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/sci/ - Science & Math

File: 997 KB, 240x320, kleinBottle_anim[1].gif [View same] [iqdb] [saucenao] [google]

Anonymous Sat Dec 20 10:27:19 2014 No.6960830 [Reply] [Original]

What's this? A thread... for discussing mathematics and not qualia or conciousness or homework? Absurd!

ITT: Post and inform anons of the existence of cool geometric figures/objects/constructions.

>>	Anonymous Sat Dec 20 10:29:37 2014 No.6960833 >hey /sci/ pls entertain me Yeah, nah, fuck off. If you have nothing interesting to contribute to start your own thread, then don't expect anyone else to feed you.

>>	Anonymous Sat Dec 20 10:30:22 2014 No.6960834 >implying you can separate mathematics from everything else

Anonymous Sat Dec 20 10:31:00 2014 No.6960837
File: 106 KB, 400x398, borromean_A[1].jpg [View same] [iqdb] [saucenao] [google]

>>6960830
First up is the obvious kelin bottle. A container with no clearly defined inner area. It has only one face.

Next is the Seifert surface surface bounded by the Borromean knot.

>>	Anonymous Sat Dec 20 10:33:45 2014 No.6960842 >>6960833 >Waits literally 1 minute before attacking OP for not posting more than 1 picture you know how 4chan works, right?

Anonymous Sat Dec 20 10:40:18 2014 No.6960848
File: 49 KB, 800x375, GabrielsHorn[1].png [View same] [iqdb] [saucenao] [google]

>>6960830
Gabriel's horn, a figure with a finite volume, yet an infinite surface area.

It can be defined by
<span class="math">1/\sqrt{x^2+y^2}, -1\leq z < \infty[/spoiler]

It is an exercise in integration to show that the volume enclosed by this and <span class="math"> z =1 [/spoiler] is finite, while the surface integral across the horn diverges.

>>	Anonymous Sat Dec 20 10:45:26 2014 No.6960856 File: 31 KB, 416x535, 10314758[1].jpg [View same] [iqdb] [saucenao] [google] >>6960830 A tripple kein bottle. 3 nested bottles in such a way so that are inseparable. However, no bottle can be defined to be inside any of the others.

>>	Anonymous Sat Dec 20 10:53:19 2014 No.6960867 File: 1.49 MB, 458x211, 5DvhiW4[1].gif [View same] [iqdb] [saucenao] [google] >>6960830 Shapes that are non-spherical, yet have constant width, such that the roll smoothly.

>>	Anonymous Sat Dec 20 10:56:28 2014 No.6960872 File: 75 KB, 288x288, deltcaus[1].gif [View same] [iqdb] [saucenao] [google] >>6960867 Similarly:

>>	Anonymous Sat Dec 20 10:57:33 2014 No.6960874 >>6960837 > borromean > knot its not a knot you shit. They're called the borromean rings. They are a link. A brunnian link.

>>	Anonymous Sat Dec 20 11:03:26 2014 No.6960881 >>6960874 >comes on /sci/ to call everyone a shit

>>	Anonymous Sat Dec 20 11:05:10 2014 No.6960884 >>6960874 You are correct. I had knot theory on my mind and it just fell out onto the keyboard. Jesus though, you seem rather hostile. Mummy not putting out?

>>	Anonymous Sat Dec 20 11:11:36 2014 No.6960892 >>6960867 Slick gif, in application: https://www.youtube.com/watch?v=6BCgl2uumlI

>>	Anonymous Sat Dec 20 11:15:47 2014 No.6960899 File: 2.09 MB, 350x350, how-to-drill-a-square-hole1[1].gif [View same] [iqdb] [saucenao] [google] >>6960892 Neat. I've only ever seen that shape used for cutting square holes.

>>	Anonymous Sat Dec 20 11:19:44 2014 No.6960905 >>6960848 I find it interesting that you could use the paradoxical nature of that construct to prove the universe is quantized.

>>	Anonymous Sat Dec 20 13:42:29 2014 No.6961130 >>6960899 That's a cool mechanism. Is there any derivation for the red curves?

