I. Notre Dame de Chartres - Ratios in the Floor Plan

1. Church Length:Transept Length = 3:2

2. Nave:Side Aisle = 2:1

3. Transept Length:Transept Width = 2:1

4. Choir(Length:Width)=4:3

5. Crossing = 1:1

II. South Tower Base

16.44 m ´ 13.99 m

If the side of a regular pentagon is 6.44 then the radius of a circumscribing circle is 13.984 (very close to 13.99).

III. The Golden Ratio

The Golden Ratio is a root of the quadratic equation Thus we have the following relations for the powers of :

(1:1)

(2:1)

(3:2)

IV. Dimensions of the Interior Elevation

Let Y be the distance from the floor to the point where the Nave Columns split.

Y=the distance from the top of the Nave Arch to the top of the Clerestory

²Y=the distance from the floor to the first vaulting of the side Nave Arch

³Y=the distance from the first side Nave Vaulting to the top of the Nave Arch

⁴Y=the height of the Triforium

Construction Assignment - Powers of the Golden Ratio.

In this assignment you will construct the lengths Y, Y, ²Y, ³Y, and ⁴Y where Y is 6 inches.

1. On a clean sheet of paper construct a right angle in such a position that it can serve as the right angle in a right triangle whose legs have length 6 inches and 3 inches. Using a ruler measure (as exactly as you can) 6 inches along one ray of the right angle and 3 inches along the other. Label the vertex of the right angle C. Let AC be the 6 inch side and BC the 3 inch side. Connect A and B to form right triangle ABC.

2. With the point of the compass at B and the pencil at C sweep out an ard that crosses AB. Call the point of intersection D. Then AD is the golden ratio with respect to the unit AC. (That is if AC = Y then AD = Y.) We take Y to be the 6 inch line.

3. On a separate sheet construct Y, Y, ²Y, ³Y, and ⁴Y using the relations above. For example, Y and Y are already constructed. Then ²Y=Y-Y. Simply subtracting Y from Y will give ²Y.