OT: Möbius strip [NCA / SHAM]

posted by Helmut Homepage – Vienna, Austria, 2020-06-24 13:29 (1393 d 04:24 ago) – Posting: # 21572
Views: 5,292

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 🖖🏼 Довге життя Україна! [image]
Helmut Schütz
[image]

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

Complete thread:

UA Flag
Activity
 Admin contact
22,985 posts in 4,823 threads, 1,653 registered users;
48 visitors (0 registered, 48 guests [including 6 identified bots]).
Forum time: 17:53 CEST (Europe/Vienna)

Complex, statistically improbable things are by their nature
more difficult to explain than
simple, statistically probable things.    Richard Dawkins

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