OT: Möbius strip [NCA / SHAM]

posted by Helmut Homepage – Vienna, Austria, 2020-06-24 09:29 (326 d 12:17 ago) – Posting: # 21572
Views: 2,413

Hi Nastia,

» Hey, how did you know that I've got a model of it? :-D

I didn’t know but I’m not surprised.

» Unfortunatelly I am not good at topology…

cup → bagel → cup → …
[image]
© Lucas Vieira Barbosa

Welcome to the club. The worst is knot theory – I have books about it. Headaches guaranteed.
For sure you know what happens if we cut a Möbius strip once. Do you know what happens if we cut it twice? Makes a great party joke.

» But I know the answers for the questions what do we need to drill a square hole…

Punch, OK. But drill?

» … and also what profile one should use to ride a bike with square wheels ;-)

So do I.


https://www.r-bloggers.com/topological-tomfoolery-in-r-plotting-a-mobius-strip
library(rgl)
library(plot3D)
###############
# Möbius band #
###############

R <- 5
u <- seq(0, 2 * pi, length.out = 100)
v <- seq(-1, 1, length.out = 100)
m <- mesh(u, v)
u <- m$x
v <- m$y
x <- (R + v/2 * cos(u /2)) * cos(u)
y <- (R + v/2 * cos(u /2)) * sin(u)
z <- v/2 * sin(u / 2) 
invisible(open3d())
bg3d(color = "#F3F3F3")
surface3d(x, y, z, color= "#87CEFA")
title3d(main = "Moebius band")
# Rotate with mouse-left, wheel to zoom.
################
# Klein bottle #
################

u <- seq(0, pi, length.out = 100)
v <- seq(0, 2 * pi, length.out = 100)
m <- mesh(u, v)
u <- m$x
v <- m$y
x <- (-2 / 15) * cos(u) * (3 * cos(v) - 30 * sin(u) + 90 * cos(u)^4 * sin(u) -
      60 * cos(u)^6 * sin(u) + 5 * cos(u) * cos(v) * sin(u))
y <- (-1 / 15) * sin(u) * (3 * cos(v) - 3 * cos(u)^2 * cos(v) - 48 *
      cos(u)^4 * cos(v) + 48 * cos(u)^6 * cos(v) - 60 * sin(u) + 5 * cos(u) *
      cos(v) * sin(u) - 5 * cos(u)^3 * cos(v) * sin(u) - 80 * cos(u)^5 *
      cos(v) * sin(u) + 80 * cos(u)^7 * cos(v) * sin(u))
z <- (+2 / 15) * (3 + 5 * cos(u) * sin(u)) * sin(v)
invisible(open3d())
bg3d(color = "#F3F3F3")
surface3d(x, y, z, color= "#87CEFA", alpha = 0.5)
title3d(main = "Klein bottle")

Dif-tor heh smusma 🖖
Helmut Schütz
[image]

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes

Complete thread:

Activity
 Admin contact
21,462 posts in 4,487 threads, 1,514 registered users;
online 7 (0 registered, 7 guests [including 2 identified bots]).
Forum time: Sunday 21:47 UTC (Europe/Vienna)

Pharmacokinetics may be simply defined as
what the body does to the drug,
as opposed to pharmacodynamics, which may be defined as
what the drug does to the body.    Leslie Z. Benet

The Bioequivalence and Bioavailability Forum is hosted by
BEBAC Ing. Helmut Schütz
HTML5