Thread: Geometry Help Please Help

I have a diagram of 25 congruent circles in a 5 x 5 pattern, but all touching, somewhat like this:

OOOOO
OOOOO
OOOOO
OOOOO
OOOOO

Just forget the spaces between the lines, imagine they are all bunched up together to form a perfect square. The question says I am to shade at least one circle so the figure has rotational symmetry of 90 degrees, but no line of symmetry. After looking at this, I fail to see how it's possible, but obviously it must be. Thank you all for your time and answers
Rocker 1414

OO#OO
OO#OO
#####
OOOOO
OOOOO


The #'s are the circles you should shade in.
That's the answer. No line symmetry whatsoever, but it has 90 degree rotational symmetry.

Originally Posted by desperatesoul

OO#OO
OO#OO
OO#OO
#####
OOOOO
OOOOO


The #'s are the circles you should shade in.
That's the answer. No line symmetry whatsoever, but it has 90 degree rotational symmetry.

ok, what do we mean by rotational symmetry? because rotating this 90 degrees, say clockwise, yields:

OO#OO
OO#OO
OO###
OO#OO
OO#OO

Hello,

Originally Posted by desperatesoul

OO#OO
OO#OO
#####
OOOOO
OOOOO


No line symmetry whatsoever.

As Jhevon said, it seems there is no 90° rotational symmetry. Plus, there is a line of symmetry :

Code:

  |
  |
OO#OO
OO#OO
#####
OOOOO
OOOOO 
  |
  |

A solution without line symmetry is

Code:

OOO#O
#OOOO
OOOOO
OOOO#
O#OOO

Another possibility is to shade circles so that they form a swastika.

Oh sorry about that! Must have had a brain fade.