## South African Skeptics

February 25, 2020, 09:44:31 AM
 Skeptic Forum Board Index Help Forum Rules Search GoogleTagged Login Register Chat Blogroll
 Pages: [1]   Go Down
Author Topic:

# Rotational symmetry

0 Members and 1 Guest are viewing this topic.
brianvds
Hero Member

Skeptical ability: +14/-0
Offline

Posts: 1894

 « on: February 19, 2015, 04:52:47 AM »

Short and to the point: can a 2D shape have an order of rational symmetry of 1? What kind of shape would that be?
 Logged
Rigil Kent
Clotting Factor
Hero Member

Skeptical ability: +19/-3
Offline

Posts: 2474

Three men make a tiger.

 « Reply #1 on: February 19, 2015, 06:35:42 AM »

Apparently not, as explained here.
 Logged
brianvds
Hero Member

Skeptical ability: +14/-0
Offline

Posts: 1894

 « Reply #2 on: February 19, 2015, 15:06:40 PM »

And I assume then that an asymmetrical shape would have a symmetry order of zero?

I just wanted to make sure the stuff in the grade 6 textbook is correct. :-)
 Logged
Mefiante
Defollyant Iconoclast
Hero Member

Skeptical ability: +62/-9
Offline

Posts: 3766

In solidarity with rwenzori: Κοπρος φανεται

 « Reply #3 on: February 19, 2015, 16:01:13 PM »

Actually, it would have a rotational symmetry of order 1 because there is only one orientation in which its outline matches…

'Luthon64
 Logged
brianvds
Hero Member

Skeptical ability: +14/-0
Offline

Posts: 1894

 « Reply #4 on: February 20, 2015, 04:14:03 AM »

Actually, it would have a rotational symmetry of order 1 because there is only one orientation in which its outline matches…

'Luthon64

Well, that is my whole problem. In the textbook's "teacher's guide," which contains answers to the exercises, such a shape is claimed to have a symmetry order of zero. Now I still can't work out whether that is correct or not, because your smiley face indicates that your reply above may or may not be entirely serious.

If something like a propeller has an order of 2, i.e. we count the original position (or the 360 degree rotation, which comes to the same thing), then logic would suggest that in a shape lacking rotational symmetry, we should still count the original position as 1. I can't work out whether this is what is in fact done because of conflicting reports from various authorities. :-)
 Logged
Mefiante
Defollyant Iconoclast
Hero Member

Skeptical ability: +62/-9
Offline

Posts: 3766

In solidarity with rwenzori: Κοπρος φανεται

 « Reply #5 on: February 20, 2015, 07:34:27 AM »

By convention, it would have a rotational symmetry order of 0, i.e. no rotational symmetry.  This is a holdover from reflectional symmetry where the number of reflection axes/planes are counted (0 would be none, i.e. no reflectional symmetry).  Symmetry gets rapidly trickier as the dimensionality of the mathematical space grows.

It’s a bit like the question whether 1 is a prime number or not.  While convention dictates that it is not, some authors on occasion validly consider 1 to be prime.

'Luthon64
 Logged
BoogieMonster
NP complete
Hero Member

Skeptical ability: +19/-1
Offline

Posts: 3149

 « Reply #6 on: February 20, 2015, 09:01:06 AM »

Some people say atheism is a belief, and some say it's a lack of belief.

So some may say the object is has a rotational symmetry of 1, some may say it's asymmetrical: lacks symmetry.
 Logged
brianvds
Hero Member

Skeptical ability: +14/-0
Offline

Posts: 1894

 « Reply #7 on: February 20, 2015, 14:34:26 PM »

By convention, it would have a rotational symmetry order of 0, i.e. no rotational symmetry.  This is a holdover from reflectional symmetry where the number of reflection axes/planes are counted (0 would be none, i.e. no reflectional symmetry).  Symmetry gets rapidly trickier as the dimensionality of the mathematical space grows.

I can just imagine. :-)

Quote
It’s a bit like the question whether 1 is a prime number or not.  While convention dictates that it is not, some authors on occasion validly consider 1 to be prime.

I.e. the orders of rotational symmetry are 0, 2, 3 etc. Weird, but I can live with it.
 Logged
BoogieMonster
NP complete
Hero Member

Skeptical ability: +19/-1
Offline

Posts: 3149

 « Reply #8 on: February 20, 2015, 15:11:16 PM »

You could remove this weirdness by defining it to be the number of additional times it self-resembles the original position. (iow, don't count the original position)

Then you'd have a nice 0, 1, 2... sequence.
 Logged
 Pages: [1]   Go Up