• Mar 31st 2008, 09:42 AM
MUSICismyBOYFRIEND
I have to make a Cairo Tessellation with these steps:

1: On another sheet of paper, construct segment AB, with midpoint M.
2: In the same half plane, construct two 45 degree angles with vertex M. Call them (angle)AMX and (angle)BMY.
3: Locate C on ray MY such that C lies on the circle having center B and radius AB.
4: Locate E on ray MX such that E lies on the circle having center A and radius AB.
5: Locate D, the intersection of the circle having center C and radius AB and the circle having center E and radius AB.
6: Pentagon ABCDE is the Cairo tile. Recopy it and create the Cairo tessellation!
• Mar 31st 2008, 10:40 AM
Mathnasium
What are we supposed to do? We can't possibly construct it for you, and the instructions are pretty straightforward. I don't know how to improve on the step-by-step instructions you've provided.

Have you started? What have you done? Have you constructed a segment and found the midpoint?

I would suggest using a geometry textbook with a section on constructions - most geometry books have a chapter or at least a few sections. Any diagrams they have there will most likely be more helpful than a description found here.
• Mar 31st 2008, 10:53 AM
MUSICismyBOYFRIEND
Quote:

Originally Posted by Mathnasium
What are we supposed to do? We can't possibly construct it for you, and the instructions are pretty straightforward. I don't know how to improve on the step-by-step instructions you've provided.

Have you started? What have you done? Have you constructed a segment and found the midpoint?

I would suggest using a geometry textbook with a section on constructions - most geometry books have a chapter or at least a few sections. Any diagrams they have there will most likely be more helpful than a description found here.

i found midpoint M and i'm assuming that you just bisect the angle to get a 45 on each side but after that, i'm totally lost... "Locate C on ray MY such that C lies on the circle having center B and radius AB" how am i supposed to do that?
• Mar 31st 2008, 10:59 AM
earboth
Quote:

Originally Posted by MUSICismyBOYFRIEND
I have to make a Cairo Tessellation with these steps:

1: On another sheet of paper, construct segment AB, with midpoint M.
2: In the same half plane, construct two 45 degree angles with vertex M. Call them (angle)AMX and (angle)BMY.
3: Locate C on ray MY such that C lies on the circle having center B and radius AB.
4: Locate E on ray MX such that E lies on the circle having center A and radius AB.
5: Locate D, the intersection of the circle having center C and radius AB and the circle having center E and radius AB.
6: Pentagon ABCDE is the Cairo tile. Recopy it and create the Cairo tessellation!

I've done the construction according to your description (and I can't imaging why you can't do it)

I then reflected the pentagon about the midpoint of oneside to get a garland of pentogons.
• Mar 31st 2008, 11:02 AM
earboth
You can't cover the plane completely what I would presume by the word "tesselation". If you try to cover the plane there'll be some "holes".

I've marked them lightgrey.
• Mar 31st 2008, 11:25 AM
topsquark
FYI: This is the origin of things like, in Mathematics, Penrose tiling, and in the physical sciences, quasicrystals.

-Dan