Able to Leap Tall Buildings

Introduction | Task | Process | Guidance | Conclusion | Questions

Introduction
     The buildings with the tallest rooftop is the Sears Tower in Chicago, with a height of 1450 feet. However, the tallest building is the Petronas Twin Towers in Kuala Lumpur, Malaysia, whose architectural spires rise to 1483 feet. In this project, you will be exploring how geometry and algebra can help you describe unusual or large structures of the world.

The Task
Your school is having a mathematics fair. Your class has the following assignment. Each student needs to research a large or unusual structure. You need to present facts about the structure including the dimensions you can find. Finally, you need to relate the size of the structure in some way to another item. Be sure your project contains the following:

• a poster or Webpage presenting information and facts about the structure;
• pictures and/or diagrams of the structure;
• a comparison of your structure to some familiar item using a table, graph, diagram, or other method of showing the comparison.

You will get more ideas about completing this project in the exercises in your textbook in Unit 3.

The Process
To successfully complete this project, you will need to complete the following items.

• Research large or unusual structures either in the U.S. or in another part of the world. Select one of the structures for your project. For help, try these Web sites.
  www.yahoo.com and search for skyscrapers
  www.spaceneedle.com
  www.sears-tower.com
  www.emporis.com/en/bu/sk/
  www.xs4all.nl/~hnetten
  www.cnn.com/TRAVEL/DESTINATIONS/9705/seven.wonders/pyramids.html
  www.cntower.ca
  
• Find dimensions and other interesting information for the structure you select.
• Brainstorm about some familiar items that you may want to use to compare to your structure. Here are some ideas.
  How many of my bedrooms would fit on one floor of the structure?
  How many average swimming pools full of water would fill the structure?
  How many people could stand side-by-side around the perimeter of the structure?
  
• Determine how you are going to show the comparison of your selected item and some dimension of the structure. Remember you can use perimeter, area, surface area, and volume for comparisons.
• Be creative. Add some additional data, information, or even pictures to your poster or Web page.

Guidance
Here are some additional questions and ideas you may want to consider for your project.

1. What purpose did or does the structure serve?
2. What is the history of the structure? For example, how long did it take to build the structure? Has it been used for different purposes over its lifetime?
3. What are special features of the structure? Is it similar to any previous structures?
4. Were any unusual methods or materials used in building the structure?
5. How are large structures destroyed if they are no longer safe to use?
6. What was the cost of the structure?
7. Interview an architect or building designer. Ask whether there is a limit on the height of tall buildings. What special problems do designers of tall buildings face?

Conclusion
Here are some ideas for concluding your project.

• Present your project to your class or at a family night.
• Present the information in a brochure instead of using a poster or Web page. Include pictures and diagrams to present your information and ideas.
• Compile the projects of all students in your class into a booklet. Publish it using desktop publishing software.

Questions

Lesson 9—8
Laurie was interested in pyramids for her project on structures. She found this drawing of the Summum Pyramid in Utah.

1. Consider the face of one side of the pyramid or triangle ACD. The height of the triangular face is AB and one-half of the base is BC. Angle ABC is a right angle. Which trigonometric ratio is the ratio AB/BC?
2. The ratio AB/BC is approximately 1.618. What is the measure of angle C? Round to the nearest degree.
3. Research well-known mathematical ratios. What is another name for the ratio that is approximately 1.618? (Some Egyptian pyramids also contain this ratio.)

1. A restaurant in the Space Needle is circular, with a diameter of 94.5 feet. What is the area of the restaurant? Round to the nearest unit.
2. The halo near the top of the structure has a diameter of 138 feet. What is the circumference of the halo? Round to the nearest unit.
3. Suppose the halo around the top was a square. What would be the approximate length of one side of the square, if it had the same perimeter as the circular halo?
4. How many 16-inch diameter pizzas would cover the floor of the restaurant in the Space Needle?

Lesson 11—3
Tyrone is researching pyramids on the Giza Plateau in Egypt. The pyramids of Khafre and Menkaure have the dimensions shown in the table. The base of each pyramid is a square.

Pyramid	Base on each side (feet	Height(feet
Khafre	704	471
Menkaure	345.5	216