Geometry/Algebra 2

In every generation, there is a stereotype that if you are good at math or just like it, you are a nerd and that you are not very popular. I notice this in our generation especially because I have some friends that go to public school and they talk about their social dynamic that is based on their intelligence. People who are good at math are considered nerds and they do not have a life outside of school, and that might be true for a small majority of students but it is not at all the case for all of them. For the majority of public schools, it is not really considered "cool" if you get good grades or you just like school. At Academy, there is a different social dynamic because the reason we are here is that we are good in all the subjects or at least the majority. So it is better to understand the material and if you don't understand it then ask a teacher. There is a type of pressure put on by the other students to get good grades, it is like a competition. We are always

I decided to talk about Leonardo de Vinci in this blog because his art is amazing, and most of his sketches were influenced by mathematical ideas. Some of his sketches were influenced by the Quadrature of the Lune.  In the context of Leonardo da Vinci, the lunes are interesting because Leonardo often used them in his designs of ornaments, and in the failed (of course) mathematical attempts of quadrature of the circle. R epresented below is one of his numerous designs  related to a combination of polygons and circles  in the "modern". The image below is known as Leonardo's claw.

All animations are made up of a series of different types of transformations. If an animator wants to move a character or object left/right or up/down all they have to do is reflect the object/character in respect to the x-axis or y-axis. An example of rotations and dilations is in animation is in the Spider-Man animated series.  In the cartoon, as he is flying, he rotates a certain number of degrees through the air. Then if he is going away from the camera he dilates a negative amount.

A tesseract is the 4-dimension of a cube and a hypercube is the n-dimension of a cube. A tesseract is to a cube as a cube is to a square. We will never know internally what a tesseract looks like because we are in the third dimension. To create a cube, you move a square one unit length perpendicular to the plane it lies on, and by doing this you create a three-dimensional cube. Then to create a tesseract, you move the cube one unit length into the fourth-dimension. Charles Howard Hinton was the first to coin the word tesseract, in 1888 in his book A New Era of Thought . After watching many videos and reading a couple of articles, I have to say that tesseracts and hypercubes are such a hard concept to fully understand. I have a simple understanding of what a tesseract is, and how to create a tesseract. But at the same time, it is hard to fully grasp the complete idea of a tesseract. Cause it does not just stop at a tesseract, there is an infinite number of dimensions, which means a

The pitch of a roof is equivalent to the hypotenuse of a triangle. The 11/18 in an 11/18 pitch, is the slope of the pitch, and we know that the slope is the rise of the run. With the knowledge that the slope is rise/run, we can deduce that the two legs are 11 and 18, with 11 being the rise and 18 being the run. Then from there, it is quite simple to find the angle of elevation. To find the angle of elevation you first set up the tangent equation: Tan A=11/18. Then you multiply each side by the inverse tangent: A= tan^-1 (11/18). Then you will get that the angle A is equal to 31 degrees. Next, we had to find the "rafter line" if the full length of the "run" is 22ft. This was pretty easy to figure out, first, I had to set up the equation: Cos31=11/x. I chose to use the Cos equation because we were trying to find the length of the rafter which is equivalent to the hypotenuse of a triangle, and we were given the adjacent leg. Next, we simply solved the equation: x=Cos

The grade of a road is the tangent of the angle of that surface to the horizontal. If the grade is 0% then there is no slope, but the greater the % the higher/steeper the degree of tilt is. Knowing the grade of a road is important for cars because they have something called the gradeability. The gradeability of a car is the highest grade a car can go at a certain speed. So if the grade is high the driver then knows that they have to go a greater speed to prepare for the steep hill. The grade of a road is equal to the slope of a line. Also, the grade of a road is equivalent to the hypotenuse of a triangle, so if we can use trigonometry to find the hypotenuse we can use trigonometry to find the grade of a road.