Did I scare you or confuse you with the weekend assignment that was to spend 2 hours and create/write something beautiful that has to do with Math? I did not see any one actually do it even though a few people responded in a beautiful way on the blog.
My style of teaching is so different than what you are used to that probably you do not understand yet my intent but I am not going to give up on you since I believe that each and every one of us has a unique gidt, a flower of creativity that is waiting to be opened and Mathematics (the queen) is part of it. So here I am offering you more structure but am asking that you will be honest and devote 2 hours for every class time we have from now till then end of the semester and if you do it you will learn a tremendous amount. Part of that time should be used to write your thoughts/projects/creation etc. in the blog to share with me and others. I also remind you to look again at .
Pick one or more of the following topics (you can use google and other web tools)
1. Study what the concept Dimension mean? What does it mean for you personally and what does it mean in principle.
2. Download SeeLogo from http://www.ithaca.edu/dani/SeeLogo/index.htm and create the spiral of life art design and master how to do it. (after you download click lessons what is Math and Spiral of Life Introduction
3. Go for a trip downtown with some friends and visit some churches (start with the chapel at IC and sketch some of the divine art take pictures and share with class)
4. Study what the divine proportion means and describe it in your own words after you get the feeling. (google)
5. Do several activities from the book "Math for Smarty Pants" and write about them.
6. Pick a beautiful Math Thought and write about it (from the following link:)
Math Thoughts
http://www.ithaca.edu/dani/classes/Wim/Math_Thought_of_The_Day/Math_Thoughts.html
23 comments:
This past weekend I had the opportunity to watch Cirque du Soleil perform in Syracuse. When the show started I was completely mesmerized by the different acts being presented on stage and found myself wondering "how the heck are they doing that!" As I began to think more deeply I realized that all the performers were using math in their routines. Almost everything was a matter of displacement, balance, addition, subtraction, division, multiplication and as I kept watching I couldnt help but be blown away at how magical math truly is. I do not think I would have been able to draw that connection without being a student in this class. Quite honestly, I have never really thought about how math fits into everything day life before listening to the discussions presented to me this semester. I am thankful for the eye opening experience, it made the circus that much more enjoyable!
Dani, I know we were supposed to write about one of the topics you posted in the last blog, but I've truly been inspired to talk about something else that makes me really excited: Brainetics. Invented by Mike Byster, Brainetics is a system of math tricks that allow you to do math computations without a pen and paper or a calculator. I was watching Dateline Friday night, and there was a special on this concept. Mike Byster is considered the fastest mathematical minds on the planet. Now he's sharing his gifts with kids all over the country. If only I had learned this before, I might have scored way higher on the math portion of the SAT and ACT. How does it work?
Well, there seems to be a trick for all types of numbers. Mike shares a few examples on his website (www.mikesmath.com). For example, here's the rule for squaring any number that ends in 5.
Example: 35 x 35
Step 1: Take the tens digit and multiply it by the number one greater than it. 3 x (3+1) = 12.
Step 2: Tack 25 onto the end of the number from Step 1.
Answer: 1,225.
And it works everytime! I tried it 8 times in class with other numbers and it never fails. Can it work with a number greater than two digits? Absolutely! Lets try 105 x 105.
Step 1: 10 x (10+1) = 110
Step 2: Tack on 25
Answer: 11,025
Still not convinced? Lets try another trick. Squaring numbers in the 50's.
Example: 57 x 57
Step 1: You start out with 25 and add the ones digit to it.
25 + 7 = 32
Step 2: Square the ones digit. 7 x 7 =49 Tack this onto the end of the answer from step 1
Answer: 3249
These are only two examples of the many tricks Mike has come up with. He plans on coming out with a full website for Brainetics and a video later this November. If you want to learn more tricks, I encourage you to go to Mikesmath.com. It's great!
