried to find patterns involving the number 18, since the numerical value of "chai", or life, is 18.
My observations this weekend began with math, and led toward more philosophical realizations about life. I went to the gorges on Friday and hurt my foot when I jumped into the water. I was pretty upset about it, and knew that it will affect future feelings I have about going to the gorges, (even though 9/10 of my trips there had been great). As I continued to think about it, (sitting on my couch with an ice pack on my poor foot), I realized that until Friday, my experiences with Ithaca's gorges had been nothing but wonderful! I shouldn't let one negative experience discolor my entire perception of the gorges. On the other hand, I still needed to learn and take something from that experience to make sure that didn't happen again. It's interesting that if I've been to the gorges 10 times, the first thing that pops into my head is the 1 negative experience I had. As with so many things in life, sometimes it takes effort to think positively. I think that for many of us, that extra effort is necessary for math, too. Being able to continue trying to positively explore a topic that hasn't brought positive experiences is a valuable skill that we can learn from this class.
Math is everywhere. It is connected to the universe in every possible way. Math forms the basis of life itself...When exploring the question "What is Math?" we are not just talking about equations and numbers. A more appropriate question to ask might be "What is life?" because math is life. When thinking about math this weekend, I couldn't help but think about my life and the way it exists in this universe. I believe that the outcomes that you receive in life is affected by the energy that you put out into the world. I was feeling very down last week, and had been omitting negative energy. I knew that I had to change my pattern of thinking in order to change my mood, but I didn't do it. As a result, I had a weekend that was filled with disappointment after disappointment. Had I controlled the variable (my thinking) I could have reaped a better outcome (end result). Life is obviously not just a pure equation, but it is so closely related to math it is certain that the two are intertwined very closely. I will continue to think about this as the semester progresses.
When I first heard the assignment, I didn't know exactly what to write about since I'm usually scared of anything that has to do with math. On our outdoor excursion, a few classmates and I talked about fractals in nature. We then came to the conclusion that there are an infinite number of fractals in nature. For example, leaves grow in a fractal pattern. There are an infinite amount of leaves that are produced from one tree. There are an infinite number of trees, therefore there are an infinite number of fractals in nature.
Over the weekend, I was watching Dateline and came across a story about a man named Mike Byster who invented what he calls "Brainetics." Mike is not a math teacher at all. He used to work for the Chicago Mercantile Exchange. Mike was born with a gift to computate numbers in his head like a calculator. He then decided that he wanted to share his gift with young math students starting at the age of 10. Mike is strictly a volunteer and does not get paid for his services. He's developed a system of shortcuts that help kids solve math problems without the use of a pencil and paper or a calculator. They showed one example of how his shortcuts work. This is the rule for multiplying duplicate numbers that end in 5. For example, 25 x 25. First take the first number and multiply it by the first number plus 1. So, 2 X (2+1) = 6. Now multiply 5x5 = 25. When you put those two number together, its equals 625 which is the answer to 25 X 25. Mike is working on a website and an intructional video that is set to premiere some time in November. Can't Wait!
For my exploration this weekend I choose to look at the golden ratio and find out more about it. I did some research on the internet and found out many interesting things about the ratio that is 1.618. I learned that the golden ratio was not just confined to mathematics but biologists, artists, musicians, historians, architects, psychologists, and others have discussed the ratio. I also spent some time learning about the aesthetic properties of the ratio. Written by Luca Pacioli, De Divina Proportione talked about the mathematics of the golden ratio and how it yields pleasing, harmonious proportions. It was interesting to look at pictures and sculptures where the ratio was applied. I am excited to continue to explore this phenomenon.
13 comments:
In my outside explorations this weekend, I considered the existence of fractals in nature, the 1=2 proof, and the number 23.
I reflected for quite some time on what we had learned about fractals appearing in leaves and other natural places. I also showed my roomate the 2=1 proof, eventually helping him to see what was wrong with it. It is fascinating to me what happens when you divide by zero, which is the reason it is something we are told not to do in algebra.
I also reflected on the number 23. You may or may not be familiar with the recent film of the same name which details a long list of interesting coincidences surrounding the number. For example, Shakespeare was both born and died on the 23rd of february. Human beings have 23 pair of chromosomes. Blood circulates completely through the body (on average) every 23 seconds. So maybe these are all coincidence, but at the same time, with a little bit of "creative math" you can derive the number 23 from almost anything. For example, driving down the road awhile ago, I saw a sign saying "Exit 34, 1/2 mile away". No 23's, right? Well, if we divide 23 in half (the 1/2 coming from the exit being 1/2 a mile away) we get 11.5. 5 is 2+3, so it can be removed from 11.5, leaving just 11. so subtract this from the exit number, and you get 23. The speed limit at the time was 65, which happens to be 2*3 (6) and 2+3 (5).
For you skeptics out there, no I don't believe there's some mystical property surrounding 23, but I do find it fun to figure out ways to derive it. It only proves in the end that you can find anything anywhere if you want to find it badly enough.
