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

*(this is the South; we like to be detailed about how you are breaking our hearts, fucker). This is*

**I'd Be Better Off (In a Pine Box) (On a Slow Train Down to Georgia)***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

**edgewitch**: Link to solution with proof!.

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