I'm not entirely sure I follow the last part of what you wrote today. Do you mean that you want us to start writing our blogs about one of the things you listed as opposed to our personal math discoveries in class and on our own? Or, did you mean that we should be considering that as a long term project to begin thinking about now?
Either way, I would like to share more of my personal discoveries in this partiicular entry. I have some more to say about the number 23. First of all, I want to be clear that I don't think the number 23 in and of itself has any special or mystical properties. The entire 23 "phenomenon" is rather an illustration of the human mind's ability to see what it wants to. Once the idea of 23 being everywhere is pointed out, one's mind begins to take any coincidental set of numbers and somehow derive 23. Yes. This could be done with any number. I am merely talking about the number 23 because there happens to be a large group of people who find it's recurrence to be some "sign". Rather, I posit the following: 23 is an illustration of the human mind's ability to sort information and form patterns from random information.
Once it has been suggested that 23 is everywhere, one notices that the earth's axis is tilted 23.5 (the 5 being 2+3, and therefore also 23) degrees.
In short, it's psychology, not the number itself.
So why 23? Why not 42? Why not 987?
Well, 23 is a prime number, to begin with. Both of it's digits are also prime individually, the first (2) being the only even prime number (3 being the 2nd odd prime). Also, aside from one and two, 2 and 3 are the only prime numbers that occur in sequence on a number table. It is also interesting to note that they also appear in sequence in a Fibonacci sequence, followed by 5, which is 2+3. So perhaps that's why people choose to pick out 23 as the "special" number that can be found everywhere. I don't really know, but, having been introduced to this psychological phenomenon, I find it amusing and sometimes challenging to derive 23's from seemingly randomly occuring numbers and patterns.
My conclusion? Don't read too much into it. I pointed it out, and you'll notice it if you let your mind dwell on it, but it could have easily been any other number. The human mind has sorted many random facts into patterns and synchronicities, sometimes discovering deep fundamental truths, other times assigning meaning to what is really random. I can hardly imagine it's nearly infinite capacity...
Today in class my group discussed the current and future states of the environment, and how this relate to math. Math can be used to examine and further understand past climate information, and then predict future climate conditions. I would like to focus more on these topics as this class progresses.
Some information about how rapidly our earth is declining, and the variety of facets these changes present themselves in is surprising. I was searching on google for articles concerning these topics, and found this article concerning ozone loss over Antarctica in the past 25-30 years:
http://www.atm.ch.cam.ac.uk/tour/part2.html
It provided some really interesting, (and intimidating) facts. These facts were gathered using measurements that require math. Math really is a part of almost all science-based research and tests.
This is my first time posting on this blog and I wanted to share something about one of my passions as related to mathamatics. I am a senior outdoor adventure leadership major and i have recently taken up the sport of whitewater kayaking. recently while thinking about how one actually kayaks it was alarming just how mathematically everything in kayaking must be in order to be successful. For one water currents are amazing and powerful. without proper angle and use of the boats edges in the current you will not be able to stay upright. Surfing in a kayak is a great example of natural spirals (whirlpools), curves lines that are constantly changing. understanding that you must go with water and edge around whirl pools is essential and seems somewhat related to the divine proportion. after reading about the divine proportion and seeing a real life example makes the concept much more clear.I feel as though the divine proportion translates into my kayaking and my own personal lifestyle/philosophy about my life in that you have to go with the flow. the flow of the water the flow of your life. I dont mean you have to go with anyone elses flow in either instance in that you will never be in exactly the same place in your life as someone else just like you will never be on the same part of water with the same water currents. So live your life free and flowing and if you get flipped upside down flip yourself back up. Just a thought hope that made sense to someone.
In my previous comment I detailed my interest in the passion of math. While reading my history textbook I noticed the mention of Archimedes of Syracuse who discovered the approximate value of pi, and worked with the geometry of spheres and cylinders.
