Thursday, April 10, 2014
3 Tessellating Regular Polygons
After reading the interesting blog on the new "pi", you threw in the question of why are there only three regular polygons. Well, I was quite intrigued by this as I figured that there would surely be at least one more but thinking a little bit more on it, I figured something like a pentagon wouldn't be able to completely surround itself with more regular pentagons as there would be extra space between the repeating shapes. My theory was confirmed when I went to this site which put my brief and simple explanation into a genuine one with actual reasoning. It stated that the following regular polygons each had interior angles which divided evenly into 360 degrees; the triangle at 60 degrees, the square at 90 and the hexagon at 120. Due to this, the uniform tessellation (uniform meaning all polygons at one vertex are of the same type) is possible without any extra "space" as I had thought of at the start.
Tuesday, January 14, 2014
A Few Math Jokes
1. http://ecomatheasy.wordpress.com/2011/11/11/math-jokes/
3. http://gailsmcmillan.cmswiki.wikispaces.net/Math+Jokes
4. http://imgur.com/nkQkF98
5. http://sciencefun.wordpress.com/2007/01/31/foxtrot-always-does-great-math-jokes/
6. http://xwhy.comicgenesis.com/d/20110127.html
7. http://www.pixton.com/comic/15c4bw6c
8. http://www.pinterest.com/pin/314900198916695639/
9. http://www.pinterest.com/pin/314900198916356453/
10. http://explosm.net/comics/1695/Wednesday, November 13, 2013
Srinivasa Ramanujan
I decided to research a little more on Srinivasa Ramanujan, the famous mathematician known for his theories and new concepts of math, a shocker as he was self-taught as well. I found several sites talking about his earlier life and one went into a little detail of what his earlier college days were like. Ramanujan had a deep love for math which deepened when he obtained the book, A Synopsis of Elementary Results in Pure and Applied Mathematics leading him to plunge into it and become completely focused on mathematics. This would take a toll on his other subjects, causing him to fail college exams and eventually drop out. He then relied upon the charity of his friends as he was from a poor family and struggled to continue his deep interest in mathematics until he sent his theories and ideas to G.H. Hardy who led Ramanujan to England where his career took off.
I use math everyday when I think about things and organize the facts that I learn mentally and I often find myself using mental images to calculate numbers. Often times, this would be imagined as rows and columns of small blocks like the ones we used in elementary school: the blue plastic blocks that were available in singles, tens, sheets of 100 and a cube of 1000. Now with that aside, I found it extremely strange how devoted Ramanujan was to mathematics to the point of failing other subjects and becoming nearly homeless. I didn't understand his theories and some of Ramanujan's ideas but I found this info at: http://www.usna.edu/Users/math/meh/ramanujan.html
I use math everyday when I think about things and organize the facts that I learn mentally and I often find myself using mental images to calculate numbers. Often times, this would be imagined as rows and columns of small blocks like the ones we used in elementary school: the blue plastic blocks that were available in singles, tens, sheets of 100 and a cube of 1000. Now with that aside, I found it extremely strange how devoted Ramanujan was to mathematics to the point of failing other subjects and becoming nearly homeless. I didn't understand his theories and some of Ramanujan's ideas but I found this info at: http://www.usna.edu/Users/math/meh/ramanujan.html
Thursday, October 17, 2013
Beauty and Geometry
This interview seems to highlight the collective personality of Tom Zhang as he was constantly thinking throughout the interview. Math is definitely not a subject that everyone is focused or interested in but we still use it constantly like how it was mentioned in your other blog. Tom had taken an interest in twin prime conjecture when he was a child, and while this is the first time I have even heard of this, it is apparent that he had a love for math that reached out to learn new material.
Everyone does find something they love in math even if they don't realize it at the time and I believe that is the beauty of math as it represents the way your mind processes information and facts that it gets. We process a problem and eliminate uncertain and wrong answers as we center in on a correct answer. I personally love finding a fitting answer that just completes all of my questions and that is what I like about math even if it doesn't relate directly to the subject itself. Tom Zhang simply points out that if you love something and have an interest in it, you will find a way to love it and embrace it.
Everyone does find something they love in math even if they don't realize it at the time and I believe that is the beauty of math as it represents the way your mind processes information and facts that it gets. We process a problem and eliminate uncertain and wrong answers as we center in on a correct answer. I personally love finding a fitting answer that just completes all of my questions and that is what I like about math even if it doesn't relate directly to the subject itself. Tom Zhang simply points out that if you love something and have an interest in it, you will find a way to love it and embrace it.
