Lyr Req: Tangent, Cotangent...

Subject: Tangent, Cotangent...
From: -=Jim=-
Date: 11 Nov 99 - 08:14 PM

I asked about this a few months ago, and thought I'd try again. I remember a ballad in 3/4 time that an old math teacher used to sing... the chorus began:

"Tangent, cotangent, cosecant, cosine, singin' tangent, cotangent, cosecant, cosine."

Has anyone heard this? Got lyrics?

-=Jim=-

Subject: RE: Lyr Req: Tangent, Cotangent...
From: Bruce O.
Date: 11 Nov 99 - 10:54 PM

From 'The Academy Songbook', (with music) 1895. Amherst song by F. Browning, '61. Air, "Villikens and his Dinah"

Sing Tangent, Co-tangent

There was a professor in New York did dwell.
His name it was Loomis, we know him quite well,
He wrote a big treatise on angles and lines,
With chapter on spheres, surveying, and sines.
Sing tangent, co-tangent, so-secant, cosine.
Sing tangent, co-tangent, so-secant, cosine.

Prof. Coffin, from cones cut by planes that passed through,
Made all kinds of figures that ever he knew,
Some round, like an apple, some lengthened like eggs,
Some rounded like sand-hils, some pointed like pegs.
Sing origin focus, directrix, and curve. [bis]

Old Robinson added the third of the three,
An Algebra hard as the hardest could be,
With theorems difficult, problems like steel,
Intended of course for the student's good weal.
Sing Robinson, Horner , Prof. Napier, Sturm [bis]

There was a poor student in Amherst did dwell,
The first in his class, and all liked him right well;
He drank some cold conics, supposing 'twas wine,
And screeched, as he died, "I am chocked by a sine!"
Sing tangent, etc.

Beware of them sines, now my classmates, I pray,
And follow not tangents, but a straightforward way;
And then by plain sailing your port shall be made,
In a harbor of rest, by no mortal surveyed.
Sing tangent, etc.

[Put a couple spaces before the chorus lines]

Subject: RE: Lyr Req: Tangent, Cotangent...
From: Bruce O.
Date: 11 Nov 99 - 10:55 PM

Agah! that should be co-secant in the chorus.

Subject: RE: Lyr Req: Tangent, Cotangent...
From: -=Jim=-
Date: 12 Nov 99 - 03:30 PM

WOW! Thanks Bruce! -=Jim=-

Subject: RE: Lyr Req: Tangent, Cotangent...
From: Caitrin
Date: 12 Nov 99 - 09:38 PM

*shudders* Trig. Ugh.

Subject: RE: Lyr Req: Tangent, Cotangent...
From: Bruce O.
Date: 13 Nov 99 - 01:34 PM

Trig was where I discovered what math was good for. At the time of my retirement I was a high resolution Fourier transform spectroscopist. The basic mathematics of which is trig. To put it bluntly, scientists, engineers, mathematicians, and many others, take a person to be poorly educated that hasn't had math through statistics, matrix algebra, and integral calculus. They haven't learned the basic tools for any quantitive comparisons.

Subject: RE: Lyr Req: Tangent, Cotangent...
From: Caitrin
Date: 13 Nov 99 - 01:42 PM

I personally have no desire whatsoever to be able to do any kind of calculus. If there's an engineer out there who thinks I'm undereducated, so be it. I do not enjoy math, nor do I feel the need to be but just so involved with it. There are intelligent human beings who are not math people. Everyone needs basic mathematics, but I don't think everyone needs stats and Calculus.

Subject: RE: Lyr Req: Tangent, Cotangent...
From: Bruce O.
Date: 23 Nov 99 - 06:02 PM

There is the much quoted story about David Hilbert, who one day noticed that a certain student had stopped attending class. When told that the student had decided to drop mathematics to become a poet, Hilbert replied, "Good--he did not have enough imagination to become a mathematician."

From p. 95 of Paul Hoffman's 'The Man Who Loved Only Numbers: The Story of Paul Erdos', 1998.

There's some masterful trigonometry in Erdos's paper on the optics of a two mirror imaging system, in Journal of the Optical Society of America. It took great imagination to even consider that such a treatment might be possible.

