# math: squeezing Moebius strips using either 'tame' or 'wild' embeddings, but only with overlaps

<< In math, three-dimensional space sprawls out to infinity in every direction. With an infinite amount of room, it should be able to hold an infinite number of things inside of it - pearls, peacocks or even planets. >>

<< But a recent proof (..), shows that one relatively well-known mathematical object can’t be packed an uncountably infinite number of times into an infinite amount of space: the Möbius band, a two-dimensional loop with a half-twist. >>

<< "Tame" embeddings extend to the entire space, so it’s possible to stretch or squish the space to make the embedded sphere into a standard round sphere. >>

<< "Wild" embeddings, on the other hand, are not so easily visualized and generally require some infinite process to describe. With a wild embedding, there is no way to transform the space to make the wildly embedded version a round sphere. >>

Evelyn Lamb. Möbius Strips Defy a Link With Infinity. Feb 20, 2019.

https://www.quantamagazine.org/mobius-strips-defy-a-link-with-infinity-20190220

https://twitter.com/QuantaMagazine/status/1126601994494455809

Olga D. Frolkina. Pairwise disjoint Moebius bands in space. Journal of Knot Theory and Its Ramifications. Vol. 27, No. 09, 1842005 (2018). doi: 10.1142/S0218216518420051

https://www.worldscientific.com/doi/abs/10.1142/S0218216518420051