I discussed certain classes concerning math with another person during Friday's exploration period. We were trying to figure out why math classes seem so terrifying and overwhelming. When I first walked into the classroom I saw a formula and a triangle up on the board and I nearly had a heart attack. It bothers me that I am not more comfortable with math, because it is such a fundamental part of life.
I enjoy doing math when I understand it, but all of my previous teachers have just told me to do it without answering the big question, "Why?". I would like to study the origins of math, and how Pythagoras came around to discovering his theorm. I want to know what drove these men to come to such remarkable studies because I feel that they hold the answer to "Why?" which has so long been neglected in all of my classes.
I really liked the idea of discovering math by exploring our surroundings at IC, but experience was a bit distressing. When we left the classroom, I was excited to go out and find patterns of math outside, naturally existing and growing. I wanted to see my school in a new way and I thought it'd be great to be able to tie math into nature. However, I found that while there were plenty of patterns, most of them were not left to flourish and develop on their own. Everything seemed to be forced into some other, perhaps more "attractive" formation. Outside of the campus center I noticed that every tree along the walkway has been carefully planted in between each bench. Even in a set of two benches, there was a tree stuck right in between. Outside of park was the same thing, tree, pillar, tree, pillar. This is not to say that those patterns aren't interesting or valuable and they certainly are aesthetically pleasing, it just wasn't exactly what I was hoping for. I find it kind of unfortunate that we are conditioned to find a bland pattern like that prettier than wildly growing and intertwining plant life- which i believe is much more interesting and exciting in it's naturally functioning and beautiful chaos.
I just read 3 comments Sunday night.
Chuck Hannah and Ashton. I understand that this is what is. Most of us may not be ready to put a continuous effort into expanding the mind but everything happens in its own time and I am not going to distress about it or to take it as my own personal failure, but at least these three entries did rejuvenate me and quality is more important than quality. Each one of them expressed a different idea and yet all three were somehow connected. In my own mind what Chuck wrote is that we create our own reality and give meaning to things (did you read the book man's search for meaning? What Ashton express was a sincere desire to go beyond the fear of Math and she feels intuitively that there is immense beauty and creativity in Math which is waiting to be discovered. And Hannah expressed the idea that the nature has beauty that is hidden within the seeming chaos...
In my weekend exploration i went 3 hours away to STate College Pennsylvania, where Penn State University is located. It seemed like the football game I was at on Saturday was all about numbers. The first numbers of the day were the 150 dollars i paid for my ticket to see this game. We then drove 3 hours to the stadium and parked in lot 3. After parking we walked toward the stadium to see thousands of people dressed all in white because this game was what penn state calls a white-out. Whenever a huge opponent like Notre Dame comes, everybody wears white, and this was the first ever FULL STADIUM white out. once we got to our seats i wondered how many people the stadium could hold. I was sitting in row 72 out of 400 in my section. I tried to add up how many sections and seats there could be but this stadium s one of the largest in the United states. After Penn state defeated Notre Dame 31-10, we were informed that the game had a record breaking crowd of 110,078 people in attendance. I think its truly amazing how one game can bring that many people together in one place at a time. Another fun fact is that State College registered a really small earthquake because of all the noise the stadium made on Saturday.
I'm not sure if I'm doing exactly what I'm supposed to, but I found it really interesting to keep math in the back of my head all weekend. It actually worked - I saw Math everywhere. I first began noticing it in architecture; how all the buildings were beautiful because of perfect symmetry, etc. I went to my boyfriend's nephew's 7th (lucky number!) birthday party and helped him count his money. I timed he and his friends in their big-wheel/bicycle race. When I was trying to show my boyfriend how to bake brownies, he asked me how he'd get 2/3 cup when the only measuring cups I had were 1, 1/2, 1/3, and 1/4. At first I thought he was joking but then I just told him to use the 1/3 cup twice. He felt kind of stupid. I can't even remember specifics right now but all weekend I was commenting on how Math really is everywhere, and everyone kind of thought I was crazy at first, but then they started noticing it too.
Being a fan of music, i looked into how music and math are related. I realized that Music is made up of sound. Sound is made from repeating sound waves. The musical pitch of each note has a corresponding frequency measured physically cycles per second. When i got home that night, i looked into it further on the Internet and found this site, http://members.cox.net/mathmistakes/music.htm
which puts basically everything i do on the guitar and relates it to math. Going in, i knew that math was definitely in music, but after reading this website, i noticed that music really is math.
