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Friday, March 2, 2012

Tremendous Two Week Tessellation!



 

tessellation

A repeating pattern of closed figures that covers a surface with no gaps and no overlaps

Example:
 






This growing tessellation started with three yellow hexagons. The design grew out  from those three polygons. It was designed and assembled over a two week period.




Photo by Royce

Here is a photo of the tessellation after two days.




Below is the final design after two weeks of work! 

It's a masterpiece!





Sadly, the time came for the pattern blocks to be put away. 




Do you have a tessellation in your house? 

Most kitchens and bathrooms have square tiles that tessellate.






 
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17 comments:

  1. kereruclassMarch 2, 2012 at 9:46 PM

    Hi , What great patterns, we have tried this in paint and also on this website. http://gwydir.demon.co.uk/jo/tess/tess.htm

    Kereru class Pukekawa

    ReplyDelete
  2. Mrs McKenzie and B4March 3, 2012 at 12:11 AM

    Dear Mrs Yollis and Grade 3
    What a stunningly beautiful tessellation! It reminded me of a kaleidoscope pattern.

    I had noticed your tessellation in an earlier post, but it had certainly grown by the time you had to undo it.

    As you were building it, did it ever have to have some redone to ensure the tessellation pattern was correct?

    yours in admiration
    Mrs M♔Kenzie

    ReplyDelete
    Replies
    1. Mia and AlexandraMarch 5, 2012 at 2:29 PM

      @ Mrs, Makenzie,

      Thank you for leaving our class a comment! We agree that our tessellation pattern looks like a kaleidoscope. Kaleidoscopes are mixed shapes that go together just like a tessellation.

      Mr. Mannell showed our class a picture of a mandalas, and we think it is spectacular! A mandala is colored sand made into a picture, almost like a tessellation. They usually take about three or four days to make. Here is the link to the picture: Picture of mandalas

      Have you ever heard of a mandala?

      Your blogging buddies,
      M♥a ⚔ and Alexandra♥

      Delete
  3. AnonymousMarch 3, 2012 at 12:55 AM

    Dear Mrs Yollis and class,

    What a tessellation of a post! I really enjoyed your video of your awesome tessellation you all made.
    Great effort by all making your colourful tessellation but I cannot believe what I saw in the video how it took a second to dismantle it. :(

    I do have tiles on my floor of my kitchen which are square as well as in my bathroom.

    From your friend,
    AA

    ReplyDelete
  4. David and AdeleMarch 3, 2012 at 8:28 AM

    We've been tesselating tiles down the centuries and across the world, some of the bets are found in Mosques, where the tiles are marvellous, but the artist always makes a slight deliberate mistake as only God is perfect. The Romans came to England around 1500 years ago and just as Mrs Yollis said they tiled away in their grand houses and bath houses. Even I have a stone floor that tesselates.
    I love the short video, mainly because I learnt that the reverse feature can be cunningly used. I expect we will be experimenting with that feature shortlyYou are a lovely group of people and I want you to know that sharing your work with everyone is a really supportive action, that is much appreciated.

    Mr E
    Hawes

    ReplyDelete
    Replies
    1. ⚡⚔⚓⚒R♔yce and Br◱nd⚏n⚒⚓⚔⚡March 5, 2012 at 1:37 PM

      @ Mr E,

      Great comment!

      There are a lot of tessellations in the world:

      • roof tiles (not always)

      • bathroom tiles (not always)

      • floor tiles (usually)

      • the tiles in the shower (mostly)

      • air vents (not always)

      • tiles in the kitchen (most of the time)

      • wine racks in a house (if you have one)

      • geometry shapes (such as a hexagon and a square)

      • bricks on a fire place (not always)

      • on rugs (sometimes)

      • on a calender (all time!)

      • back porch / front porch (bricks)

      • sidewalks (always!)

      • window shades (mostly)

      • cubbies ( every time!)

      • shelves (mostly)

      We can not think of any more tessellations in the world, but there are way more.