Anonymous Sat Dec 20 13:46:23 2014 No.6961140
File: 1.25 MB, 2560x1920, Mandel_zoom_00_mandelbrot_set.jpg [View same] [iqdb] [saucenao] [google]

>>6960848
To this we can add fractals which usually have infinite something in N dimensions but finite in N+1 dimensions.

Pic related, it is the mandelbrot set with infinite circumference but finite area.

>>	Anonymous Sat Dec 20 14:04:03 2014 No.6961163 >>6960856 i shuold make a bong out of that....

Anonymous Sat Dec 20 14:08:44 2014 No.6961169

>>6960830
The Loch Ness Monster: a strip of the plane, infinite to one side, with an infinite number of handles added to it. Betty cool guy.

Also, do you think if we add an infinite number of handles to the plane, say along the x-axis, and take the one-point compactification of this 'two-sided Loch Ness', we get a sphere with an infinite number of handles?

Also, why is the latter not a compact surface (I have an idea, not made it rigorous)? We know it is compact, as it is closed and bounded in R3. But it can't be a surface then, because surfaces only have a finite number of holes. So it must be the condition of local Euclidean which doesn't hold. Where does it go wrong?

>>	Anonymous Sat Dec 20 14:21:57 2014 No.6961185 File: 12 KB, 300x346, Koch_snowflake.gif [View same] [iqdb] [saucenao] [google] >>6960848 And here's a 2 dimensional equivalent.

>>	Anonymous Sat Dec 20 14:22:51 2014 No.6961186 >muh shapes fucking autists

>>	Anonymous Sat Dec 20 14:35:50 2014 No.6961204 >>6960905 Care to explain that?

>>	Anonymous Sat Dec 20 14:36:51 2014 No.6961206 >>6961186 >something I don't understand >better call them autistic >>6961204 pls don't

>>	Anonymous Sat Dec 20 16:05:25 2014 No.6961419 >>6961186 You are on /sci/, autism is not an insult.

>>	Anonymous Sat Dec 20 16:07:45 2014 No.6961422 >>6961419 it is, it's just autists think it's some type of special ability. fucking autists

>>	Anonymous Sat Dec 20 16:23:48 2014 No.6961456 >>6961185 Yeah that's an easier example than the mandelbrot set.

>>	Anonymous Sat Dec 20 16:26:35 2014 No.6961466 File: 62 KB, 650x425, foret_de_percage_carre.jpg [View same] [iqdb] [saucenao] [google] >>6960899 Pic related, a neat application.

>>	Anonymous Sat Dec 20 16:39:29 2014 No.6961499 >>6961422 you're a cheerful fella aren't you

>>	Anonymous Sat Dec 20 17:12:41 2014 No.6961570 >>6961466 >not posting a wankel engine Pleb

>>	Anonymous Sat Dec 20 18:17:14 2014 No.6961671 File: 57 KB, 1360x804, perko1.jpg [View same] [iqdb] [saucenao] [google] Seifert surface for 10_161, the perko pair

>>	Anonymous Sat Dec 20 18:18:50 2014 No.6961673 File: 38 KB, 1360x804, hopf1.jpg [View same] [iqdb] [saucenao] [google] hopf link

>>	Anonymous Sat Dec 20 18:20:23 2014 No.6961679 File: 43 KB, 1360x804, p135.jpg [View same] [iqdb] [saucenao] [google] p(1,3,5)

>>	Anonymous Sat Dec 20 18:21:30 2014 No.6961680 File: 55 KB, 1360x804, whitehead.jpg [View same] [iqdb] [saucenao] [google] whitehead

>>	Anonymous Sat Dec 20 19:15:02 2014 No.6961762 >>6961570 ur a wankel

>>	Anonymous Sat Dec 20 19:35:50 2014 No.6961798 what book / course would be good initiation into learning about creating these forms? i would like to incorporate into structures, i'm arch major.

>>	Anonymous Sat Dec 20 19:51:58 2014 No.6961830 File: 80 KB, 793x610, interf26.jpg [View same] [iqdb] [saucenao] [google] >>6961798

>>	Anonymous Sat Dec 20 20:20:40 2014 No.6961864 File: 35 KB, 415x481, 1419054639932.jpg [View same] [iqdb] [saucenao] [google] It's a 4 dimensional mobius strip, you retard.

