Hi again all, I have a question,
in group theory
Is there cyclic gorup of 3 elements the same group
(up to is isomorphism)
as the group of rigid mothins of a two color
metal triangle? The top color (white) must stat on
the top for this (cyclic) group.
Does this group have another name that involves
Lie Groups? accordin to Wikipedia ?boggle?
I assume a Lie group is also a (smoothish)
differentialable manifold. With no cusps or
tairs. (Pretty sure)
Back to C3 ( cyclic goroup for a triangle)
To be clear the tryangle has 3 possibilities.
It can stat still (e), it can rotate clock wise 6o
degress clockise , or it can rotate 120 degress
clockwise. It cannot flip (that is the set of
dihedral groups on a regular polygon)
I give a cayley table (for group theory edification)
(X,Y)mod3 | e , a1 , a2
___________|_______________________
e | e a1 a2
a1 | a1 a2 e
a2 | a2 e a1
Just like addition with 'clock math' (mod function)
This ends thie 'askii art' Cayley table.
I'm pretty sure it represents the cyclic group C3,
That is the rigid motions on an equilateral triangle
without flips. (that group D3 would have 6 elements)
I'll put this message under general Math directory.
Matt
Correct me if I am wrong.
Cheers,
Matt