Dividing an ellipse

[Terp]

Hello

I am wondering if there's a mathematical solution for dividing an ellipse into equal parts. I'm not talking about dividing the ellipse into "pie slices" with lines from the center to the perimeter, but instead by vertical or horizontal lines. I'm not looking for a solution that include weighing

To apply this to an everyday setting - imagine you have a lasagne in an elliptical dish and you want to divide it into let's say three equal sized pieces.
Is there a mathematical solutions to that when only knowing the length and the width? (I'm not looking for a solution that include weighing)

Picture attached for clarification

- Thanks

 

[khansaheb]

Hello

I am wondering if there's a mathematical solution for dividing an ellipse into equal parts. I'm not talking about dividing the ellipse into "pie slices" with lines from the center to the perimeter, but instead by vertical or horizontal lines. I'm not looking for a solution that include weighing

To apply this to an everyday setting - imagine you have a lasagne in an elliptical dish and you want to divide it into let's say three equal sized pieces.
Is there a mathematical solutions to that when only knowing the length and the width? (I'm not looking for a solution that include weighing)

Picture attached for clarification

- Thanks

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem

 

[blamocur]

Hello

I am wondering if there's a mathematical solution for dividing an ellipse into equal parts. I'm not talking about dividing the ellipse into "pie slices" with lines from the center to the perimeter, but instead by vertical or horizontal lines. I'm not looking for a solution that include weighing

To apply this to an everyday setting - imagine you have a lasagne in an elliptical dish and you want to divide it into let's say three equal sized pieces.
Is there a mathematical solutions to that when only knowing the length and the width? (I'm not looking for a solution that include weighing)

Picture attached for clarification

- Thanks

I believe this is solvable using integration -- are familiar with that? If you are here is a hint: you can slightly simplify the problem by assuming that your dish is a circle.

 

[Agent Smith]

Hello

I am wondering if there's a mathematical solution for dividing an ellipse into equal parts. I'm not talking about dividing the ellipse into "pie slices" with lines from the center to the perimeter, but instead by vertical or horizontal lines. I'm not looking for a solution that include weighing

To apply this to an everyday setting - imagine you have a lasagne in an elliptical dish and you want to divide it into let's say three equal sized pieces.
Is there a mathematical solutions to that when only knowing the length and the width? (I'm not looking for a solution that include weighing)

Picture attached for clarification

- Thanks

Nice problem!

Did you try to solve it with a rhombus//?

Why are you excluding weight? If the ellipse is of uniform density, is the via-weight solution easy?

Try to fit the ellipse inside a rectangle and see if you can gain some useful insight into the problem.

 

[Dr.Peterson]

I am wondering if there's a mathematical solution for dividing an ellipse into equal parts. I'm not talking about dividing the ellipse into "pie slices" with lines from the center to the perimeter, but instead by vertical or horizontal lines. I'm not looking for a solution that include weighing

To apply this to an everyday setting - imagine you have a lasagne in an elliptical dish and you want to divide it into let's say three equal sized pieces.
Is there a mathematical solutions to that when only knowing the length and the width? (I'm not looking for a solution that include weighing)

The suggestion of starting with a circle is good; assuming the cuts are perpendicular to an axis, the solution ends up being the same, as you can show by stretching.

In that case, the area formula is found here:

Circular segment - Wikipedia

en.wikipedia.org

You'd use the form with R and h.

But that formula can't be solved algebraically for h; you'd need a numerical solution. (This is still "mathematical".)

Did you try to solve it with a rhombus//?

Why are you excluding weight? If the ellipse is of uniform density, is the via-weight solution easy?

Try to fit the ellipse inside a rectangle and see if you can gain some useful insight into the problem.

Why do you think this would help? Have you tried it?

 

[blamocur]

I believe this is solvable using integration -- are familiar with that? If you are here is a hint: you can slightly simplify the problem by assuming that your dish is a circle.

As shown by @Dr.Peterson, you don't really need integration.

 

[Agent Smith]

The suggestion of starting with a circle is good; assuming the cuts are perpendicular to an axis, the solution ends up being the same, as you can show by stretching.

In that case, the area formula is found here:

Circular segment - Wikipedia

en.wikipedia.org

You'd use the form with R and h.

But that formula can't be solved algebraically for h; you'd need a numerical solution. (This is still "mathematical".)


Why do you think this would help? Have you tried it?

No, I haven't tried it, but it seems so apropos.