Subject: RE: Lyr Req: Tangent, Cotangent...
From: Mary in Kentucky
Date: 23 Nov 99 - 10:22 PM

Yea Bruce. I knew I liked you. I taught HS math for five years and often fell into the trap of trying to convince skeptical students that math really was worthwhile for everyone. I sincerely believe that a person's ability to think rationally and creatively is limited by language--and mathematics is just one of many languages. Not until I studied calculus could I express the idea of changing change. I also believe music is a language, and I wish I understood more theory. BTW, there is a good thread here about harmonization.

Subject: RE: Lyr Req: Tangent, Cotangent...
From: Bruce O.
Date: 23 Nov 99 - 11:38 PM

Then you know that creative people resort to words only when they can't draw the picture.

Subject: RE: Lyr Req: Tangent, Cotangent...
From: Bruce O.
Date: 24 Nov 99 - 12:12 AM

I should have noted that when gets higher than 4 dimensions, pictures fall down, as do most projections, and mathematics is the only adequate language.

Subject: RE: Lyr Req: Tangent, Cotangent...
From: Mary in Kentucky
Date: 24 Nov 99 - 09:20 AM

Have you read the book "Flatland" or "Flatlands" (don't know the autor)? It's a whimsical look at what our world would be like if everything we know is in two dimensions. Caitlin--this is a verrrrrrrry short book and would be great for outside reading in any class. If you've a bent for philosophy, creativity, imagination and just "thinking outside the box," you would enjoy this one. You might even have a kinder opinion of mathematics. ;-) And if you like this one, check out the original Lewis Carroll's "Through the Looking Glass" (Alice in Wonderland).

Subject: RE: Lyr Req: Tangent, Cotangent...
From: jeffp
Date: 24 Nov 99 - 10:23 AM

I can second the recommendation for "Flatland." The full title is "Flatland: A Romance of Many Dimensions." It was written in 1880 by Edwin A. Abbott. Amazon.com has a Dover paperback edition. I read this several times when I was younger and found it enjoyable on many levels. It not only treats with the different mathematical dimensions, but also lampoons the Victorian class system and our difficulty in believing anything we haven't seen with our own eyes. It's a short read and a lot of fun.

Subject: RE: Lyr Req: Tangent, Cotangent...
From: Pete Peterson
Date: 24 Nov 99 - 09:53 PM

"Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable subhuman who has learned to wear shoes, bathe and not make messes in the house." (Lazarus Long as reported by Robert A. Heinlein)
I am not sure I fully agree with the above as one of the more interesting things I try to do (sometimes) is explain a mathematical concept to someone who claims not to understand math & to hate it. Taking Bruce O. and Caitrin as thesis and antithesis, my own synthesis (IMHO) would be in the direction of Bruce O. But I also believe strongly that where two people WANT to communicate a concept they will find a way; if B doesn't know that particular branch of math it will simply take both of them a little longer.

Subject: RE: Lyr Req: Tangent, Cotangent...
From: Caitrin
Date: 24 Nov 99 - 10:56 PM

Mea culpa! Mea Maxima Culpa! I did not intend to offend anyone by my statement. I have to admit to being somewhat embittered against math, having spent the last year in pre-calculus under the supervision of Mrs. Riddick, who has no patience with those of us to whom math doesn't come easily. It's possible that with a better teacher and a better attitude toward the subject, I might find that I would enjoy math. The closest I have ever come to being interested in math was when the tesseract was described by Mrs. Whatsit in A Wrinkle in Time. So I suppose I'll give Flatland a try.

Subject: RE: Lyr Req: Tangent, Cotangent...
From: Bruce O.
Date: 25 Nov 99 - 02:09 PM

Its been so long since I've read 'Flatland" that I remember little of it, but it doesn't really take any math background to read it. I hope you enjoy it Caitrin. I did.

