High School math

Bob Doyle

SPFG, Supreme Picture Framing God
Joined
Jul 14, 2002
Posts
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Location
South Berwick, Maine
I remember from high school there was a simple (at the time) formula for ovals but I can't remember it now. Does anyone know it?

Had to do with two loci (foci?).

Anyway I want it because I am trying to remember how to draw an oval by hand. I know you can draw one using two pins, a piece of string and a pencil, but where do you put the two pins in a matboard, how long is the string, and should the pencil be sharp or dull?

I can figure out the last question on my own by trial and error (I betting on sharper is better, but you never really know til you try) Any help on the first two would be appreciated.

I have a couple of oval cutters, a hand held Logan and a C&H boat anchor junior, but this question has been bothering me and I couldn't get the answer by googling it so I thought I'd question other framers!

I also remember that there was a similar way to draw an ovoid oval, with three foci (loci?) instead of two. But again I can't remember the formula for figuring out the location for the eccentricity of the oval.

Thanks for any help. (Yes, BTW, this is a serious question!)
 
To draw an ellipse inside a rectangle. Scribe an arc using the contact point of the short axis of the rectangle as the center and the adjacent corner of the rectangle. When you have done this for both sides, the intercept points of the two arcs are the foci of the ellipse thats 2 axis' are described by the rectangle.
Using the foci and one of the two centers of the two arcs make a triangle of some non-stretching string and use the string to guide your pencil around the ellipse.
Need a drawing, I'll fax it to you.
 
Before I had my Oval Master, I had an oval mat cutter that consisted of a hand-held cutter (kinda like a Dexter) with a retractable loop of wire attached. The loop could be adjusted. Then there were a couple of spindles with nails that you'd pound through the matboard into a softwood backing.

I think I actually did cut some oval mats with this contraption, but I'll be damned if I remember what happened to it or how you spaced the spindles and adjusted the wire.

Now I would just ask Wally.
 
Bob,

It depends on how you want to do it. Check out this site; it ought to give you what you want.
 
Ouchie! Bill, that made my head hurt.

I hate math.

Bob, can't you just order it pre-cut from LJ? I heard they were offering that service now...
 
Originally posted by Bill Henry:
Bob,

It depends on how you want to do it. Check out this site; it ought to give you what you want.
I remember when I used to HAVE TO read that stuff in university (and understand it)...Now I can just hit the little x in the top right corner!

Have a good week everybody

James
 
Thanks Wally, I can see how that would work. I can't imagine myself, knowing how <strike>lazy</strike> unmotivated a student I was going to that effort to draw ovals in Math class. Maybe when I find that elusive "free time" I will put your suggestion to work!

I have this idea, albeit a low nagging one, in the back of my head that I want to be able to have egg shaped ovals, and need to figure out how I did it when I was a kid! The oval with two foci was the step you had to learn before drawing the three foci egg-shaped oval. No need for it now, but I want to recall it before I get asked for it!
 
Canuck Phoneguy, thank god for that little "x" eh!

Bill, I found that page before in my quest, but like our canadian friend I read so much then clicked on the "x"! Actually I printed it out, scratched out data, underlined stuff, scratched my head, then bought the C&H Boat anchor! At $100 it was cheaper than the time I lost researching the problem!

The oval master, and the handheld logan/fletcher machines, does use the trammel method for drawing an oval, the principle was easy to understand.

Baer, in actuality I am looking for an understandable theory that I could put into practice to cut an eccentric oval, one that is 12 by 16 but not centered properly like the 12 inch peak being 2 inches from the center of the oval, and wanted to get the basics down first. I think I'm putting too much time into this idea! But it has been nagging at me since last November when the customer brought in the old lopsided oval photo.

Ron, I think if I added a third spindle to your old contraption I could have replicated the customers old oval.

Everyone, thanks for letting me waste your time with my foolhardy questions!
 
For an egg shape, take one of the two foci and move perpendicular equidistant for two new foci. drawing it would be the same as before, though I'll have to work on how to guage the distnace apart for the two new foci.
Just checked it out and it works, though haven't quite git the math for it yet.
 
Bob,

Here is exactly what you asked for.

Notations
the distance from the center to one of the foci (e)
larger axis (D)
smaller axis (d)
square root (V)
D2 = D square = D x D
d2 = d square = d x d

Your formula is

e = [V (D2 - d2)] : 2

In plain words that is: distance "e" from elipse's center to the point you need to place a needle at (foci) is e = square root of (D square minus d square), and everything divided by 2.
In order to trace an elipse the "old way" you need a string (fishing line?) that's not going to stretch under moderate strains. Trace the axis first and clearly marque the limits of the elipse to be drawn. Then calculate value "e". Place firmly two needles/nails into the long axis, at distance "e", left and right from the center. Take a string, passe it around the two foci and make a knot in such a way it will allow your pen reach tightly the limit of either one of the axis. Turn the pen around and there yoau are.
 
By Jove I think he's got it!

Thank you very much WhyNot, that looks like the type of High School Math I knew, and have since forgot!

If I could remember half of what I've forgotten over the years I'd be a 1000 times smarter than I am now. <small><small>But probably just as unbearable!</small></small>
 
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