Parabolas

Parabolas are very commonly used in the real world. They are used to construct many of our everyday buildings. Another example would be bridges. More specifically, the Golden Gate Bridge uses parabolas to make sure the bridge is sturdy enough. The suspension cables on the bridge are parabolas. The parabolic shape of the suspension cables actually do a lot to keep the bridge up. Their shape helps relieve the tension on the bridge from all the weight, and instead distributes it elsewhere through the cables. These cables are constantly being pulled on by the weight of both the bridge itself and the cars that pass by on it everyday. Parabolas are actually very important and they are very useful for many other things besides math class.

What If...

Thinking over the question of why there are only three regular polygons that tessellate I began visualizing a picture in my head. The reason the hexagon, triangle, and square are the only regular polygons to tessellate is because of their angles. 360 is divisible by the angles of all three of these polygons. The polygons all tessellate at one point which means for them to tessellate the polygons need to be able to go around the certain point enough times that there are no spaces in between them. A regular triangle has angles of 60 degrees, therefore it will go around a certain point six times and repeat at different points. A square with angles of 90 degrees will only go around 4 times and a hexagon with angles of 120 degrees will only go around 3 times. All equaling 360.

Pascal's Triangle

The sum of the rows in Pascal's triangle are equal to 2 raised to the power of each of the rows. The 1st row is 2 raised to 0 power and so on. The sum of the rows are 1, 2, 4, 8, 16, 32...and so on.
In order to find 11 raised to the 7th power by using Pascals triangle we need to add the numbers first:

1

                                                                              1   1

                                                                            1   2   1

                                                                          1   3   3   1

                                                                        1   4   6   4   1

                                                                      1   5  10  10  5  1

                                                                    1   6  15  20  15 6  1

                                                                  1   7  21  35  35  21 7 1

Then you start with the first numbers:

17

To get the numbers in the middle you just add them as if you were adding numbers by moving the tens digit over:

19487171

Math Puns

GA2
Growing up teachers would always say that we would use this math in the long run. As math class got harder technology advanced. As we grew up time became much more limited, we don't have as much time to do harder problems as we did for easier problems. With limited time we can't write down every step and that's when we turn to technology or take shortcuts. The more shortcuts we take the easier it is to forget the knowledge we learned in class. Using technology helps but it doesn't help your learning, when you mess up there is no way of knowing where you messed up and how to fix the problem. If you can't fix a problem you won't be able to learn from what you did wrong causing you to forget a lot of what you learned. The lazier we get the easier it is to not care, like in sports everyone knows what the coach means when they say to give more than 100% percent, we all know it's wrong but we simply don't care because it's very common to say that and not just in sports. The more we stop caring the more illiterate we become in math. Technology has dramatically changed our society, with all this technology the use of math seems irrelevant, why do a math problem on paper when you can type it in to your computer or calculator and get the right answer. The advance of technology has people questioning why we need math, and the answer is without math you wouldn't know how to find the answer to a problem. Sure you can type it into a computer but how do you know what to type if you're illiterate in math, if people realized this they would see how important it is to be literate in math.

GA2
I think this blog is about learning to be open-minded and try new things even if it isn't what you're used to. Fear of the past shouldn't prevent you from trying new things. Just because you thought you weren't able to maintain the flowers it changed your perspective and therefore; decided not to even mess with the flowers. Once you decided to cut the roses with the advice from your neighbor you realized that maybe it was possible for you to maintain all the beautiful flowers; and all because you tried. Throughout the process you even gained a new hobby, making jam. The combination of the smell of roses and jam reminds you of your home in Grand Junction, positive memories of how changing the way you think to try new things can lead to experiences you never thought possible.

Unlike most people math is an enjoyable subject for me. Algebra seems to be easier for me unlike geometry. Geometry isn't as easy as algebra for me, although I do find them both to be challenging, it's more difficult for me to understand it. Like your love for the smell of the roses and peaches, I love when I understand the material. Math has always been one of my stronger subjects and I hope I can keep it that way.