There is a relationship between mathematics and architecture. That relationship is, at times, a partnership where one draws equally upon the other. Sometimes it is a marriage, a coupling that is inseparable, and at other times it is a fierce competitor where old standards are unwilling to give way to new discoveries.
This relationship is the focus of my paper and I will examine only a few of the many intricate parts of architecture. It is aimed at high school geometry students. Yet this same material could be modified for any level math student whether higher or lower. It is designed to stimulate curiosity and lead to personal research beyond the content of the paper. Some sections are designed to expand upon the current topics being studied in a geometry class, and here I will deal with geometric proofs, constructions, the Golden Ratio, and the Fibonacci Series.
Through this seminar, I have realized that there is a major distinction between building and architecture. That difference seemed moot at first, yet further studies shed light upon it. The tradition of architecture reaches back to the ancient Greeks and beyond. Yet that Greek culture was the first western civilization to incorporate a wide variety of ideas and ideals and to personify them through their architecture. Mathematical concepts and traditions owe a great deal to this civilization. Euclid organized a great body of geometric data in his “Elements”. The Pythagorean Theorem and conic sections grew here also and are still being taught in today’s high schools.
Howard Roark, the hero of “The Fountainhead” would disagree strongly with this view of architecture, yet it is still a valid one. One that allows me to trace not only its development, but the development of mathematical concepts as well.
Architecture involves math, engineering, design, handling raw materials and much more. Yet, the sum is more than its parts. There are two large parts that I wish to examine. They are: The Tangible and The Intangible.
The Intangible aspects of architecture affect the emotions and other perceptions. Things such as size, color, shape, space and proportion, directly and indirectly engage the senses. For insights into this area I am indebted to our seminar leader Professor Kent Bloomer of the Yale School of Art and Architecture for showing me such information existed and to the 18th Century author Edmund Burke for his detailed analysis of this phenomenon.
The Tangible aspects of architecture deal with those mathematical principles that are involved in designing and constructing buildings. I will refer to geometric concepts mainly, but also involve other mathematical ideas such as the Golden Ratio and the Fibonacci Series. I am grateful to the works of Euclid, and to Leonardo of Pisa (Fibonacci), as well as to Harry Reid, Head of the Math Department at Lee High School, and to Ray Davie, a fellow math teacher, for their timely assistance.