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The Dome

Author: Robert Diaz
Description:

To learn how domes are constructed using mathematical proportions and how they were used in the past.

By the end of the lesson, you will have the general knowledge of how domes are constructed through a means of mathematical equations. Math plays a critical role in architecture, especially in structure and design. After exploring the mathematical content...

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Tutorial

DRIVING QUESTION:

Is it possible to construct a ceiling in a shape of a dome that expands over 20, 50, 80 feet in diameter without structural support within the radius of a circular space?

OBJECTIVE: (part 1 of 2)

To learn how domes are constructed using mathematical and geometric proportions and how they were used in the past.

PRODUCT:

By the end of the lesson, you will have the general knowledge of how domes are constructed through a means of mathematical equations through geometry. Math plays a critical role in architecture, especially in structure and design. After exploring the components that build a dome, you will then explore how domes were constructed in the past in places such as Rome, Italy.

What is a dome?

A good definition in explaining what a dome is can be expressed from National Geographic:

"A dome is a curved formation or structure. It is shaped like half of a sphere. Imagine cutting an orange in half, and placing it cut-side-down on a table. This is the shape of a dome, although most domes in nature are not perfectly rounded.

Volume of a Sphere

Calculate the volume of a sphere. Theoretically, you will calculate a sphere but then divide your answer by 2 to get the volume of a dome.

Kahn U - Volume of Sphere

From Kahn Academy, watch and learn how to calculate the volume of a sphere. Remember, this is the calculation process of a sphere. To get the volume of a dome, simply divide the volume of a sphere by 2.

Surface Area of Sphere

Calculate the Surface Area of a sphere. Remember that this is a sphere, to get the SURFACE AREA of a dome, simply divide your answer by half.

Dome formula

The formula to calculate the dome area, circumference, etc.

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ANALYSIS:

Below are images of difference construction types of domes that can be built using a similar structure methodology. Look at each dome type, examine its structural components, and explain in a few short words, on a separate sheet of paper, how each dome might be constructed. At the end of this lesson, turn in your responses to your teacher.

1. Geometric dome construction.

2. Cross-section of dome

3. Dome proportions and geometry

4. Constructing a dome

5. Telescopic dome, dome in practice.

6. Washington Capitol Dome, cross section

U.S. Capitol

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Hagia Sephia: An Engineering Fete

One of the largest domes in the world, the Hagia Sophia has marveled the world not just for its size, for the construction of its dome and its ability to withstand many earthquakes.

A short film exploring the design and construction methods of domes and their direct application to serve the community.

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Source: Rob Diaz