You have worked with figures that are similar and have learned how to calculate angles and side lengths to identify similarity. Put these skills together to plan a design for a scale model. Showing how these concepts effectively work in the real world involves clear communication and the ability to defend your conclusions to others.
describe your design to your peers:
• State the real-world figure you will model and the scale factor you will use.
• Identify at least two different but significant items on your model.
• Explain how you will determine the calculations and dimensions for these items to make them mathematically similar to the actual items.
• Describe the specific mathematical skills you will need to create the design and give examples.
• Describe some outside sources you may need for the calculations.
Design Description:
For my scale model, I have decided to model the Eiffel Tower in Paris. The scale factor I will use is 1:100, which means that every centimeter on my model will represent 100 centimeters or 1 meter of the actual tower.
Two significant items on my model will be the base and one of the tower's legs. The base is an important element that provides stability to the tower, and the legs are iconic and recognizable features of the Eiffel Tower.
To make these items mathematically similar to the actual ones, I will use the concept of similarity and apply the following calculations and dimensions:
1. Base: The actual base of the Eiffel Tower is a square with sides measuring approximately 125 meters. To create a mathematically similar base on my scale model, I will calculate the side length by dividing 125 meters by 100 (scale factor). So, my model's base will be a square with sides measuring 1.25 meters (125 meters / 100).
2. Leg: One of the tower's legs has an inclination to the vertical axis. To maintain this angle in my scale model, I will use trigonometry. I will measure the angle between the leg and the vertical axis in the actual Eiffel Tower and replicate it in my model. This will ensure that the leg in my model is mathematically similar to the real one.
The specific mathematical skills I will need to create this design include:
1. Calculation of scale factors: I will use the concept of ratios and proportions to determine the appropriate scale factor for my model.
2. Trigonometry: I will use trigonometric functions such as sine, cosine, and tangent to calculate angles and lengths accurately.
3. Geometry: I will apply geometric principles, such as similar triangles, to determine corresponding angles and side lengths.
To perform calculations and obtain accurate dimensions, I may need some outside sources such as architectural plans or detailed photographs of the Eiffel Tower. These resources will provide precise measurements and assist in maintaining accuracy and detail in my scale model. Additionally, I may consult books or online references on trigonometry and geometry to refresh and deepen my understanding of these mathematical concepts.