Tuesday, January 5, 2010

Italian floor tiles and Euclid



Experimenting with a square detail from the blackberry leaf I discovered the Café Wall optical illusion, and created a snow crystal. This reminded me of a tiled floor I first saw in a church in Italy and prompted me to re-create the pattern using the leaf on a parallelogram. The pattern is a tessellation of parallelograms. The parallelogram is constructed from two equilateral triangles and is also known as an equilateral quadrilateral or rhombus. Three rhombi form a hexagon. So the floor pattern is also a tessellation of hexagons.



Giving each rhombus a distinct colour emphasises the illusion of three-dimensional cubes. Patterns such as this, based on symmetry, belong to the Wallpaper Group (or Plane Symmetry Group or plane crystallographic group). Apparently, there are 17 distinct groups; and this pattern would appear to belong to Group p6m.

The hexagon is a six-sided polygon with six vertices. It can be constructed with a compass and a straight edge following Euclid’s method in his Elements, Book IV, proposition 15. The most colourful edition is Oliver Byrne's The first six books of the elements of Euclid : in which coloured diagrams and symbols are used instead of letters for the greater ease of learners. Printed by Charles Whittingham at the Chiswick Press for William Pickering, 1847. (I first saw a copy of this book in the library of the Book Club of California.)



The basic snowflake ice crystal is a hexagon. Other examples of hexagonal forms in nature are the honeycomb and the basalt columns of the Giant’s Causeway in Ireland.

22 comments:

  1. I saw this site, always going in a very nice theme.such matters is very difficult to find many great subject now is really nice, but I really liked your site.
    Hexagonal floor Tile

    ReplyDelete
  2. This is quite cool !!! The hexagon floor tiles, I cant get my head round them

    ReplyDelete
  3. You made such an interesting piece to read, giving every subject enlightenment for us to gain knowledge. Thanks for sharing the such information with us to read this... cheap bathroom tiles UK

    ReplyDelete
  4. I haven’t any word to appreciate this post.....Really i am impressed from this post....the person who create this post it was a great human..thanks for shared this with us. Ceramic tile kentucky

    ReplyDelete
  5. Rockfon Soffit System B Adhesive is an easy to install adhesively bonded solution for basement car parks

    ReplyDelete
  6. I recently came upon your blog and wanted to express how much I liked reading your postings about Discount Floor Tiles for Home. I'm hoping you'll write again soon. Thank you very much for the excellent information.

    ReplyDelete
  7. Your blog took to me an entirely significant spot. It is a beneficial and factual article to enhance knowledge. Wall Crack Repair Methods.Thanks for sharing an article like this.

    ReplyDelete
  8. Really, this is very important information which is shared by you. This info is meaningful and important for everyone to increase our knowledge about it. Always keep sharing this kind of info. Thank you. Read more info about Marble floor tiles

    ReplyDelete
  9. I found decent information in your article.DLT Interiors I am impressed with how nicely you described this subject, It is a gainful article for us. Thanks for share it.

    ReplyDelete
  10. I am grateful that I was able to learn something useful from this article. After reading it, I believe you possess excellent expertise. Thank you for sharing about Basement Floor Epoxy Coating Specialists in Canada. Keep up the good work.

    ReplyDelete
  11. The article you've shared here is fantastic because it provides some excellent information that will be incredibly beneficial to me. Thank you for sharing about Patterned Wall Tiles Kitchen. Keep up the good work.

    ReplyDelete
  12. I found one successful example of this truth through this blog. I am going to use such information now. tile installation contractors

    ReplyDelete
  13. You've written a fantastic article about Flooring Contractors Hawthorn Woods. This article provided me with some useful knowledge. Thank you for providing this information.

    ReplyDelete
  14. Moroccan tiles are a testimony to their deep heritage and rich culture and are usually handmade or handcrafted Moroccan tile

    ReplyDelete
  15. You are providing good knowledge. It is really helpful and factual information for us and everyone to increase knowledge. about MOSAICS TORRA SL .Continue sharing your data. Thank you.

    ReplyDelete
  16. Excellent post. I really enjoy reading and also appreciate your work.Cement Tiles This concept is a good way to enhance knowledge. Keep sharing this kind of articles, Thank you.

    ReplyDelete
  17. You wrote this post very carefully.anti static flooring The amount of information is stunning and also a gainful article for us. Keep sharing this kind of articles, Thank you.

    ReplyDelete
  18. You are providing good knowledge. It is really helpful and factual information for us and everyone to increase knowledge. about Garage Floor Tiles UK .Continue sharing your data. Thank you.

    ReplyDelete
  19. I am attracted by the presentation of this article. It is a genuinely a gainful article for us. Keep posting, Thank you.External Tiles Gold Coast

    ReplyDelete
  20. The article you've shared here is fantastic because it provides some excellent information that will be incredibly beneficial to me. Thank you for sharing about Wood Look Tile Flooring. Keep up the good work.

    ReplyDelete

Podcast: David Esslemont on the history of the Gregynog and Solmentes Presses

Gregynog Hall Nigel Beale aka The Literary Tourist , came to visit and recorded our conversation in which he asked me about the history...