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Trivially Speaking: Circles have a degree of history and math - Loveland Reporter-Herald

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“Why are there 360 degrees in a circle,” a regular reader once asked me.

My first response was to say, “Because Miss Helland told me so.”

Miss Helland was my high school teacher for plane geometry (not plain geometry), advanced algebra, trigonometry and solid geometry and she was very competent — she even allowed me to return a few years later as a “practice teacher” in plane geometry. This was very unusual but the powers that be made an exception in my case. But, I digress.

I didn’t give the smart aleck response, I simply said, “I don’t know.” That brief  moment of honesty led me to research the answer to the question.

Let me interrupt to state that I don’t call questions “stupid questions” nor do I avoid answering. This excludes me from present cabinet appointments or press conferences.

Thus, backtracking through time — don’t we all wish we could do that for real and not paper trails as I follow — we’ve got to skip a couple of millennia.

We’ll try to pin it on the Sumerians (looks like guys who knew math, at least arithmetic).

If that won’t stick, we’ll put it on the Babylonians. One theory suggests that ancient astronomers — probably not a high-paying job — paid attention to the movement of the sun (not really, it’s the earth rotating but it’s too late to quibble with them) and deduced that it made its transition through about 360 days (close but no Babylonian cigar).

A more scientific explanation is that the Babylonians subdivided the circle using the angle on an equilateral triangle as the base unit — is this too technical for non-geometry students (some in my classes were)? They then further divided this into 60 parts following their sexagesimal (looks more exciting than it is and certainly not in my geometry classes) numeric system (a  base of 60 not 10).

The Babylonians were followed (not too closely) by their Greek (and perhaps geek) fellow astronomers.

The earliest trigonometry was based on chords of a circle (this chord not a musical one) and a chord (line) equal to the radius of the circle was made a natural base quantity. One-sixtieth of this using the sexgesimal approach was a degree.

The old Greeks liked this, and a gaggle of them including Aristarchus and Archimedes (last names unknown) exploited the Babylonians’ knowledge and techniques systematically. These guys were the first Greeks known that divided the circle into 360 degrees of 60 arc minutes.

If this isn’t so much that it discourages regular readers from asking questions, note also, that 360 is readily divisible with 24 divisors (eight of the first 10 numbers: 2, 3, 4, 5, 6, 8, 9, 10).

That’s all well and good except in most mathematical work beyond practical geometry — yes, there is impractical geometry — angles are typically measured in radians. This gets us into that whole “Pi” thing and I’d like to avoid that for now since Pi a la mode is tricky.

This elaborate response may be just a good example of “No good deed goes unpunished”.

As an aside, I attempted to take astonomy as a three-credit math course the spring quarter of my senior year. I thought lying on my back looking at the stars would be a great way to finish my college education. My sign is Scorpio and I thought maybe the class would dip into astrology.

Unfortunately, too few students signed up and the class was canceled. The department “allowed” me to take nuclear physics for the three credits needed instead — I have never forgiven them.

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Trivially Speaking: Circles have a degree of history and math - Loveland Reporter-Herald
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