I felt compelled to research more about his personal life and find out what drew him to math. One quote by a colleague describes Archimedes eccentric behviaour, "-being perpetually charmed by his familiar siren, that is, by his geometry, he neglected to eat and drink and took no care of his person; that he was often carried by force to the baths, and when there he would trace geometrical figures in the ashes of the fire, and with his finger draws lines upon his body when it was anointed with oil, being in a state of great ecstasy and divinely possessed by his science."
Some might view this as a crazed obsession but I view it as a fascination with the whole of the universe. Archimedes was constantly drawn to the "siren" of math. Even in the description, math becomes a metaphor for a siren. The siren is a beautiful temptress that fulfills mans most inner desires. From this quote I can determine that math could be a siren for all of us. It just takes a little longer on the journey of our life to find her.
i have been learning about math as it relates to plants and how they grow. i found an interesting article called 'the mathematical lives of plants' which talked about how the golden ratio and how it occurs a lot in the natural world. nature has good design, and i think it's a pretty interesting thing to learn about. stuff we think of as human discoveries has in fact been known by the sunflower for ages. of course you have to have good design to be able to get energy from the sun... and even that we are learning to emulate.
someone also told me that the golden ratio appears in the human body a lot . i think i will keep reading about plants and the golden ratio. someone in santa cruz even wrote his dissertation on that stuff, so i am going to look into that.
the circque du soliel thing looks really beautiful from the pictures i found online, maybe we could watch a clip in class?
I was in Lael's group concerning math and environment. My interest was sparked when i first saw a link on the what is math site that talked about a "mass extinction underway". I clicked on it and was blown into disbelief. Scientists and mathemitician each using math have come to several conclusions about our environmental state. ONe regards the extinction of plant life and mammals over the next 50 years being like 40% due to global warming. I decided to do more research and found more articles talking about how scientists are calculating the global warming is causing more and more climate shifts (hurricanes) and polar ice caps are melting at alarming rates. I was kind of oblivious of all of this stuff going on around us and if Lael was interested.. i would like to go into more research on the environment and math.
When I left class yesterday, I was reading a book about chefs and cooking, so I thought I would spend a couple hours thinking about the ways food related to math. I found that there was a lot more than I ever thought of. I think food is a beautiful thing, so I was really excited that I could find something to relate math to that I really like. I found that proportion played a huge role in cooking, for example:
When making a Hollandaise sauce, why does it form an emulsion (math - how much oil will how many egg yolks hold in the emulsion), and why and how does lemon juice (an acid) effect the formation and stability of this emulsion, and what percentage of acid to use?
and
How much flour and how much oil to combine to make a roux, and how much flour roux will it take to thicken a given amount of liquid?
This was one very important mathematical factor to cooking. Cooking time and weight are also very important. Weight often affects cooking time. Consider the following hypothetical situation: you are cooking an 8 pound turkey for Christmas dinner. If the turkey needs to thaw in the refrigerator for 24 hours, per 5 pounds, we need to take the turkey out of the freezer in advance. 5 pounds is to 24 hours as 8 pounds is to x hours. By cross-multiplying and dividing, we can find an answer of 38.4 hours of thawing, which is the solution for x.
This exercise really showed me how math relates to everything and opened my eyes to how helpful this class could be to me.
Yesterday my roommate came home and he was very frustrated about something that had happened to him regarding his photography. He had been trying to hang it up at No radio records (which everyone should check out) and became so confused while measuring the wall and trying to figure out the spacing between each photo and how high is needed to be from the ground etc etc. At first the idea of my roommate getting all frazzled made me laugh, but then i began to think about how much math was involved in this instance and how it was math that was frustrating him so much. This really interested me because of the joining of math and art in this situation.
When i was a senior in high school, my intent was to go to art school to study two dimensional design with a concentration in painting. I never really considered how math and art were linked, but they are so incredibly linked. The entire concept of perspective revolves around math and measuring. Matting and framing are all mathematic equations and I'd been using and mastering them all this time without even realizing. I'm really beginning to open up to the idea of math being literally in and around everything. I'm trying to consciously acknowledge it and incorporate it even more into the things I do and love.
