+
The Dome

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...

(more)
See More

Try Our College Algebra Course. For FREE.

Sophia’s self-paced online courses are a great way to save time and money as you earn credits eligible for transfer to over 2,000 colleges and universities.*

Begin Free Trial
No credit card required

25 Sophia partners guarantee credit transfer.

221 Institutions have accepted or given pre-approval for credit transfer.

* The American Council on Education's College Credit Recommendation Service (ACE Credit®) has evaluated and recommended college credit for 20 of Sophia’s online courses. More than 2,000 colleges and universities consider ACE CREDIT recommendations in determining the applicability to their course and degree programs.

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.

Full Screen

Structure of a Dome

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

 

Basic dome construction

    3. Dome proportions and geometry

 

   4. Constructing a dome

 

   5. Telescopic dome, dome in practice.

 

 

6. Washington Capitol Dome, cross section

 

 

Dome

U.S. Capitol

more text

more text

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.

Roman Aquaducts

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

Homework

Full Screen

Source: Rob Diaz

,

Now that you have read and watched this lesson, work on your homework and then proceed to part 2;

How to Build a Geodesic Dome