Mon (emblem)

Mon (紋?), also monshō (紋章?), mondokoro (紋所?), and kamon (家紋?), are Japanese emblems used to decorate and identify an individual or family. Mon may have originated as fabric patterns to be used on clothes in order to distinguish individuals or signify membership in a specific clan or organization. Japanese traditional formal attire generally displays the mon of the wearer. Rules regulating the choice and use of mon were somewhat limited, though the selection of mon was generally determined by social customs. There are no set rules in the design of a mon. Similar to the blazon in European heraldry, mon are also named by the content of the design, even though there is no set rule for such names. The degree of variation tolerated differ from mon to mon as well. Japanese heraldry does not have a cadency or quartering system, but it is not uncommon for cadet branches of a family to choose a slightly different mon from the senior branch. Virtually all modern Japanese families have a mon.

Tessellations A translation is a shape that is simply translated, or slid, across the paper and drawn again in another place. The translation shows the geometric shape in the same alignment as the original; it does not turn or flip. A reflection is a shape that has been flipped. Most commonly flipped directly to the left or right (over a "y" axis) or flipped to the top or bottom (over an "x" axis), reflections can also be done at an angle. If a reflection has been done correctly, you can draw an imaginary line right through the middle, and the two parts will be symmetrical "mirror" images. Rotation is spinning the pattern around a point, rotating it. A good example of a rotation is one "wing" of a pinwheel which turns around the center point. In glide reflection, reflection and translation are used concurrently much like the following piece by Escher, Horseman.

MbE Activity You will need: a square of paper, maybe 10cm across some more paper A good pair of scissors Sticky tape What you do: Use the scissors to cut a shape out of one side of the square Put the pieces you cut off on the opposite side of the square. Make sure you match the straight side of the square with the straight side of the piece you cut off (don’t spin the pieces) Use a small piece of sticky tape to stick the small piece to the square. What’s happening: The shapes you have made cover a flat surface with no gaps. A tessellation is a tiling that repeats. Mathematicians are especially interested in tessellating with regular shapes – those shapes where all the sides are equal and all the angles are the same. Applications: Tessellations are used all the time to design things like bricks and bathroom tiles. Tessellations are used for more than just tiling. Manufacturing companies also use tessellations. Further information: Tessellations Some famous tessellations by artist M C Escher