I'm a voice major here at IC, and for as long as I've been studying voice, I've never really stopped to think about how magnificent it truly is. Today in my private voice lesson, my teacher and I talked about how fast your vocal chords vibrate, as much as up to 400 times per second. It is amazing to think that something so small and compact, found inside your body, is responsible for such a large sound, and can move that quickly. Obviously, everyone’s voices (speaking and singing) are unique, and this is because the voice is not purely produced with the vocal chords…it is affected by your breath and resonating cavities in your face, including your sinuses. The more space you have in your face, the larger the sound will be. It is actually a very mathematical formula…the vocal placement has to be just so in order to get the maximum resonation, while at the same time it is crucial to maximize your breath intake (correctly) to support the chords. There are many abstract ways of looking at correct singing technique, but it is a very mathematical concept. I never realized how “simple” of a formula healthy singing is.
One of my main reasons for taking this course was to find a way to let math back into my life. After a DISASTROUS experience my junior year of high school, I shunned the Queen and all of her majesty entirely. I have always, however, been interested in sort of 'obscure' math concepts. This lead me to the massive undertaking that was my senior writing project on Chaos Theory. I loved researching fractals and the idea of an equation whose goal is to be incomplete and indefinite. Unlike a circle or a parabola, a fractal constantly repeats. I really enjoyed how it related to fluid dynamics (how the 'pattern' of heated water changes once that water begins to boil) weather patterns (how hurricanes form and how tornadoes come from conflicting electromagnetic charges) and how important initial conditions are in any situation and how a slight variation in those conditions changes the outcome ENTIRELY.
I think the thing for me is that I enjoy 'math' so long as it can be discussed using words. Once we have to start doing linear algebra and integrated calculus, I am lost in an attempt to make sense of the numbers instead of the concepts. I hope in this class I can get over that fear and see math for what it truly is.
For my math time I extended my studies into golden ratio or phi. The biggest thing that stuck out for me was the Fibonacci Series (1,1,2,5,8,13,21,etc) which Dani showed us in class. The coolest thing about this series of numbers which Fibonacci developed is that it is the process that plants grow. A plant would grow one flower then another one, then two flowers, then five and so on. I just think this is an amazing formula relating math to something completely natural. Other really cool things about Phi are its relationship to the pyramids of Giza, and Stradavari used the golden ratio to determine fingerboard size and placement of f-holes in his violins. I am so impressed that it is possible to find phi in so many places in life and history.
Throughout the day yesterday I tried to notice everytime I used math, and was surprised by how much I actually used it. I'm one of those people who's not a very big fan of math, but little did I know how much I'm actually using it in my day to day life! For example, yesterday my roommates and I had cable installed into our apartment and we had to divide the total up among the three of us to see what we would each be paying each month. That prompted me to look at my finances and create a budget based on how much money I earn each week compared with how much I need to set aside for bills and savings. I easily spent half an hour working through all of the details of my "budget" for the semester, and had never really realized how much time I actually spend dealing with numbers on a day to day basis. Aside from money, I have to budget my time, estimating how much time I'll need to get work done and comparing that with my class and work schedule.
I guess my conclusion is simply this- math is so present in my life I have barely taken the time to notice. Without being prompted from this class, I probably would have never realized how much I use math, and I now find myself disliking it less and less, as it helps me manage my life :)
Class on Monday was very intense for me. I suppose it related to Math in someway but was teeming with negative energy which was difficult to handle. I wound up listening to a guy who sits to the left of me in class spout off anything and everything he could possibly describe about our school and society in general that irked him or he wished was different/didn't exist. This began with a discussion regarding how expensive it is to go to school here and where exactly is obtained by the students in compensation for what is paid. I can related to this entirely as I pay my way through school and frequently feel frustrated by the way the costs seems to add up ad nauseum. However this individual began to berate me with his woes regarding live and technology in general. I suppose how this relates to math besides in terms of its financial components is the energy which was put forth by him onto to me. The force was so great I had to recalculate my own perception and mood in order to successfully continue with my day. Challenging class but not necessarily negative. I look forward to a change this afternoon however.
