Free The Stone Lions by Gwen Dandridge Page A

Tahirah. “Let’s see, Suleiman
taught you mirror symmetry across a vertical line, right?” The
snake rested unblinking in his new location. “My thought is that
the second one learned should be mirror symmetry over a horizontal
line. We should probably review both.” She pulled out a quill and
paper and launched into her lecture.
    “You remember that symmetry is a relationship
of characteristic correspondence, equivalence, or identity among
constituents of a system. In mathematics it is a property that
generates repeated patterns. Band symmetry, which we are focusing
on here, runs in one direction like a frieze or border. Euclid
stated in his treatise that there is a connection between—”
    “Actually no, I don’t remember what you’re
saying at all,” Ara interrupted, startled by the complicated words.
Layla sat beside her, looking despondent.
    “No?” Tahirah asked, surprised. “That’s the
way my instructor presented it to me. How did Suleiman explain it
to you?”
    “Well, a lot simpler. He did talk about
repeated patterns though,” Ara answered uncomfortably.
    Suleiman raised his head, “Ssssymtry is
sssimple.”
    “I see. Let’s start over, shall we?” Tahirah
took a deep breath and tried to recall herself as a young girl.
“I’ve got it. Symmetry is about two things, pattern and motion—in
particular, which motions a pattern can make and still remain the
same.
    “Let’s draw some simple patterns. Ara, you
draw one, and Layla, you can draw the next. I’m going to explain
reflection or mirror symmetry across a horizontal line.”
    “Suleiman called it a flip,” Ara
interjected.
    “He did, did he?” Tahirah frowned at the
snake in her lap. “All right then, reflection, mirror or flip—all
three are names of this motion. Each of you draw something simple
on the parchment. Just one thing each!”

    She smiled at them. “Lovely. Those are
excellent. Now we shall pretend there is a line below them that
they reflect…oh, sorry, flip over. Watch. I will draw the
horizontal mirror image, or flip, of each of your images. The
horizon is an imaginary line that stretches left to right across a
landscape,” she added by way of explanation. “See how these images
are now ‘flipped’ across the imaginary line below them. A perfect
match, if we were to see it in a mirror.” Tahirah hesitated as she
looked at each girl. Ara’s eyes were bright with comprehension as
she focused on the drawing. The dawning of understanding crept more
slowly across Layla’s face.

    “But what about the line? How can you find an
imaginary line?” the girl asked.
    “Good question, Layla,” Tahirah said, then
considered. “Well, you are looking for a place where the pattern
would be repeated. In the drawings you just did, we placed the line
beneath the first pattern. That was the easy way, starting with an
object, drawing a line under it or beside it and completing the
symmetry yourself. But how do you find the symmetry in an already
completed object?” She looked at both girls. “Any guesses?”
    “Maybe you could cover a pattern until only
half of it shows?” asked Ara.
    “Yes,” Tahirah agreed. “And there are other
ways. Think about mirrors.”
    “You could hold a mirror up to it and see if
the other half of the pattern is repeated,” Layla offered.
    “Good. Now, let’s continue. The vertical flip
goes left or right, correct?” Tahirah ran her hand across the
contented snake. “That’s what you learned from Suleiman and the
kind of symmetry you were searching for. In the horizontal flip,
the pretend line goes across, and the pattern flips up or down.
Let’s practice the symmetry in repeated patterns. Here, I will draw
a few and you tell me if they are horizontally symmetric or not.”
She reached for her quill and ink. “This is a test,” she said,
smiling. “Here I will present a whole row of the symmetry as you
would see it in the tiling of the Alhambra.”

    “That’s easy,” said