Activity 3: The Blue Room in the White House
One of the most unusual rooms in the president’s residence, the White House, is the Blue
Room. Unlike most rooms, the Blue Room is elliptical or egg shaped. (See Figure 1.)
Figure 1. The Blue Room.
A history of the Blue Room as well as pictures can be found at:
The Blue Room was designed by architect James Hoban. Rooms in most homes (the
president’s or yours) are rectangular with adjoining walls forming right angles with each
1. Why do most architects or home designers use right angles?
2. Suppose you wanted to use some other angle (say, 45 degrees or 120 degrees) for
corners to meet in a home. Describe any problems that might arise.
Hoban chose to make the Blue Room 39 feet and ¾” long and 29 feet and 4 ¾” wide.
3. Use the graph in Figure 2 to sketch an ellipse similar to the Blue Room floor plan.
For the remainder of this activity, approximate the length of the Blue Room to be 40 feet
and the width to be 30 feet.
Figure 2. Graph for your drawing of the Blue Room.
The longest part of an ellipse is called the major axis. The short side is the minor axis.
4. What is the length of the major axis of the Blue Room? The minor axis?
The equation of an ellipse is
, where a is half the major axis and b is half the
5. What is the equation for the ellipse traced by the Blue Room?
An ellipse is formed by identifying two focal points (sometimes called foci). Formally,
an ellipse is the set of points whose distance from the two foci is always a constant (a
constant bigger than the distance between the two foci). That’s hard to understand but
easy to see from a picture. Imagine two foci (the dots in the picture in Figure 3) and a
string attached between them (the string is longer than the distance between the two foci).
Put a pencil on the string and stretch the string taut. No