How to cut fried eggs with mathematical elegance and perfection

geometry geometric-construction recreational-mathematics euclidean-geometry

Solution 1:

I think the Ham-Sandwich theorem can help in this case , which states that for every positive integer n , given n measurable "objects" in n-dimensional Euclidean space, it is possible to divide all of them in half (with respect to their measure, i.e. volume) with a single (n − 1)-dimensional hyperplane.

So even if you increase the number of eggs you can always find a line that cuts them exactly in half.

Numberphile did a great video on the subject ,Ham Sandwich Problem - Numberphile,i suggest you check it out

Related

Find $f(f(\cdots f(x)))=p(x)$
What is this function related with continued fractions?
Is many sorted logic really a unifying logic?
Partially tiling a square with parallelograms
What is the number of squares in $S_n$?
Covering a compact set with balls whose centers do not belong to other balls.
Is $\Bbb Z[\sqrt{6}]$ a UFD?
$\int_0^\infty \frac{\ln\left(1+x-\sqrt{2x}\right)}{1+x^2}\,dx$
Expression for the value of $\int_0^1 x^{1/x}dx$
Which matrices $A\in\text{Mat}_{n\times n}(\mathbb{K})$ are orthogonally diagonalizable over $\mathbb{K}$?
Derive the recurrence relations
Is the converse of Ramanujan's Master Theorem also true?