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Uploaded by kojocho2 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/)
Science & Technology
Standard YouTube License
@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.
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TheseEyesGod 1 year ago
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
Bender3014 1 year ago
it's linear algebra
fatachu 2 years ago
can you tell me what software you use to work with multiple vectors ?
etiennealive 2 years ago
what type of math do you need for this calculas?
hotelroyale100 2 years ago
I like the dimensional changes along each axis, changing from a plane to a 3 dimensional object as it rotates, very nice.
vampiresofmlm 2 years ago
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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.
♥ ☼ ♥
TheseEyesGod 1 year ago
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
Bender3014 1 year ago
it's linear algebra
fatachu 2 years ago
can you tell me what software you use to work with multiple vectors ?
etiennealive 2 years ago
what type of math do you need for this calculas?
hotelroyale100 2 years ago
I like the dimensional changes along each axis, changing from a plane to a 3 dimensional object as it rotates, very nice.
vampiresofmlm 2 years ago