      When the video went in reverse, it looked like we summoned the tiles! They come right to our hands like magnets! :-)

      In our class, we always work together! For example, we built the tessellation together.

      Sincerely,
      ⚡⚔⚓⚒R♔yce and Br◱nd⚏n⚒⚓⚔⚡

      Delete
  5. AnonymousMarch 3, 2012 at 11:56 AM

    Aloha Mrs. Yollis and third graders,
    Wonderful tesselations! I have always loved pattern blocks because there is so much you can do with them. Just the other day I was at the mall with a friend and I pointed out the beautiful pattern formed by the stones.
    I do have patterns in my bathrooms but I would much prefer your patterns to the plain ones I have.
    A hui hou,
    Mrs. Jacobs

    ReplyDelete
    Replies
    1. KellyMarch 5, 2012 at 1:28 PM

      Aloha Mrs. Jacobs,

      Thank you for your lovely comment. I agree with you, I would prefer that tessellation to my bathroom tiles. Did the rocks you saw at the mall have water near them?

      What is your favorite tessellation in your house?

      Also, what does a hui hou mean?

      Love,

      Kelly♥ ⚔

      Delete
  6. mrs toddMarch 3, 2012 at 12:18 PM

    Hi Mrs Yollis and third Grade
    Your tesselations look amazing and beautiful!It has taken a lot of thought to create your pattern. Tesselations are fun to create, and thank you for showing your work.
    I have tesselating tiles in my laundry, but they are not as colourful as your tesselations.I love looking at art from around the world that uses tesselating patterns.
    Look forward to seeing what other exciting things you are doing in your class.
    Kind Regards
    Mrs Todd and 4T

    ReplyDelete
  7. Mr MoriartyMarch 3, 2012 at 1:11 PM

    What an amazing tessellation! Such a beautiful, mathematical pattern. I liked the use of the reverse feature, too! How did you do it?

    We created tessellation art in our class earlier in the term and I am sure this post will inspire many of the students in our class!

    http://parkvalemoriarty.blogspot.co.nz/

    ReplyDelete
    Replies
    1. AidanMarch 5, 2012 at 2:28 PM

      Dear Mr. Moriarty,

      Thank you for your kind words.

      I also think it is a beautiful mathematical pattern.

      In our art class, we did not do a tessellation, but we once did a project called The Tree of Houses. It was my my favorite art project. It looked like a tree with houses on the branches. Did you ever do that project? Right now we are doing art that Pablo Picasso did. It is about the Blue period, the Rose period, and the Cubism period. The Blue period is sad because his best friend died, the Rose period is happy because he was in love, and the Cubism period was geometric and not realistic.

      Sincerely,
      Aidan

      Delete
  8. rmannellMarch 3, 2012 at 1:59 PM

    Dear Mrs. Yollis and class,

    Have you heard of mandalas?

    This is a special art form of patterns. Your work on your tessellations reminded of sand painting mandalas. Tibetan sand mandalas act as a form of meditation. They can take a number of days to be made with coloured sands. Once completed the sand paintings are destroyed as a way of showing all things pass in time.

    +++++

    Here is a link to a Wikipedia image of a sand mandala made in the UK House of Commons on the occasion of the Dalai Lama’s visit in 2008…

    http://en.wikipedia.org/wiki/File:Chenrezig_Sand_Mandala.jpg

    and a Wikipedia link to information on the Tibetan mandalas…

    http://en.wikipedia.org/wiki/Sand_mandala

    +++++

    Did you feel relaxed when you were working on the tessellations?

    For your tessellations, completing an intricate pattern is an achievement. I’m impressed by the detail in your patterns and that you worked on them over days. Like the sand paintings, the time comes when the pattern must be put away but the experience stays with you. :)

    @RossMannell
    Teacher, NSW, Australia

    ReplyDelete
    Replies
    1. ⚓ Leila ⚓March 5, 2012 at 2:35 PM

      Dear Mr. Mannell,

      I have not heard of mandala, but when I looked at the pictures I decided that they are gorgeous! How do they dismantle them? I doubt they mess it up with their hands, like we did. I was surprised to hear that it only takes a number of days to make. It looks like it would take years to make!

