Howard published a piece in late 2008 that gives me faith in the critical thinking skills of America’s youth. If Wally Balthus’ students are a representative sampling, the world will be in good hands soon enough.
“A few figs from thistles…“
by Howard A. Tabor
Fibonnaci and the “Golden Section.” Who knew the Medieval Italian mathematician had made a pit stop in Iowa?
Last week I ran into Wally Balthus at the Koffee Kup; he teaches CADD at Fennimore County High. Wally told me of an interesting discovery made by his students while taking measurements of the old First Baptist Church building. He and history teacher Rowan Oakes are collaborating on a project to record Agincourt’s oldest buildings for the Historic American Buildings Survey at the Library of Congress. Rowan’s students do the background research and write the narrative; Wally’s students make the drawings from photographs and on-site measurements. I hope each group of students is learning from the other.
Translating their rough field notes into CADD drawings, several students noticed a recurrent number: 1.6183…, a non-repeating decimal most often called “The Golden Ratio.” It also happens to be related to a whole-number numerical sequence called a Fibonnaci Series, where each number in the series is the sum of the previous two: 0,1,1,2,3,5,8,13,21… One of the curious things about Fibonnaci’s series is that the ratio between any two numbers in the sequence approaches 1.6183… as the numbers get bigger! I know, too much information. We’d all rather get our technical data filtered through Sarah Palin.
Fibonnaci was an Italian, and he seems to have borrowed this idea from mathematicians in India. But the “Golden Ratio” also shows up in ancient Greece.
The Greeks, who practically invented geometry as a cornerstone of Western mathematical knowledge, were preoccupied with harmony and proportion. They were convinced that the “Golden Ratio” was perfect and strove to build its harmony into all their buildings—the Parthenon included. Don’t ask me why, but the “Golden Ratio” just looks right and it shows up again and again in both art and nature.
So what did Mr. Balthus’ students observe at First Baptist? Simply that the anonymous builders of that church in the 1860s relied on 1.6183… for many aspects of the design. The width of the church and the length of its first sanctuary are related that way, as is the width and length of the new entry vestibule added several years later. The large windows that light the sanctuary are also proportioned according to the “Golden Ratio,” and so are the entry doors facing the courthouse across the street. Any one of these could be a happy accident, but all of them together are downright creepy.
A quick trip to the Fennimore County History Center and a consultation with the late Hal Holt’s copious notes tell us a little about the building’s origins. It was built about 1868 in a 19th century style called “Greek Revival,” and that Greek-ness may account for the pervasive reliance upon the “Golden Ratio.” Amos Beddowes, an early member at First Baptist, had come here from Connecticut and may have brought the Greek Revival with him to this part of Iowa. He was, among other things, a carpenter who is mentioned in church records. The distinction between architects and builders was minimal on the frontier, so it may be that Beddowes acted as both designer and builder of the original church. But that begs the question of other, later applications of the perfect proportioning derived from 1.6183….
At the public library I ran across a fascinating book about this mysterious number. It’s by Mario Livio and is titled The Golden Ratio and is well worth the read. Less familiar than “pi” (3.14159…), this other number is called “e” and can be found virtually everywhere in the physical world, from designed objects produced by the human imagination to natural phenomena such as the pattern of seeds in a sunflower or the vibrating strings of a violin. Without it, our world would neither look nor sound the same. So I, for one, am grateful for the design sensitivity of Amos Beddowes and the keen observational skills of students in Wally Balthus’ computer draughting class.
Some time I’ll have to tell you about Cissy Beddowes, Amos’ wife and a medicine woman of the Sac and Fox people. She lived to be almost 100. Cissy’s home still stands near the entrance to Riverside Park.