Math as a Muse (Part I)

I have had an affinity for math for as long as I can remember.  Even in elementary school, when working with numbers or shapes, it always seemed like magic to me.  Now, as an adult, I find this magic hiding in unexpected places, like the relationships between notes in music, and in the geometry of architecture.  It was the latter that called out to me last week.

I was standing in a place of worship.  Admittedly, I do not spend a great deal of time in such places.  On this particular occasion, in a church, my mind was wandering, and I began examining all of the geometry around me: the slopes in the roof, the shapes of the stained glass, and the angle in which the sunlight came through them.  When my gaze returned forward, I began to carefully examine all of the equally spaced columns (known as pews) between me and the front of the church, where the Reverend stood.  Almost immediately, a fun math problem presented itself to me, and I spent the next twenty minutes analyzing it in my mind.

As shown in the figure below, I can see less and less of each column the further they are from me, as each column is obstructed by the one that precedes it.  But, what governs how much of a given column I can see?  I called the column directly in front of me n = 0, and then came 1, 2, and so on.  My aim was to find a function that described the height of each column that I could see for each column, h(n).  I decided that it depended on three other parameters: the column spacing (s), as well as the vertical and horizontal distance from my eyes to the zeroth column immediately in front of me (H and L).

Searching for visible height h as function of pew number n (mad paint skills, I know...)

You can Count on Asimov

Isaac Asimov is on a short list of my favourite science authors.  The list has two names on it: Arthur C. Clarke and Isaac Asimov.  Both write excellent science fiction (Asimov's "I Robot" and Clarke's "Fountain's of Paradise" are my personal favourites) and both write excellent topical science articles and essays.  While Orson Scott Card writes some compelling sci-fi (Ender's Game is probably my favourite novel of all time), he is not a "popularizer" of science - it is rare to find an author that is skilled in both fiction and non-fiction.

Asimov may have been the most prolific author ever, having published upwards of four hundred pieces.  His direct style in story-telling and, at times, redundant style of communicating in non-fiction does not appeal to everyone, but it does appeal to me.

Asimov's largest volume of work involves the communication of science, but physics in particular.  I just finished reading "Asimov on Numbers," which involves mathematics, but really focuses on, well, numbers.  It is a collection of essays written over a period of many years, beginning in 1959.  Although all articles are between four and five decades old, they have aged well.  The only instances where the book feels old is when population and financial figures are discussed, as the absolute values of both have inflated significantly in the ensuing years.

I learned a lot in reading these essays, mostly about the history of mathematics (very fascinating) and the Earth's geography (which, as it turns out, can be described so well numerically).