      Making the tessellation was quite relaxing and when you start making it you never want to finish.

      I think it is great that we made the tessellation in two weeks. You're right, it is an achievement.

      Sincerely,
      ⚓ Leila ⚓

      Delete
  9. Mrs MonaghanMarch 4, 2012 at 2:43 AM

    Beautiful tessellations, and I am very impressed that you managed to keep it going for two weeks without anyone knocking it out of shape!
    In A Room with a View we have been looking at Indian Rangoli patterns, which are incredibly beautiful and can involve some tessellation, however for the MOST amazing tessellations you just have to look at the work of M C Escher, a dutch graphic artist whose work is all mathematically inspired, and whose woodcuts have fascinated me from an early age. The way he tessellates animal and natural shapes is simply awe-inspiring, and a great way to combine maths and art!
    Mrs M
    A Room with a View, UK

    ReplyDelete
  10. RoyceMarch 4, 2012 at 12:16 PM

    Dear Mrs. Yollis,

    That tessellation was a truly awesome sight!

    I like how the video also showed us messing up the tessellation backwards. My 5 year old sister got tricked and thought that we rebuilt the tessellation really quickly. She does not know how to read, so she didn't know that you wrote "Do you want to see that in reverse?"

    I know of some tessellating figures:\

    • equilateral triangle

    • isosceles triangle

    • right triangle

    • scalene triangle

    • trapezoid

    • square

    • rhombus

    • rectangle

    • equilateral pentagon

    • non equilateral pentagon

    • equilateral hexagon

    • non equilateral hexagon

    • equilateral heptagon

    • non equilateral heptagon

    • equilateral octagon

    • non equilateral octagon

    • equilateral nonagon

    • non equilateral nonagon

    • equilateral decagon

    • non equilateral decagon

    I do not know the agons from there.

    I have a lot of tessellating figures in my house. In fact, my whole front hall is made up of tessellating rectangles and squares. There are big squares, small squares, big rectangles, and small rectangles.

    All three of my bathrooms have tessellating floors. Two of them also have tessellating walls inside the shower! The bathroom near my bedroom has different colored, little squares in the shower.

    The bathroom in my mom and dad's room has a big area of little, different colored squares just like the bathroom near my room in the shower. The rest of it is all big squares, and that is only the top half of their shower. The bottom half is non equilateral pentagons and 28 squares made up of nine little squares.

    I also noticed that an air vent can have tessellating rectangles. My air vent does.

    My kitchen floor is the same as my front hall, but not all of my kitchen wall tessellates. Only the wall near the stove does. It has a big area of little squares. Those little squares have a brown square border, and they are grey with 12 brown squares to make it a little more fancy.

    Other than that, my kitchen has tessellating rectangles and some more tessellating squares on the wall near the stove.

    The only other tessellation in my kitchen is the wine rack. It is brown and has eight rectangles for bottles of wine to fit in.

    Both of my fireplaces have tessellating rectangles on them. I also have a big white cabinet with four white rectangles that tessellate.

    I do not know of any more tessellation in my house.

    Sincerely,
    Royce

    ReplyDelete
  11. AnonymousApril 1, 2012 at 11:03 AM

    Dear Mrs Yollis’ class

    That tessellation looked awesome! We are doing a similar activity in our class were we have to colour in a tessellation sheet and make eye catching patterns. You are right there are lots of tessellations in and around the house. We have tiles that tessellate in our kitchen and bathroom but that is mostly it.

    Your Kiwi friend
    Georgia, Room 24

    ReplyDelete
  12. AylaApril 3, 2012 at 5:55 PM

    Dear Mrs Yollis and class,
    That is so amazing WOW. I have done one before but not like that. I do not have any teselation in my house.
    Regards Ayla

    ReplyDelete

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