# Intersections between Architecture, Math, and Science

When I look at anything, I see mathematics in it. There is not an object or natural phenomenon that does not seem mathematical in nature to me. According to cosmologist Max Tegmark—as quoted in the July 2008 Discover story Is the Universe Actually Made of Math?—”There is only mathematics; that is all that exists.” Though the way I see the world may be strange to some, I am not the only one who sees it this way!

Taper Courtyard pond at the Skirball. What principles of geometry apply here? Photo by Thomas Amiya.

Every exterior and interior of every structure at the Skirball Cultural Center has a mathematical aspect, as well as a cultural purpose—from the geometry of the slate tiles in the Taper Courtyard (where music fans gather for Sunset Concerts and other programming) to the “tent of welcome” in the Ziegler Amphitheater.

Recently, I’ve been working to create a Math Trail through the Skirball, a walking tour in which students and teachers use the sights and sounds of the campus to complete mathematical challenges. The project is inspired by the Skirball’s current exhibition, Global Citizen: The Architecture of Moshe Safdie. One example of math in architecture that we’ll be using on the Skirball Math Trail can be found in the Ziegler Amphitheater.

Ziegler Amphitheater, on the south side of the Skirball campus. Photo by Thomas Amiya.

Slope = rise/run = change in height divided by distance moved forward = 5.5 in/12.5 in =
0.44 = 44/100 = 11/25

Problem: Begin at the stage and measure the height and depth of a stair step. Estimate the slope of the stairs. Describe your process.

Answer: To solve this problem, I used the stairs on the south end of the amphitheater. Using a tape measure, I found that the height of a stair step is 5.5 inches and the depth is 12.5 inches. To determine the slope of the stairs, I calculated the ratio of the height to the depth—that is, rise/run or 5.5/12.5. In this case, the slope is 0.44.

How does the slope of these stairs compare to other stairs that you use every day? Measure other stairs for comparison! If the height and depth of each step is the same, the slope of the staircase will be the same as the slope of each step.

Amphitheaters like the Ziegler have been used for centuries. In the 4th century BCE, the Theater at Epidaurus on the Peloponnese in Greece was built by Polykleitos the Younger. Here is a diagram of it. Audiences of up to an estimated 14,000 were able to hear actors and musicians—unamplified—from even the back row of the architectural masterpiece. You can try this too. On your next visit to the Skirball, have a friend or family member stand in the middle of the Ziegler Amphitheater and sing a song. See if you can hear it from the top of the amphitheater!

To me the most interesting part of this project has been pulling together the cultural and the mathematical and illustrating them through Safdie’s architecture. This kind of work is what I enjoy most about teaching: the opportunity to help teachers and students make connections between their world and what they are learning.

Are you a teacher? Then join me on the Skirball Math Trail to learn more about the intersections between art, math, science, and culture in architecture. Attend the Skirball’s professional development program for teachers, Building STEAM, on February 22. See you there!

Diane Kinch has been a math educator for more than forty years, beginning with a three-year tour in the Peace Corps in Liberia, West Africa, which took her to Managua, Nicaragua, the Northern Cheyenne Reservation in Montana, Belmont, MA, and Pomona, CA. She is currently on the board of TODOS: Mathematics for All, and a past president of California Mathematics Council–South. Since retiring, she has worked with math teachers in many venues, including writing and teaching online math courses for the Center for Distance and Online Learning at the Los Angeles County Office of Education, working with the California Mathematics Project and other institutions.

## 2 thoughts on “Intersections between Architecture, Math, and Science”

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