Okay, I give up: I need someone who knows geometry.

I'm trying to enclose a rectangle of known dimensions within an ellipse and expand the ellipse thirty feet from each angle. No, Pythagorean theorum didn't work (why????????), I tried expanding the rectangle theoretically by thirty feet at all diagonals, I tried magic.

I have Pythagged, sined, cosined, tangented and right now I could pass my junior trig and geometry with a A, but I cannot make a fucking ellipse that's perimeter entirely encloses a rectangle of known dimensions that is at least one hundred feet from the closest point in the rectangle.

What. Do. I. Need. To. Do?

Assume all measurements in feet, m is the multiplier to get the ratio to recalculate w, h to a, b for second rectangle and expanded ellipse.

Formula to calculate an ellipse: https://www.mathsisfun.com/geometry/ellipse-perimeter.html <--approximation 3

Current Rectangle:
w = 2640
h = 450
d = Sqr(x) = (w ^ 2) + (h ^ 2) = 2678.0776
p of rec = 6180
p of ellipse = 5487.4475

Increasing the diagonal by 100 at all angles
d2 = 2678.0776 + (100*4) = 3078.0776

(Corrected 30 to 100; I couldn't make thirty work at all).

I thought it was working with this formula:
New Rectangle:
m = d2/d = 3078.0776/2678.0776 = 1.1493
a = w * m = 2640 * 1.1403 = 3034.3126
b = h * m = 450 * 1.1403 = 517.2123
p of new rect: 7.103.0501
p of new ellipse = 6304.7578

It could work, but I'm not sure, because when I start expanding the rectangle itself and apply the formula to get real ellipse and new ellipse, it doesn't work and I don't know why. The only explanation I have is that I'm changing the height and width too much, but the same results occur no matter what I do.

Second group:
w = 10560
h = 24390
d = Sqr(x) = (w ^ 2) + (h ^ 2) = 26,577.9175
p of rect = 69,900
p of ellipse = 57,070.34402

Increasing the diagonal by 100 at all angles
d2 = 26577.9175 + (100*4) = 26977.9175

I thought it was working with this formula:
m = d2/d = 26977.9175/26577.9175 = 1.015
a = w * m = 10560 * 1.015 = 10718.92893
b = h * m = 24390 * 1.015 = 24757.07165
p of rect: 70952.00116
p of new ellipse = 57,747.0583

What is wrong with my brain that this isn't working? I verified my results with google and it agrees something is wrong with either a.) my brain or b.) geometry. I think it's geometry. I get ellipse calculations are complicated, but I double checked that part a few times and it's working, I think. At least, google thinks so when I enter my numbers to get the smallest ellipse but this is making no sense why I can't get that second one to work.

I'm listening to country music and not like, Girl in a Country Song but stuff like The Dance and The Thunder Rolls and Straight Tequila Night and The Bluest Eyes in Texas and I'd Be Better Off (In a Pine Box) (On a Slow Train Down to Georgia) (this is the South; we like to be detailed about how you are breaking our hearts, fucker). This is Southern wake after the death of grandma level shit here; this is when we drink Southern Comfort and Wild Turkey and a metric ton of margaritas (if your Southern is Texan), eat potato salad and fried anything, and everyone gets drunk, talks about their rifles and family scandals and at some point one to three parents have a knock-down drag out among the funeral flowers and someone hides in the closet with a brownie and...we're not talking about my childhood, right.

...this is where I am right now. Fix my geometry or I won't be understandable when I talk to anyone not in a central Texas bar; I already have too many vowels in my words and all my gerunds are missing a very important ending 'g'. I will write all my entries in the dialect of a central Texas rural farmer if I have to, and don't think I won't.

This has been a mathematical cry for help.

ETA: Oh God, I Want to Be Loved Like That just came up on rotation. Help.

ETA 2: If you saw an ealirer version, I was using '30 feet' not '100 feet'; I switched when testing the formuals to 100 because thirty simply didn't work and I wanted a dramatic change. All math here is based on an increase of 100 from all angles, or an increase of 200 of each diagonal.

ETA 3: Aded figures worked out in pencil, verified in excel and google, cited my formulas, and still WHAT.




Answered by [personal profile] edgewitch: Link to solution with proof!.
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