Bioequivalence and Bioavailability Forum • OT: Möbius strip

OT: Möbius strip [NCA / SHAM]

posted by Helmut – Vienna, Austria, 2020-06-24 13:29 (1768 d 04:47 ago) – Posting: # 21572
Views: 8,432

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!
Helmut Schütz

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