Sunday, September 22, 2013
Fractions in Life
I never really thought about fractions in my life, but after reading your blog, I see that I use them almost everyday without even thinking about it. Often times I automatically resort to fractions to see how much progress I have made. This happens in running and when I see that I'm almost 1/2 done with the run, I use that to push myself to finish that last half.
Similarly, over the summer I found myself using this subconsciously using fractions to get through the day. During the summer I worked on campus in grounds keeping. It was a long day but after each hour I could mark that I was 1/7 done. With a break at 10:00 and then an hour off for lunch, I would break up the day into thirds rather than sevenths (I would not count the lunch). When it was time for break I would be 1/3 of the way done, then when I was at lunch I would be 2/3 done with the day.
I would also divide up my work into fractions, giving 1/2 of the area we had to rake to my partner and then 1/2 for myself. I would calculate how much I could get done and often times find myself aiming for a specific fraction. An example would be striving myself to finish 1/3 of the weeds by break time so that I could finish another 1/3 by lunch and then hopefully finish up the last third by the end of the day.
Similarly, over the summer I found myself using this subconsciously using fractions to get through the day. During the summer I worked on campus in grounds keeping. It was a long day but after each hour I could mark that I was 1/7 done. With a break at 10:00 and then an hour off for lunch, I would break up the day into thirds rather than sevenths (I would not count the lunch). When it was time for break I would be 1/3 of the way done, then when I was at lunch I would be 2/3 done with the day.
I would also divide up my work into fractions, giving 1/2 of the area we had to rake to my partner and then 1/2 for myself. I would calculate how much I could get done and often times find myself aiming for a specific fraction. An example would be striving myself to finish 1/3 of the weeds by break time so that I could finish another 1/3 by lunch and then hopefully finish up the last third by the end of the day.
Saturday, September 7, 2013
9%
The idea of a grade in the road is called the slope (known as rise over run, a bigger number means a higher or steeper slope of the surface compared to it being flat, or horizontal. Slopes are seen everyday in life; just recently our class studied trigonometric functions and finding the length of a side in a right triangle given an angle and the length of a side, or finding the angle of the slope and given the length of two sides, finding both solutions when plugged into the right equation.
Slopes can be found in our lives such as when we drive along hills, using less gas and simply letting the car go on its own when we have a steep hill, or using a lot when we go up a hill. The amount of slope or "grade" can also be seen directly at school as we occasionally have large thunderstorms, flooding our lower campus due to the gradual but large steepness of the school.
Slopes can be found in our lives such as when we drive along hills, using less gas and simply letting the car go on its own when we have a steep hill, or using a lot when we go up a hill. The amount of slope or "grade" can also be seen directly at school as we occasionally have large thunderstorms, flooding our lower campus due to the gradual but large steepness of the school.
Thursday, August 29, 2013
Math Illiteracy
Math has been introduced to us since a very young age. Often times the teachers would slap down a math book with basic steps in it and teach them to us, only for us to go home and repeat similar steps in our homework. Now I see why this would be the way to teach kids the mindset of learning methods and combining them with other methods to find a solution that works, and when it does, it's great! But often times, we are stuck with only "regurgitating" the information that was given to us a few classes ago and then forgetting about it.
In a class like history where repetition is key to learning the facts, we constantly piece together the bits of history to create a broad view of the events that happened. In math, this is not what happens and shouldn't happen either (since it is math after all); but the idea that we simply take in the methods we learned to solve problems, do homework, then forget about it is what I believe causes people to lose their connection to math and learning it.
Another reason why I believe Americans aren't very math savvy is the mindset of being lazy and getting through with the most minimal amount of effort. This is simply learned through the way technology is advancing, letting us find answers to questions and having much more at the touch of our fingertips. While this does not relate directly to math, the idea of "oh I'll just look it up" continues on in our life to the point that it applies to math as well.
In a class like history where repetition is key to learning the facts, we constantly piece together the bits of history to create a broad view of the events that happened. In math, this is not what happens and shouldn't happen either (since it is math after all); but the idea that we simply take in the methods we learned to solve problems, do homework, then forget about it is what I believe causes people to lose their connection to math and learning it.
Another reason why I believe Americans aren't very math savvy is the mindset of being lazy and getting through with the most minimal amount of effort. This is simply learned through the way technology is advancing, letting us find answers to questions and having much more at the touch of our fingertips. While this does not relate directly to math, the idea of "oh I'll just look it up" continues on in our life to the point that it applies to math as well.
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