Authors: Gwen Dandridge
Tags: #history, #fantasy, #islam, #math, #geometry, #symmetry, #andalusia, #alhambra
Tahirah sighed and shook her head before
tossing him a treat. “Suleiman, here, have a pastry. I can’t stand
to watch a grown dog drool.”
It disappeared in one snap, and with a
muffled
bismillah
, Suleiman gulped it down.
“The lions were miffed at the cat. Discipline and Reason growled at
him.”
“You mean
YOU
,” Ara
interrupted. “You were the cat.”
“Perhaps in the strictest sense, that may
have been true,” he conceded, getting up to circle uncomfortably.
“Anyway, they, the lions, wanted me to use my enchanted time
better. To learn and understand from each transformation.”
“And are you?” Tahirah questioned.
He sat down and studied his paws. “As a
lizard, I learned how it feels to be powerless. As a snake, I
relearned the value of life. In mouse form, I understood that size
does not define spirit.” He whined again before speaking. “The cat
learned that not all things can be done alone.” He wagged his tail
and perked up his ears. “But dogs, dogs are great. I can see this.
Allah has, in his ultimate wisdom, given us the best traits.”
“Which are…” Tahirah encouraged.
“Isn’t it obvious? We’re loyal to our pack
and brave and joyous. A true companion. Best at work, best at—”
“Best at modesty,” Ara said wryly, “most
humble, most…”
“You are picking on me.” Suleiman tucked his
tail under his rump, his ears drooping once again. “Don’t you like
me anymore?”
Instantly ashamed, Ara leaned over and patted
him on the head. “You are perfect. Whatever shape you take, I love
you. I’m sorry. Everything seems to be happening too fast. I’m
hiding things from Father, and I’m scared.”
Suleiman grinned and gave her a couple of
quick, understanding licks.
Tahirah reached out and put her arm around
both friends. “Speaking of which, we need to complete the next
lesson. Suleiman, would you like to teach this one? I think
rotation would be best.”
He barked twice, then looked chagrined.
“Sorry, when you speak many languages, it’s hard not to fall into
careless habits. Actually, I
would
like to
explain rotation.” He looked around for an example, and in turning,
discovered to his wonder, his tail. He continued circling, trying
to grab it. “See, here is a perfect example.”
The girls saw nothing but a silly hound
chasing his tail. “Perfect example of what?” Layla asked.
He continued the pursuit, making an
occasional half-hearted grab for it. “Rotation. I’m turning around.
It’s obvious.”
Ara turned a cartwheel while Layla did a
pirouette. “You mean like that?”
Grinning, he sat. “Yes, but now you have to
look at it in slow motion to see how it’s different from a vertical
reflection. Tahirah, would you pull out the tiles again?”
She drew out four tiles and placed them
before the dog. Suleiman placed a paw on the first tile. “Each of
these is identical, like a translation, right?”
“Yes, “ Ara agreed, “just as before.”
Suleiman wagged his tail and woofed. “But now
we will create rotations. We take the first one and place it so.”
He nudged two tiles into place. “See how with the first tile, the
blue part of the design is on the top? And then how the second is
turned one hundred eighty degrees? It is rotated.” He placed a paw
dead center between the two tiles. “With rotation, you pretend
there is a point or hub in the center around which the object moves
so that it appears to have spun.
Now you try it.”
Ara looked at the tiles with interest. This
was a lot like a game! She turned the next tile one hundred eighty
degrees and placed it beside the first two.
Suleiman lay down beside them. “Pretend that
you’re holding your paw—sorry, I mean finger—in the middle. An
immovable point. That point, at your finger, must stay in place as
you turn the tile around.”
“This is the third of the four motions,”
Tahirah said, joining in. “Reflection—which we also call a
flip—translation or slide and now rotation,” she finished, having
ticked them off on her fingers. “One of the remarkable things about
rotation is that double reflections also rotate.”
Ara looked up. “Because it looks the same
upside down and right side up?”
“Exactly. It includes a one hundred eighty
degree rotation in the design, so it looks the same upside down or
right side up.” Tahirah turned both tiles upside down and then back
again.
The dog woofed. “You forgot to mention that
there
cannot
be a flip in a rotation.”
The mathemagician smiled, patting his head in
agreement. “That is correct. For it to be considered rotation, it
can’t have a mirror in the design. It does not reflect. If it did,
it could be a double reflection or possibly the seventh band
symmetry which you have not yet learned.”
Layla asked. “Could we see another
example?”
“Take these same tiles and make another
rotational symmetry,” Tahirah suggested.
Uncertain, Layla picked up a tile. “How do
you start?”
Suleiman woofed encouragingly before stuffing
his nose under her arm. “You can do this. Look at all you’ve
learned so far. Try.”
She placed the first piece with the blue part
facing down. The next tile she lined up exactly the same, then
turned it one hundred eighty degrees to the right. Encouraged, she
took the third piece and, placing it the same way as the second
tile, rotated it one hundred eighty degrees yet again. The last
tile she turned one hundred eighty degrees until the design
cartwheeled across the floor.
