## Search found 5 matches

Wed May 30, 2012 9:45 am UTC
Forum: Mathematics
Topic: Fitting circles under a curve
Replies: 18
Views: 4055

### Re: Fitting circles under a curve

If a n is the radius of the nth circle, then for large n (1/a n ) - (1/a n-1 ) ≈ 2. This can be used to get good estimates for the tail of the sequence, e.g. if you want to numerically find the area covered by all of the circles. Might I ask how you derived this? Also, if a circle touches e^(-x) at...
Wed May 30, 2012 7:32 am UTC
Forum: Mathematics
Topic: Fitting circles under a curve
Replies: 18
Views: 4055

### Re: Fitting circles under a curve

Are you sure that's right, Timefly? I got the intersection of the circle and curve to be approx. x=0.498 and the centre of the circle at x=0.328. Now you say that, I think I've found a mistake in my working. Yeah, eta oin shrdlu says it should be 0 = (x-a)^3+2(x-a)^2+(x-a)-a^2(x-a)-2a^2, which work...
Wed May 30, 2012 3:50 am UTC
Forum: Mathematics
Topic: Fitting circles under a curve
Replies: 18
Views: 4055

### Re: Fitting circles under a curve

Ben-oni wrote:It doesn't actually look too bad. The first circle is essentially arbitrary. Once you find the second circle, similarity should solve the whole thing.

I don't think the areas of the circles form a geometric series because their centers get closer as you add more.
Wed May 30, 2012 2:22 am UTC
Forum: Mathematics
Topic: Fitting circles under a curve
Replies: 18
Views: 4055

### Re: Fitting circles under a curve

Are you sure that's right, Timefly? I got the intersection of the circle and curve to be approx. x=0.498 and the centre of the circle at x=0.328. Here's what I did: The cirle has radius r, and has been shifted r right and r up. We have r^2=(x-r)^2+(y-r)^2, which can be rearranged to give y=r+sqrt(2r...
Mon May 28, 2012 11:04 am UTC
Forum: Mathematics
Topic: Fitting circles under a curve
Replies: 18
Views: 4055

### Fitting circles under a curve

I thought of a problem a few days ago and I have no idea as to its solution. I posted this on Reddit earlier today but I figured people here could help. Suppose you have a boundary formed by the curve y=e^(-x), and the lines x=0 and y=0. In this boundary you place the largest possible circle you can...