I have been completely absorbed in the creation of a music video for a contest called "Speak New Words" which completed after the due date on September 9th and since that date have been corresponding with the people responsible for the contest and encouraging friends and family to show their support as well.
Here is a link to the video for all who are interested: http://www.youtube.com/watch?v=8AhQ7uS5NgA
Because of leaving some parts of that project to the last minute I didn't devote nearly as much time as I should have to this class, especially since I am the one person I have heard of that isn't taking it for any type of requirement. (I completed my math req. last year with Dave Brown's History of Secrets and don't have a major so therefore don't have any additional math req.). I did , however, come to campus early this morning to take a few hours to look back at what the class has been up to and the blog and do have a few things to share.
I tried out "SeeLogo" and used the number 7 and multiples of the number 7 to see what kind of interesting results would come up.
Here are some images:
http://img.photobucket.com/albums/v256/bayjay/IT.png
http://img.photobucket.com/albums/v256/bayjay/7749.png
http://img.photobucket.com/albums/v256/bayjay/7LinesSPIN49IT.png
I also read up on dimension, Φ (Phi for those of you whose computer's can't read symbols) or "The Divine Proportion"/"Golden Rule" and the math thought about light. I still need to go back and learn about some of the other principles that you have all been discussing but I do have a few thoughts to share about these concepts that I have already mentioned.
Dimension, as I understand it, is simply a measure or scale, if you will, that we use to describe what a thing is in terms of size. In my own head somethings size, which could have to do with its volume or area depending on if it is a two or three dimensional thing, simply means roughly how many times it could fit into something else or in other words it's proportion. This is to say that dimension is practically meaningless unless we have some other thing with dimension to compare it to. This helps us understand the indirect relationship between things, meaning that we have a planet here, earth, and millions of light years away a giant star. They are in no way directly related to each other but we can relate them in terms of things that can be compared, dimension for instance. There is another way to look at this and that is that there is a great amount of chaos, despair and hatred on earth but compared to the calm and serenity and order of the cosmos it is ever so small and easily changed.
Φ to me goes along with the idea because it is simply the universal constant. That no matter what state things exist in now their end, ultimately, is a proportionate , equal and ordered one and that all things in nature, humanity and the universe inherently tend towards this rule. It is when we, as humans, try to change this universal constant, to try and fit more people on a planet that the planet that can provide for or on an individual level try to take more for ourself than is due to us that we disrupt this order and cause all sorts of problems.
To me this also relates to the concept of light. Last night I was talking to my friend from home who feels that his life is out of balance, that he is lonely and can't talk to anyone and that that he doesn't know his purpose. I told him to spend his time alone talking to himself (not necessarily out loud) so that he can begin to figure out what his purpose is and once he knows his purpose he will never feel lonely and his life will begin to balance itself out and furthermore this will eventually lead to him finding people who are passionate about the same purpose as him and he will have a deep real connection with them and not one based on arbitrary similarities of simply being in the same place, at the same time, looking and talking alike and the other things that normally initially attract people to each other socially.
To me this relates to the concept of light because my friend feels that he is a product of this society but doesn't want to be and wants to change the society but doesn't necessarily believe in the ability of himself or others around him to change. I believe that it is the responsibility of those who have even the smallest amount of light in them (the smallest amount being simply enough to know that not everything is darkness) to nurture this light until it shines so bright that it illuminates everything around them. Once this happens people close to these individuals will have the smallest amount of light in there lives and thus the process will continue and we will see a transition from particles of light to one lasting wave of the light of humanity.
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