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Sphinx Album

Task 166, Sphinx, represents every aspect of the rich process and content that is within each task. It is amazing how such an easy to state, easy to start problem has produced so much mathematics.

We suggest you begin by investigating the Iceberg of the Sphinx to understand what we mean by a task being the tip of an iceberg. Then, when you have a bit more time, move on to the links below.

Students and teachers from the middle 90s began the Sphinx adventure. The revelations below would not have happened without the input of these earlier mathematicians. The Sphinx Album continues to grow. If you have Sphinx photos to include, email them with a brief story to our Contacts above.

See the Resources link for information about ordering Sphinx Shapes.


Amy & Emma Trinity Academy (formerly Thorne Grammar) Doncaster, UK

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Sphinx Album Pages

Choose a page or go directly to an item of interest.
Page 1   Page 3
Mathematics Task Centre Logo

Story of the Logo

Page 2

Page 4

 

The video Adventure of the Sphinx made by Year 8 students in Pam McGifford's class at Cressy District High School brings together many of the pages of this album.
Our Research section reports how working like a mathematician improved test scores for these children.
 
Page 5
  • Decorated Sphinxes
    An example from Wade High School that might start a new fashion trend.
Page 6
  • Donna Dubey, Winnisquam Regional High School, USA is encouraged by her Algebra 1 students to build an absolutely huge Sphinx and discovers how much they learn. (Note: This page is stored as a teacher story in the Research & Stories link.)

 

Page 7
  • Anna Casey explains something of the development of a 642 Sphinx which took over her Year 6 class at Scotch College Junior School, Adelaide, Australia for many weeks.
Page 8
  • Saied Alavei discovers the Sphinx Album and immediately cuts up wood left over after trying to build a kayak so his Year 6 children can start exploring the Sphinx.
Nickey Harland, St. Mary's School, West Wyalong, was exploring Sphinx in a workshop. She thinks her diagram above shows you can tessellate the plane with a rotation pattern of Sphinxes from a central point. Is she right?
In 2016 Greg Huber, Deputy Director, Kavli Institute for Theoretical Physics (KITP) wrote:
I found your Sphinx Album online and was really impressed by the progress and engagement students and teachers have made on these sets of problems.
One thing that I could not figure out, though, was what is the current thinking on the total number of Sphinx tilings of Sphinxes of various sizes. The only sequence that I found on the site was this one:
1, 1, 4, 16, 153, ...
Read in our February 2017 News how this start led Greg to continue this sequence and have it registered on the Online Encyclopedia of Integer Sequences (OEIS).
And more...
  • http://www.origamiheaven.com/pdfs/sphinx.pdf begins with the leftover rectangle created when A4 (or other metric paper) is folded to remove the largest possible square. David Mitchell, Origami Heaven, shows how to fold this often discarded part to create a Sphinx. Now you can have lessons about the square and save all the leftovers for later lessons about the Sphinx. However, David's information gives away some of the answers that as teachers we would like the learners to tackle as challenges. So we approached David and with his permission have produced a modified document that gives the same instructions on Folding Sphinx Tiles and ends with an invitation to record on Sphinx Paper, without giving away any of the challenges.

  • Many thanks to Matt Skoss who has found a Google Slides presentation which also shows how to fold paper to make a Sphinx Tile. This one begins with a paper square with a different colour on each and requires scissors. Unfortunately the last slide in the sequence (Slide 19) gives away the answer to one of our Sphinx Challenges, so, if you can possibly control yourself, don't peek.

  • Sphinx is a self-replicating shape. Find out more about self-replicating shapes in Wikipedia at this Rep-Tile link.

  • In particular, this link https://en.wikipedia.org/wiki/Rep-tile#Pentagonal_rep-tiles refers to the recent discovery of two new pentagonal Rep-tiles, but the Sphinx remains the only one that repeats itself with pieces the same size.

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