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/sci/ - Science & Math

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>> No.8636724 [View]
File: 41 KB, 800x1113, cruzpepe.jpg [View same] [iqdb] [saucenao] [google]
8636724

>>8636688
https://en.wikipedia.org/wiki/Euclidean_group#Overview_of_isometries_in_up_to_three_dimensions
in R^2 the isometries are
>rotations around a point
>translations
>reflections across a line
>glide reflections
and each isometry can be written as a rotation or reflection (so a choice of orthogonal matrix) composed with a translation (choice of a vector)

so in R^2 the originfixing isometries are the rotations around the origin and reflections along a line going through the origin

>> No.8446943 [View]
File: 41 KB, 800x1113, cruzpepe.jpg [View same] [iqdb] [saucenao] [google]
8446943

>>8446917
>no finite subcover of this cover can cover E.
[proof needed]

>> No.8436923 [View]
File: 41 KB, 800x1113, cruzpepe.jpg [View same] [iqdb] [saucenao] [google]
8436923

>>8436921
looks like i did left regular representation by mistake but you should hopefully get the idea

>> No.8390292 [View]
File: 41 KB, 800x1113, cruzpepe.jpg [View same] [iqdb] [saucenao] [google]
8390292

i never trust archeologists personally

>> No.8381392 [View]
File: 41 KB, 800x1113, cruzpepe.jpg [View same] [iqdb] [saucenao] [google]
8381392

>>8380844
every non-zero element bud

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