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Klein bottle embedded in R^4 (bottle shape) - 壷の形のクラインの壷

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Uploaded by on Dec 27, 2008

壷の形のクラインの壷(Klein bottle)の4次元ユークリッド空間へのたぶんC^∞埋め込みのグラフ.アイデアは3次元のはめ込みの単射性の損失を4次元目に回避して単射にした.ソフト:NDis­play、Music by:クラシック音楽のヴァーチァルMIDI(MP3)(http://kaion.real-sound.net/)

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  • @Bender3014

    True. Maybe he's got that in his description... for all we know... But it's a good point. :) The Carl Sagan vid on 4D is great for illustrating that.

    ♥ ☼ ♥

  • Impossible to show a Klein bottle in three-dimensional universe, since it is a four-dimensional object, what we see is only its shadow 3D, just like the Hypercube

  • it's linear algebra

  • can you tell me what software  you use to work with multiple vectors ?

  • what type of math do you need for this calculas?

  • I like the dimensional changes along each axis, changing from a plane to a 3 dimensional object as it rotates, very nice.

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