h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

I have a plywood 4ft X 8ft. I want to draw an ellipse with those dimensions. Using the pins and string method, how far apart are the foci?

Better yet, what is the formula so that I can draw them of different sizes.

I get that the foci should be about 6-and-one-half-inches from the edge.

Having a little trouble putting in math symbols, so I'll post this to get you started and struggle a little off-line

Okay:

The formula for an ellipse with center at the origin (0,0), vertices (±a,0) and minor axis (±b,0) is:

(x^2)/(a^2) + (y^2)/(b^2) = 1

The foci are (±c,0), where c^2 = a^2 b^2

In this case, the center of the plywood is 4 feet from one edge and 2 feet from the other.

(x^2)/16 + (y^2)/4 = 1

and c = (±squareroot(12),0)

so the foci are (±3.464, 0) or 3 feet and about 5.5 inches from the center. Or 6-and-one-half-inches from the edge.

Or 6 feet and 11 inches apart.

Thank you Happy Nerd

I pulled my old math book from its dusty shelf and spent the last two hours trying to work it out. Either it comes back not at all or it comes in a confusing rush.

In this case my book had the first formula but not the one for c.

I've already had a couple of tonight so my brain is mush.

Had me confused there with the missing minus sign.

Ooops! Sorry. (So much easier with paper and pencil.)

So, what are you making? Really cool window frame?

I'm making a trailer for my motorbike and didn't want to use the usual rectilinear box. It doesn't fit the bike and it doesn't look good. I'm trying for the simplest curve to make.

If this one doesn't fit the bike I'll try for an egg shape but I'll have to free hand that.

Spooky

I hadn't seen your question until after I'd answered it.

on both the prescience and the project.

I agree with Happy Nerd. The foci are 2xroot(12) feet apart.

Thanks again for the help but I don't think that my plan will work.

I made a sample of the curve with a strip of wood and tried it on the bike but it hits the handlebars.

I could design a quick release for the handlebars to rotate them down for transport but that could prove to be dangerous.

That's the first we've heard about bicycles. Up to now it was only ellipses.

Maybe we could do with a different curve. I'll take a look at my bicycle.

Okay, I know there is a difference between your bike and mine, but...

How about a cartesian oval?

Here's a nice reference:

http://www.mathematische-basteleien.de/eggcurves.htm

Happy, you and I have some kind of psychic connection. I have just spent the afternoon freehand drawing curves to fit around my bike and the one that I settled on is listed on the webpage that you found. With the equation and a way to draw it with string!!!!

Now I have to decide what to make it from.

I've narrowed it down to aluminium (Robopangolin from Space) and clear shrink wrap over wicker basket.

Nice! I like the idea of a bike basket.

If I use an open enough weave,I can put some distressed looking stuffed animals inside.

Then I'll get a Druid version of the Jesusfish for the back.