Parabolic Cooking

As I read about parabolas on the mathisfun page, I couldn't help but be fascinated by the "Reflector" example. It displays many different rays, all bouncing off the inside of a parabola, coming together in a "focus point." This had never been covered in class, so it was quite new to me. It certainly made sense though. The lightbulb in a flashlight lies at the focus point, and is surrounded by a parabolic mirror.

Anyways, I realized that if a parabolic mirror were placed in the sun, it would direct all of the suns rays to its focus point. The heat would be intense at this point, because all of the energy is focused at that point. I realized that this is sort of the concept behind a solar oven. However, a traditional solar oven is much less efficient than a parabolic mirror, as it uses flat pieces of tin foil which a) don't reflect as much light b) reflect the light over a much more broad area. A parabolic mirror, forming a sort of dish, would be a super efficient solar oven. A small surface could be install at the surface point, It could be used to bake items which require lesser amounts of heat, such as chocolate chip cookies. This oven could be installed in any spot outside, on a pivot, allowing the dish to be rotated towards the sun. A parabolic mirror would not only work great as an oven, but it could be used by anyone and never require any extra energy.

Tesselations... in 3D!

After reading the Jamm'n Peaches blog, I was intrigued. I decided to look into it further, and after a bit of reading I learned of something quite interesting. Not only is tessellation possible on a two-dimensional plane, but also in three-dimensional space! Such tessellations are referred to as "honeycombs." Interestingly enough, there are many shapes that are able to tesselate in 3D: truncated octahedrons, rhombic dodecahedrons, and of course, prisms. But these prisms, just like their two-dimensional counterparts, must be either a square, a triangle, or a hexagon. The rules for space-filling tessellation are similar to that of two-dimensional tessellations; instead of leaving no area unfilled, honeycombs call for no space to go unfilled. Many of these tessellations can be found in nature. However, one tessellation is found all around us: the cubic tessellation. They can be found from hotels all the way to shelves.

http://en.wikipedia.org/wiki/Tessellation
http://en.wikipedia.org/wiki/Honeycomb_(geometry)

Math Jokes!

Math isn't always the most fun subject. It is good to insert a bit of humor into it! Here are some math jokes to lighten the mood.

Why should you never drink root beer out of a square glass? You'll end up with just beer!

Why do you never see mathematicians at the beach? They don't have the sine and cosine, so they can't get a tan!

If only the US had 53 states. Then we would truly be one nation, indivisible. (53 is prime).

And finally,

Scott Flansburg

Another so-called (even self-proclaimed) human calculator is Scott Flansburg. Flansburg, in addition to having a natural talent with mental math, show an interest in help others and thinks he knows a secret to mathematical success. In the English language, we read left to right. This is the pattern that becomes embedded in our brains from the time we learn how to read and write until the rest of our lives. In fact, I still have a seemingly random memory of preschool, when I hadn't fully learned how to write yet. I practiced writing my name on a piece of paper, and I actually wrote my name completely backwards. The letters were correct, and in the correct order, but written completely backwards, the letters pointing towards the left. I suppose at that point I regarded letters more as their own shapes rather than characters of a whole word. Of course, later on, I learned the current direction to write. Flansburg's idea is that we should read math from left to right, like English, rather than right to left, as we are taught. This eliminates carrying, which can be a tricky concept.
For example, adding 10 three-digit numbers:
457
886
432
357
536
753
657
425
124
976
Instead of going through the hassle of carrying, it is easier to do this:
400 + 800 + 400 + 300 + 500 + 700 + 600 + 400 + 100 + 900 = 5100
50 + 80 + 30 + 50 + 30 + 50 + 50 + 20 + 20 + 70 = 450
7 + 6 + 2 + 7 + 6 + 3 + 7 + 5 + 4 + 6 = 53
5100 + 450 + 53 = 5603
Simpler, right?

http://www.azfamily.com/news/Human-Calculator-uses-math-to-entertain-222999371.html
http://www.secrant.com/rant/p/40191990/Mental-Math-Genius-Claims-Humans-Are-Being-Taught-Math-Incorrectly.aspx

Shapes

Math can always feel very abstract and distant. A jumble of numbers, symbols, and letters, the answer sometimes seems to appear out of nowhere. Math begins to materialize a bit more when applied in word problems. But still, the word problems that are provided are usually ridiculous and abstract in their own ways. In this way, math can be very unattractive to people, as it doesn't seem to follow plain english.

Where math becomes fun and interesting is in shapes. Geometry is very interesting, because it takes simple equations and turns them into a circle, or a square, or a triangle, or whatever possible shape can be created. A lot of students I know seem to find geometry difficult, as their minds are more oriented for algebra. But for me, geometry sweeps away the mangled, x-filled equation with something tangible, something that I can refer to, something that works before my eyes. Numbers, when represented visually in geometry, can become engrossing.

Daily Math

Math finds it's way out of the classroom and into my daily life all the time. Mainly, I use it to determine how much longer I have to do something I don't want to do. In the slowest classes of the day, I find myself saying, "one quarter done, one half done, three quarters done." Working through the longest homework assignments, with problem after problem after problem, I encourage myself but giving myself a fractional representation of how far I've progressed. In cross country, on the difficult hill workouts, I use fractions to determine how many out of 10 I've done. My application for fractions, although somewhat negative, works for me. I can quickly break 5/8 down into a percent by knowing that 100 divided by 8 is about 12, and 5 x 12 is 60. Approximately 60%. When taking a time-pressured test, I use math to determine if I can finish in time, by seeing how much time I have left, converting that into a fraction, then seeing what fraction of the test I have left to do. Running through all of these calculations doesn't take long, and I do it almost subconsciously. Math can be a great help in our daily lives.

Why We're Bad at Math

At the very beginning, we're taught that 1 plus 1 equals 2. Then, it's taken a step further, with 2 plus 2 equals 4. After that comes subtraction, 1 minus 1 equals 0. And much later, multiplication and division. Seems easy, right? Despite this, the United States ranks 32nd in math proficiency. Why?

It's become quite commonplace for adults to say "Oh, I was never good at math," or "Math was always hard for me." Often, teachers (aside from those that teach math) will say "Now you know why I'm not a math teacher." At least for today's generation, this may be the root of the problem. If even our teachers, the people who mentor us in our academic life, don't take math seriously, why should we? Just like our teachers, we figure, "Well I'm just better at this subject." Sometimes, it's even taken as far as, "Well I'm good at this sport, why should I be concerned about school?" While it's great to have one talent, it is important to be well rounded.