Claret School of Quezon CityMahinhin St., U.P. Village, Diliman, Quezon City

Project in Advanced AlgebraFourth Quarter 2-14-2015SOLID AS A CONIC

Submitted by:2: ALBERTO, John Michael3: ANCHETA, Emmanuel8: BARTOLOME, Lorenzo Moises17: FAJARDO, Angelo Xavier32: TARNATE, Mark Anthony12 - St. Joseph the Worker

Submitted to:Ms. Maria Clarissa V. Defeo

Date of Submission:March 6, 2015

I. Background of the StructureThe title of our structure is the Claret School of Quezon City Ellipse. It is an outdoors sports field which can be used for various sports such as track and field or even baseball if set-up correctly. A good location to place this would be somewhere near Claret School of Quezon City as it may be used as a training ground or P.E area for the students. It can help people by giving them a place to train and exercise.II. Sketch of the Model*III. Mathematical Connections and ApplicationsIn our structure, conics were applied on two parts of the structure, an ellipse for the track and field oval and a parabola (paraboloid) for the spectators bleachers. The ellipse is crucial to the shape of the oval because like most track and field ovals, it can help maintain fairness if ever runners would have to use the field. As for the bleachers, the parabolic shape can help the viewers a greater angle of perimeter.Here are the following equations:Oval (Ellipse)Major Axis Length: 8.7inMinor Axis Length: 8in+Bleachers (Parabola/Paraboloid) (Opening to the Left)Length of Latus Rectum: 6.5in (end to end)Distance of Vertex to Focus: 3.5in=-3.25y

IV. Documentation

Figure 1 SketchingFigure 2 Completion of model

Figure 3 Initial typing of papersFigure 4 Adding final details to model

Figure 5 Construction of figure aesthetics

V. Reflectiona. What made you decide your model?We were deliberating on what to do when we suddenly thought of a potential way in which we can help our alma mater, Claret School of Quezon City, that we would soon be leaving. Mr. Ancheta then proposed an athletic facility, and hence, a track and field oval. Not only was it innovative or relevant but the current lesson which is conic sections can be applied in this idea.b. What are the factors that you considered in coming up with this project?Basically, our project needed to have the application of one of the conic sections. Another factor is the feasibility of the structure. We thought about the capability of modern architecture and the means of making structures and we believe that with the present ones, it is indeed possible to make our project. One major factor that we considered was the relevance of the structure. What is it really for? Is it going to be effective? Would it help the present society? With those questions in mind we came up with a structure that can potentially bring a school into a more diverse and colorful institution that has enough facilities to cater the changing society's wants and needs.c. If you are to reconstruct your model, what will you change?Our model includes a score/advertising board, crowd bleachers, stretching areas and the conic itself, the track and field oval. If we were to change or improve one thing about our model, it wouldn't be the conic itself but the bleachers. It is in reality big but in such athletic facilities, more seats for a crowd is a must. So if we are to reconstruct it, we would add more bleachers.d.What is the importance of Conic Sections to you? To our society?For us conic sections and the overall study of algebra is important. For example an inventor has an idea or a potential innovation, He/She could not just state it as an abstract idea, but a scientific theory or a systematic idea that can be translated in numbers. This mindset is much applicable to this project. We want to build something yet it shouldn't stay as an idea, it should be solidified, and to do that, we need to apply measurements to balance the structure, we need mathematics and more specifically, the lesson of conic sections, to make such structures. It is very important to learn this discipline because it organizes such abstract ideas. It helps us rationalize every inch to millimeter. Because of the study of conic sections, there is a much concrete meaning behind a structure. Without it, our society would have disorganized structures and imbalanced buildings, due to the non-knowledge of these helpful tools, the conic sections, and overall Mathematics. Lastly, through conics, the stability and formation of a vast number of structures can be predicted through careful measurements and accurate calculations.