Suleiman barked in glee and ran around the
room. “See, you did it!”
Layla grinned. “I guess I did.”
Everyone jumped at the knock on the door.
Tahirah called out permission to enter. Her servant did so, then,
bowing near to the floor, handed her a card on a silver tray. After
dismissing her, Tahirah read the card. “The sultan requests the
presence of his daughter and niece immediately in the Hall of the
Kings. He wishes the dog to be brought before him.”
She looked at the children, her eyes dark
with concern. “It seems the owner of the dog has come forward.”
Chapter 32
Ara sputtered, “But he can’t have an owner.
It’s Suleiman.” And then more thoughtfully, “This must be serious.
The wazir must know it’s Suleiman in dog form.”
Layla sat in a daze, stunned that she was
being hauled before her uncle.
Suleiman circled in the corner, whining—his
ears pinned to his head and tail tucked under.
Three guards awaited them outside Tahirah’s
rooms. Tahirah positioned herself between the men and the girls,
politely but firmly refusing to allow the girls to be taken to the
Palace Court without her. No rope was permitted on Suleiman no
matter how the guard argued. Finally, the guards agreed to wait
outside while the group prepared to set off for the Hall of the
Ambassadors. As they rounded up scarves, caftans and shoes, Tahirah
assessed the situation. “Yes, I sense the hand of the wazir in
this. He can’t be certain, nor can he prove it without divulging
what he has done. We know that Suleiman doesn’t have an owner. Let
us go prepared to deal with the worst possible likelihood, though
perchance it is but a misunderstanding,
inshallah
.”
Grabbing her caftan and trying to tidy
herself up quickly, Ara muttered, “I hope that this is only Zoriah
upset about finding a dog in her spotless rooms.”
Tahirah looked over at Ara. “I also wish this
is so, but the note said the owner of the dog was there. Someone
thinks—or wants the sultan to think—we have their dog.”
She captured and held each girl’s gaze. “You
two must show your best side. We shall proceed carefully until we
know what this is about. Whatever happens, be exceedingly polite
and respectful. The sultan is in an awkward position. You know how
much he loves you,” she reminded them, “but as sultan, he cannot be
seen to support his daughter and niece over another of his
subjects. I will do as much as I can to help, but you must be seen
as gracious and cooperative.”
Ara’s eyes brimmed with tears. “He does love
me, doesn’t he? Even though I spilled the dye in the Court of the
Lions? He’s not spoken to me since. I know I do things I ought not,
but...”
Tahirah rushed over and held her close. “He
loves you very, very much. You know this is true. You can
demonstrate
your
love by making him proud
of his daughter and by trusting him.” She gently smoothed Ara’s
hair and smiled encouragingly at Layla.
Ara wiped away her tears and rubbed her nose.
“I can do this. I
am
a sultan’s
daughter.”
Tahirah nodded. “Remember, head high, and
keep on the lookout for rotational symmetries. Time is not our
friend.”
When they stepped out into the gardens, the
impassive guards again moved to grab the dog, but Tahirah stopped
them with a look and a few firmly spoken words. Layla, to
everyone’s surprise, sauntered along whistling. The guards, stiffly
proper, kept glancing nervously at her until one of them finally
broke into a grin.
Tahirah laughed. Suleiman got caught up in
the pleasure of the melody and, untucking his tail, pranced
alongside.
Ara grinned at her cousin before joining in
with a bouncy harmony.
Tahirah laughed again. “That’s a strange tune
for you to know. How did you learn a gypsy song in the palace?”
Layla blushed at the attention. “I heard two
servants singing it last month in the kitchen. I thought it might
cheer me up, and it did.”
Tahirah looked at their little group. “I
think it cheered all of us.”
At the doorway to the Palace of the Myrtles,
they hesitated and smiled assurances at one another before
proceeding into the Hall of the Ambassadors. At the far end sat the
sultan, grim-faced. Three veiled women in hijabs sat stiffly erect
on the side benches. Layla spotted her father standing quietly to
the side. She gasped upon recognizing the man talking to him but
quickly recaptured her mask of poise. Two advisors stood near the
sultan cloaked in brown caftans, perplexed at the uproar over one
dog.
The wazir, who stood before Layla’s father,
was obviously retelling his tale, waving his hands as he spoke. He
turned as their feet tapped across the stone floor. “That’s my
dog,” he said loudly. “That’s my newly-purchased dog.”
The sultan’s jaw clenched. “Abd al-Rahmid,
sit down, please. We will conduct this as a fair and objective
discussion. All will be questioned and, by Allah’s hand, the truth
will be known.”
The wazir made a motion toward the girls but
checked himself as the guards tensed and reached for their swords.
He stood rigidly in place, his eyes turned toward the girls, then
fixed on the dog.
The sultan watched, his eyebrows pulled down
in a frown. “Sit, I said.”