A request for those into both maths and technology - I need a diagram with an ellipse & a circle, each of the same area, the circle centred on one of the foci, & the ellipse a little eccentric, but enough to be clearly different from the circle.
I can draw an ellipse, & I can probably work out where the foci are, but getting them honestly of equal area is trickier. Ideally a diagram showing a family of ellipses of equal area, sharing a focus, including the circle, would *also* be good.
An ellipse is just a circle squeezed by b/a. Then the distance c between focus and center is c²=a²-b².
I have collected a few more relations, have a look at my 'anatomy of the ellipse' here:
I can do it for you but I won't be near my computer until tomorrow night. Could you please draw by hand on piece of paper what exactly do you have in mind? In AutoCad there is option to draw geometric shapes by inputing area of shape, that wont be a problem
@ColinTheMathmo If you have a "scale" tool in whatever drawing utility you're using, then you can copy your circle and scale it by reciprocal factors in the x- and y-directions to get an ellipse of the same area. For example, scale by 6/5 in the x-direction and 5/6 in the y-direction.
@ColinTheMathmo Here's a Desmos link that might be helpful for you. It draws a picture like I think you're describing, and you can set the shape of the ellipse however you like it. You can turn the gridlines and axes off, too, if you want the diagram isolated.
@ColinTheMathmo Something like this?
@rnather That's one of the things I was looking for, thanks. If I can find a clean narrative I'd like to use that, so how would you like to be credited? Name? Handle? Link? See here for examples:
Oh, full name is sufficient: Rüdiger Nather. Anything else you'd like/need?
@rnather Not at the moment - thanks. There have been some issues spotted with my explanations, so I may be a few days getting it sorted. If there is anything I'll let you know.
And thanks again.
@ColinTheMathmo Oh, 'twas my pleasure. Quite literally, as your diagram provided me with an incentive to figure out how to use cairo from Haskell.
A Mastodon instance for maths people. The kind of people who make \(\pi z^2 \times a\) jokes.
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