Subject: RE: Lyr Req: Tangent, Cotangent...
From: Reiver 2
Date: 30 Nov 99 - 11:55 PM

Perhaps I qualify as one of those "tolerable subhumans." I don't know the song mentioned but I do remember a "Yell" performed by Engineering Students at the University of California (this dates from the early 1940s) that the song reminded me of:

Engineer's Yell

"E to the X dy! dx! E to the X dx!

Secant,cosine,tangent,sine Three-point-one-four-one-five-nine;

Square root, cube root, QED. Slip stick! Slide rule! 'ray, U.C.!"

As one of those who is not fully human, I have only the foggiest idea of the meaning, if any, of any of it.

Subject: RE: Lyr Req: Tangent, Cotangent...
From:
Date: 01 Dec 99 - 12:15 AM

3.1415926535 and I forget the rest. A story, I don't know if its true, was that the Texas Legislature considered making the legal definition as pi = 22/7, close enough for many purposes.

Subject: RE: Lyr Req: Tangent, Cotangent...
From: Rana
Date: 01 Dec 99 - 08:54 AM

A Nova/BBC documentary on Fermat's Enigma, based on the book by Simon Singh was absolutely fascinating. It brought out the drama, hopes, disappointments and much more that can be behind maths. In fact the human involvement and emotions behind it. Reading/watching this could inspire many a student, I'm sure.

Rana

Subject: RE: Lyr Req: Tangent, Cotangent...
From: Vixen
Date: 01 Dec 99 - 10:23 AM

Caitrin, fwiw, I found school the worst place to learn math. I managed to make it through stats and calculus, but I did poorly in every class, and here is why.

I learned how to APPLY the material from each course (which I had barely passed) in the subsequent course, causing me to barely grasp the material from that course, until I had to apply it in the next course. E.g., I finally UNDERSTOOD algebra when I got into geometry and trig. I didn't understand geo. and trig. until I got to calculus.

There must be some holistic strategy for teaching math so that students like me are not frustrated into thinking they're math idiots by the academic constraints of the semester schedule and grades. In school I always thought I was mathematically impaired, but now I actually find some concepts best expressed in math, and enjoy the challenge of expressing them.

Flatland is great. I hope you enjoy it.

V

Subject: RE: Lyr Req: Tangent, Cotangent...
From: Jack (who is called Jack)
Date: 01 Dec 99 - 12:34 PM

I am sitting here trying to write something about the thrill I experience from the soul stirring beauty of mathemtics. The flow of the equations, the beauty of the symbols, the way the equations transform under simple rules to reveal new ideas or express something first one way then the other. The way that they bridge the gap between the workings of the natural world and the workings of the mind. I am sitting at this moment in a research laboratory, surrounded by articles, notebooks, and scraps of paper filled with the mathematics that are the gateway to new knowlege and techniques.

Subject: RE: Lyr Req: Tangent, Cotangent...
From: Bert
Date: 01 Dec 99 - 04:04 PM

Math is a game, but unfortunately few teachers are gifted enough to stress that point. It doesn't necessarily have any relevance to life unless you choose to see it.

Good for you Caitrin to recognize that bad teaching is a problem. Read a book or take a class in the history of math. It's much more fun when you see it from that point of view. And read Lewis Carrol, his sense of humor sprang from his genius at Mathematics.

Bert.

Subject: RE: Lyr Req: Tangent, Cotangent...
From: Caitrin
Date: 02 Dec 99 - 10:25 PM

I never realized that there were really interesting math people. How fascinating. The only people I know face-to-face who like math are deadly boring. This is certainly giving me a different spin on things.

Subject: RE: Lyr Req: Tangent, Cotangent...
From: Mbo
Date: 02 Dec 99 - 10:37 PM

Math is my worst subject! I can handle complex music theory, but for some reason, math has always eluded me. When I graduated from community college this year with my Associate Degree, my GPA was 3.92. Why not a 4.0? Because I got a C in the so-called "College Algebra" which is really triginometry. Out of my whole 2 years there, it was the only class that I got a grade other than A. Thanks goodness artists don't need math, and also that at a senior institution like ECU my GPA is reset at 0.0. Math people aren't weird, as far as I've noticed, in fact my father and grandfather are & were respectively math whizzes. Needless to say, it didn't rub off on me.

--Mbo