# Sphinx Album ... Page 3

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#### Size 23 - Amy & Emma's Challenge

G'day Doug,
We don't know if you remember us but we are Emma Stewart & Amy Milner.(How could I forget!) We are now starting to construct the 23 x 23 sphinx!

We have used up all of Mr Martin's sphinx pieces now because we need 529 pieces! We are aware that Chris Collett might be constructing the same one so we are working as quickly as possible. When we have constructed we will send you a picture of us and the sphinx.

Thank you very much for featuring us on your web site. Mr. Martin printed us both a copy and we used up all his ink.

Emma & Amy

#### Size 23 - Robert Barwell's Response

In some ways Robert's picture below says it all. (Click to enlarge the image and see more detail.)

However, for those less familiar with the problem a little more explanation may be required:

• Robert has built his Size 21 from a Size 3 pattern in which each of the 9 pieces is a Size 7.
• He is showing us how to rotate each piece into place.
• 'on the back of' - If the longer horizontal side is the base, then the shorter one is the back. Imagine a Size 2 Sphinx (made of 4 of the smallest Sphinxes in the drawing) placed in the bottom left with the biggest Sphinx on its back.
• Size 2 parallelograms added are made from pairs of the smallest Sphinxes in the drawing. You can see some of them inside the Size 7s.
• You actually don't put the Size 2 parallelograms all the way around. You don't put them on the sides the arrows are pointing to because the proportions would no longer be a Sphinx shape.

Robert's hypothesis about how to build a Size 23 from a Size 21 is now public and open to scrutiny. Does his approach work??

Notice too Robert's chivalry. Amy & Emma from the same school struggled for months without actually making the Size 23. Robert seems to have achieved success first, but in recognition of their pioneering work he asks that the Size 23 be named in their honour.

#### Sphinx Banner

Amy and Emma also commented in their email above that they liked the work that Nick and his friends had done with the different coloured Sphinx Shapes. It made them ask whether Sphinx Shapes could come in different colours. This comment reminded us of a beautiful banner made in 1999/2000 by Pamela McGifford, who was teaching at Cressy District High School, Tasmania.

(Note: there is a thin black border which
is not part of the parallelogram.)

The photo doesn't really do the banner justice. Think of it as at least the size of table cloth!

Think too of the mathematical challenges:

• If the yellow sphinx is Size 1, how many red and black pieces are needed to complete the smallest parallelogram in this way?
• If the yellow sphinx is Size 2, how many red and black pieces are needed to complete the smallest parallelogram in this way?
• If the yellow sphinx is Size 3, can the parallelogram be made, and, if so, how many red and black pieces are needed to complete the smallest parallelogram in this way?
• If you were told any size for the yellow sphinx how do you work out the number of red and black pieces needed to complete the smallest parallelogram in this way?
Pam indicates the background to making the banner in this email extract:
I started working with some indigenous girls. I always used to incorporate art work into my maths because the indigenous kids loved it that way and eventually so did those who preferred more traditional styles. We had the idea of having a 'sewing bee' type atmosphere ... this worked great - we managed to cut out all the pieces and started sewing them together, but transient population and other problems related to continuing a project over time in a school atmosphere meant that we didn't get it all sewn before the opportunity evaporated ... guess someone couldn't leave it unfinished!

#### Size 100 Sphinx!

Robert Barwell, Year 7, used his computing skills to construct this Size 100 sphinx. The smallest unit (Size 1 Sphinx) is 1cm in the base. Click to enlarge the photo and you will see the smallest pieces and the markings on the ruler more clearly.

Robert appears to have first constructed a Size 5 from these pieces, then arranged a collection of Size 5s into a Size 25 on a landscape page. Next, he apparently printed out sixteen copies of this and arranged them using a Size 4 template.

That's a collection of 10,000 Size 1 Sphinxes you are looking at!

Click the photo to enlarge it.