Today, while skimming through my Scripta Mathematica volume files, I discovered the poem ” Ode to an Exponential Curve” by Elmer Brill. The poem was published in Issue 2 Volume 6 of Scripta Mathematica (you can download the PDF file containing Volume 6 here). In this post I mainly want to transcribe the poem. Maybe I can make it more searchable on the internet.
The poem is about exponential curves, but it also makes references to the Euler’s number e, the Gunter rule or scale, slide rules and John Napier. I do have a personal interest in exponential curves, logarithm functions and slide rules since I am a member and supporter of The Oughtred Society, which is dedicated to the history of slide rules. Also, the first 2 OEIS sequences that I discovered are related to e ( see my post Whittaker’s Root Series: Going Transcendental). You can also see my sequences related to ln 2 (A367596 and
A367597) and the Omega constant (A370490 and A370491).
ODE TO AN EXPONENTIAL CURVE by Elmer Brill
A constant-growth curve
Or compound-interest curve
Or exponential curve
Is so sly,
So insidious; and
When the growth factor
Is but 1.1,
So innocent-appearing at first—
Yet how awe-inspiring is the majesty
Of its irresistible upward advance
In its progress to higher and higher ordinates—
So modestly sublime
In its proud consciousness of power!
It is not alone.
It has a progeny that may be counted
“Worthy of remembrance”
In the proudly appealing phrase
Of our Anglo-Saxon forefathers.
The puissance of its offspring
Is foreshadowed by the powerful beauty
Of this physical embodiment of e.
Out of the abstract idea e—
That aid to calculation
Affectionatly known to English seamen
As “The Gunter.” ;
‘Two Gunter scales produce that marvel of ingenuity and practical value,
The slide rule.
Last and greatest of the progeny of e—
The great Scotchman’s discovery—
Most practical of all tools possessed
By the engineer and astronomer.
Even the fine arts are nourished—
The alphabet of music may be equally tempered
By Napier's number of ratios, .
Showing that what is both physically and abstractly beautiful
May well be the parent
Of one of man’s greatest instruments of power!
Side Notes
In the 70s digital calculators started to replace slide rules. I still think that slide rules can be useful educational tools, especially for people that prefer kinesthetic, tactile or hands on learning. Slide rules are still useful tools that can help you understand the properties of logarithm functions. This is why I support the efforts of the Oughtred Society, International Slide Rule Museum or similar organizations.
Exponential and logarithmic curves also have interesting properties, like constant subtangent. I recommend the work of David Dennis about geometric drawing devices. He also discusses the history of the subtangent and how it manifests itself in different types of curves. In one of the papers from the link above he talks about drawing logarithmic and exponential curves using the software Geometer’s Sketchpad ( I prefer GeoGebra).
Exponential curves and logarithms are also connected to the catenary curve ( curve made by a chain or rope hanging freely). Dr. Viktor Blasjo wrote an interesting paper entitled “How to Find the Logarithm of Any Number Using Nothing But a Piece of String” about a method developed by Leibniz.
In his speech entitled “On teaching mathematics” Vladimir Arnold says that:
“Mathematics is a part of physics. Physics is an experimental science, a part of natural science.Mathematics is the part of physics where experiments are cheap. “
We should make math education experimental like Vladimir Arnold says. Exponential and logarithmic curves gives us a lot of interesting avenues to explore math experimentally, from slide rules, geometric drawing devices, hanging chains or exploring how the subtangent remains constant using a software like GeoGebra. Math is more than symbol manipulation on a piece of paper.