In our free exploration some friends and I explored 3 and its multiples. We discussed how you can find this number in many aspects of our lives. Our eating cycle for example is a form of three, so are the triangles that make up pyramids (which are a very important shape). Then to continue my research this last weekend I tried to build on this theory of math in our lives and universe. I googled math and the universe and came across a very interesting blog in which people were discussing this topic. The blog talked about how the universe is sort of a machine and that the rules which allow it to work are based on logical processes (i.e math). This also lead to mentioning the fact that the universe is multidimensional and so there must be math embedded inside it that we cannot even wrap our minds around. But this math in other dimensions holds our world together as well as all the other dimensions. The interesting thing about this is the question "Is math anything more than just something we created as humans to explain the universe?" and that by defining math we define the universe. For example to translate the world around us. This is a excerpt from the blog explaining how we use math to define things around us: "how many atoms there are = mass
how many atoms it can pull toward itself and how fast those atoms move = gravity
how many electron move in a given time period=current" This is something I found very interesting to think about, and will hopefully pursue it more in the future.
In our group, Chuck was talking about the number 23 and its presence in nature. We came to the conclusion that it is not necessarily that that particular number has a greater significance than other numbers, just that you can find what you are looking for if you really look. This concept surrounding the number 23 was based off of a movie, which also got me thinking about Darren Aronovsky's movie "Pi". In that movie, they briefly talk about Gematria, or finding the meaning in the numerical value of Hebrew words. In class, I figured out the numerical value of several of my classmates' names and see if I found any patterns. I also found the numerical value of other common words. For example, the numerical value of the word "ahava" (which means "love" in Hebrew) is 13. The number thirteen in the Jewish culture does not have such negative connotations, and rather is a more positive number. 13 is the age of Bar Mitzvah, or the age of taking on new responsibility. I also have tried to find patterns involving the number 18, since the numerical value of "chai", or life, is 18.
My observations this weekend began with math, and led toward more philosophical realizations about life. I went to the gorges on Friday and hurt my foot when I jumped into the water. I was pretty upset about it, and knew that it will affect future feelings I have about going to the gorges, (even though 9/10 of my trips there had been great).
As I continued to think about it, (sitting on my couch with an ice pack on my poor foot), I realized that until Friday, my experiences with Ithaca's gorges had been nothing but wonderful! I shouldn't let one negative experience discolor my entire perception of the gorges. On the other hand, I still needed to learn and take something from that experience to make sure that didn't happen again.
It's interesting that if I've been to the gorges 10 times, the first thing that pops into my head is the 1 negative experience I had. As with so many things in life, sometimes it takes effort to think positively.
I think that for many of us, that extra effort is necessary for math, too. Being able to continue trying to positively explore a topic that hasn't brought positive experiences is a valuable skill that we can learn from this class.
Math is everywhere. It is connected to the universe in every possible way. Math forms the basis of life itself...When exploring the question "What is Math?" we are not just talking about equations and numbers. A more appropriate question to ask might be "What is life?" because math is life. When thinking about math this weekend, I couldn't help but think about my life and the way it exists in this universe. I believe that the outcomes that you receive in life is affected by the energy that you put out into the world. I was feeling very down last week, and had been omitting negative energy. I knew that I had to change my pattern of thinking in order to change my mood, but I didn't do it. As a result, I had a weekend that was filled with disappointment after disappointment. Had I controlled the variable (my thinking) I could have reaped a better outcome (end result). Life is obviously not just a pure equation, but it is so closely related to math it is certain that the two are intertwined very closely. I will continue to think about this as the semester progresses.
When I first heard the assignment, I didn't know exactly what to write about since I'm usually scared of anything that has to do with math. On our outdoor excursion, a few classmates and I talked about fractals in nature. We then came to the conclusion that there are an infinite number of fractals in nature. For example, leaves grow in a fractal pattern. There are an infinite amount of leaves that are produced from one tree. There are an infinite number of trees, therefore there are an infinite number of fractals in nature.
Over the weekend, I was watching Dateline and came across a story about a man named Mike Byster who invented what he calls "Brainetics." Mike is not a math teacher at all. He used to work for the Chicago Mercantile Exchange. Mike was born with a gift to computate numbers in his head like a calculator. He then decided that he wanted to share his gift with young math students starting at the age of 10. Mike is strictly a volunteer and does not get paid for his services. He's developed a system of shortcuts that help kids solve math problems without the use of a pencil and paper or a calculator. They showed one example of how his shortcuts work. This is the rule for multiplying duplicate numbers that end in 5. For example, 25 x 25. First take the first number and multiply it by the first number plus 1. So, 2 X (2+1) = 6.
Now multiply 5x5 = 25. When you put those two number together, its equals 625 which is the answer to 25 X 25. Mike is working on a website and an intructional video that is set to premiere some time in November. Can't Wait!
For my exploration this weekend I choose to look at the golden ratio and find out more about it. I did some research on the internet and found out many interesting things about the ratio that is 1.618. I learned that the golden ratio was not just confined to mathematics but biologists, artists, musicians, historians, architects, psychologists, and others have discussed the ratio. I also spent some time learning about the aesthetic properties of the ratio. Written by Luca Pacioli, De Divina Proportione talked about the mathematics of the golden ratio and how it yields pleasing, harmonious proportions. It was interesting to look at pictures and sculptures where the ratio was applied. I am excited to continue to explore this phenomenon.
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