# Elements of Architecture

## Some Mathematical Principles of Architecture

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After viewing our curriculum units, please take a few minutes to help us understand how the units, which were created by public school teachers, may be useful to others.

## Lesson Plans:

### Lesson Plan Number One:

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Objective:
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To create an awareness among students of the existence of geometric shapes in their environment.

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Activity:
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The teacher will ask the class to locate various basic geometric shapes in the classroom, such as a line, a square, a point, a rectangle, etc. A point could be located where two walls and the ceiling meet and so on.

Perhaps you can take them on a tour through the school itself, or even an outside tour to locate additional shapes. How about the ellipse in a football, or the parabola in an arch?

These activities could take from one to three class periods depending on student interest. You could also have the students draw free hand renderings of the various shapes they find.

### Lesson Plan Number Two:

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Objective:
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Teach students how to construct geometric shapes.

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Activity:
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Referring to the section on constructions, have the students duplicate the given steps using only a compass and straightedge.

Go over how to construct these geometric figures:

(1.) A line that is perpendicular to another line.

(2.) Two parallel lines.

(3.) An Equilateral triangle.

(4.) A Scalene triangle.

(5.) An Isosceles triangle.

This activity could take from 2-5 class periods depending on your students’ ability to duplicate instructions plus any additional explanations needed by the teacher.

### Lesson Plan Number Three:

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Objective:
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To expand the students’ use of rigor and logical sequence in solving geometry problems.

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Activity:
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Referring to the section on proofs, as well as your classroom textbooks, have the students do the proofs related to the constructions they have just done. The outline for these proofs is included within this paper.

This activity could last from 2-5 class periods depending on student ability to handle proofs at this point.

### Lesson Plan Number Four:

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Objective:
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To allow the student to discover the Fibonacci Series and the Golden Ratio in his own environment.

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Activity:
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This is an outside project that will ask the student to discover one or more instances of a Fibonacci Series and a Golden Ratio outside of class.

Using the section on “Proportions and the Golden Ratio”, instruct the student in using these ideas. Then, offer suggestions as to how to find the Golden Ratio and do several examples for the class.

Now turn it over to the students and have them find at least one example of a Golden Ratio and one example of a Fibonacci Series on their own. You can make suggestions, such as the rows of points in a pineapple, shell fish, celery stalks, leaves on certain trees, etc., for the Fibonacci Series, and they will have to experiment on finding a Golden Ratio themselves. Lots of buildings have it.

Have the students write a report on what they did.

The time to teach this will be 1-3 class periods. The length of time for their assignment should not be long, 2-3 days at most.