Anonymous Sat Dec 20 20:47:56 2014 No.6961895

>>6961169
It must be the new point at infinity which doesn't have a chart domain. If you write out the definition of the one-point compactification, you will see that any open neighborhood of the point at infinity contains an infinite number of handles (it is only necessary for it to contain one) so it cannot be homeomorphic to euclidean space.

>>	Anonymous Sat Dec 20 20:58:55 2014 No.6961904 File: 405 KB, 737x665, Hopf_Fibration.png [View same] [iqdb] [saucenao] [google] >>6961673 Very good.

Anonymous Sun Dec 21 01:23:16 2014 No.6962267

>>6961204
Well, the finite volume and infinite surface area is a paradox. Paradoxes by definition can only exist in abstract description and not in a physical sense. Since it is a contradiction it is impossible to make, and it is impossible to make because in the physical universe there is no such thing as infinitely-fine degrees of change. An infinitely-sharp point cannot be made because there is a minimum, indivisible size, below which is zero. The quanta of length is the brick wall for any and all attempts to create paradoxical objects.

>>	Anonymous Sun Dec 21 08:14:01 2014 No.6962682 >>6961904 Nice. What was this made in?

>>	Anonymous Sun Dec 21 09:05:24 2014 No.6962736 >>6960837 >Next is the Seifert surface surface bounded by the Borromean knot. It's a Seifert surface, not the Seifert surface. A given knot/link generally has many, non-equivalent Seifert surfaces.

>>	Anonymous Sun Dec 21 09:16:33 2014 No.6962752 >>6961570 Because it's already been posted, you fag.

>>	Anonymous Sun Dec 21 09:19:05 2014 No.6962758 File: 77 KB, 1865x408, speaker.jpg [View same] [iqdb] [saucenao] [google] Artists interpretation of a computer speaker.

>>	Anonymous Sun Dec 21 09:21:55 2014 No.6962762 File: 33 KB, 460x305, Grothendieck-460x305.jpg [View same] [iqdb] [saucenao] [google] An old wizard who used to be good at maths.

>>	Anonymous Sun Dec 21 09:23:44 2014 No.6962763 >>6962758 deep af bro

>>	Anonymous Sun Dec 21 09:24:35 2014 No.6962764 File: 507 KB, 1540x1080, Fibre Bundle.jpg [View same] [iqdb] [saucenao] [google] An example of a fibre bundle.

>>	Anonymous Sun Dec 21 09:34:43 2014 No.6962768 File: 135 KB, 480x640, 1384211416060.jpg [View same] [iqdb] [saucenao] [google] I call this one "The Hyperbolic Cranium".

>>	Anonymous Sun Dec 21 09:35:58 2014 No.6962771 File: 68 KB, 561x305, Untitled.png [View same] [iqdb] [saucenao] [google] >>6962736 > A given knot/link generally has many, non-equivalent Seifert surfaces. Infinitely many to be precise.

>>	Anonymous Sun Dec 21 09:37:36 2014 No.6962773 >>6961163 >Trying to clean out your disgusting bong water though

>>	Anonymous Sun Dec 21 09:44:38 2014 No.6962781 File: 10 KB, 194x198, Untitled.png [View same] [iqdb] [saucenao] [google] >>6961673 Seifert surface for 0_1

>>	Anonymous Sun Dec 21 10:22:37 2014 No.6962844 >>6961904 >>6961680 >>6961679 >>6961673 any engineering applications for any of this or is it all just multidimensional mathematical wankery?

>>	Anonymous Sun Dec 21 10:56:58 2014 No.6962893 >>6962844 >multidimensional >THREE DIMENSIONS. HOW CRAAAAAAAAAAAAAAZY

>>	Anonymous Sun Dec 21 11:02:54 2014 No.6962897 >>6962893 Though they sit in 3 dimensions, the objects involved are only 1 and 2 dimensional. >>6962844 Maybe topological quantum computers?

>>	Anonymous Sun Dec 21 11:04:39 2014 No.6962899 >>6962897 >ONE AND TWO DIMENSIONS. HOW CRAAAAAAAAAAAAAAZY

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