# The Symbolic Language of Architecture and Public Monuments

## Mathematics and Architecture Designs

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## Sample Lesson 4

**
Objectives:
**

To allow students to

(1) analyze the dimensions of a facade of a house from a drawing,

(2) develop a grid for that house and analyze the proportion.

**
Material:
**

Scale drawing of Chateau 1860-1890

Pencil, ruler, grid paper, tracing paper, scissors, tape.

**
Goal:
**

To determine the actual dimensions with at least 97% accuracy.

**
Procedure
**

- Activity 1: Students will be asked to work individually on this project. They will be given a 121% enlarged copy of the facade of the Chateau. Using their rulers and pencils, they will measure the different sections of the facades to the nearest fraction of an inch. They much determine the scale used, then convert scale measure to actual measure. (See attached sample of completed activity)
- Activity 2: After concluding discussion on reasons for the differences in solutions and offering suggestions on how to improve measuring skills, students will be asked to put house in a grid and determine the proportions.

**
Procedure:
**

The idea here is to allow students to understand the principles of symmetry and congruence and to apply these principles to the solution of problems. By completing this activity, they will not only understand about proportionality in buildings but will realize that architectural order and beauty is obtained by the inter-relationship of ratios and good proportions; that balance and repose are attained by symmetry.

- 1. Using copy of Chateau, cut all perimeter lines of house
- 2. Use tape and paste the figure to grid paper, centering house as shown by drawing an imaginary line through the center of the large windows
- 3. Photocopy result
- 4. Use your grid to find any required proportions (NOTE: It would be a better idea if a transparent grid was used so grid could be superimposed on house but that was not available for this project.

**
Extended Activity:
**

To calculate dimensions, it is assumed that the average height of a castle door was 10 feet, this dimension was used to calculate all other dimensions.

- 1. Identify elements o the Chateau that are symmetrical.
- 2. Write a report on the history of a famous building in New Haven Chateau Measurement:
- ____ Scale: 1/8”=1 ft.

**
Dimensions:
**

Door height | 10 ft. |

Door width | 8 ft |

Width at base | 43 1/2 ft |

Width at top of first landing | 42 ft |

Width at ceiling | 42 ft |

Height of 1st flr. (Including foundation) | 17 ft |

left (side with steps) | 18 ft |

Thickness of decking between flrs | 3 ft |

Height of 2nd flr. | 10 ft |

height of left side (to eaves) 3 | 3 1/2 ft |

Height of right side (eaves) | 29 ft |

Roof height to base of ornament | 24 ft. |

Height of roof ornament (end) | 3 1/2 ft. middle 2 1/2 ft |

Chimney height | 27 ft. |

Bay windows | 8’ by 8’ |

Small window beside bay | 8’ by 3’ |

Window above door | 6’ by 5’ |

Total height of facade (at center) | 60 ft. |

Door dimension (without arch) | 8’ by 8’ which is |

proportionate to the | |

large window dimensions. |

*(figure available in print form)*

*(figure available in print form)*