The Sphere (The Magi Series #2) (34 page)

“Very well,” the librarian said, reluctantly.

She led them to the very back of the library where no students
were gathered to study.  It was colder and darker and felt somehow like a
dungeon.

The archive room was worse!  It was messy, tightly enclosed,
and even colder.  It smelled like mildew.  Elijah thought a skeleton in the
corner would be the perfect addition to the room.

“Here’s your book,” the librarian huffed.  She stood on her
tip toes and came down with a very ordinary-looking book.  She dusted off the
cover and handed it to Becca.  Elijah didn’t know what he was expecting, but
the book definitely didn’t meet his expectations.  It looked like a basic
textbook or encyclopedia.  “If you’ll excuse me,” the librarian said, “I have
to attend to the other students upstairs.  Once you are finished, set this book
here on the table and leave it for me to file away.  I don’t trust you to do it
right.”

“Don’t you just put it back here where you got it?” Becca
said, in her sassiest voice.

The librarian grunted and walked away.

“Are you trying to get us kicked out?” Elijah said.

“Oh come off it,” said Becca.  “Let’s just look through
this.”

They took a seat at the table and opened the book.  It
opened like a brand new book with the spine creaking as it broke in the pages.

“How is this an archive?” Becca asked.  “It just looks like
a textbook.  An unused one at that.”

Becca thumbed through the pages quickly like she was speed
reading.

“Slow down!” Elijah said.  “I can’t see the pages.”

“There’s nothing to see,” Becca replied.  “It’s just a very
very old textbook.  Here.”

Elijah looked over the book.  He flipped through it slower
than Becca, but nothing jumped out at him.  He set it down and sat back in his
chair.

“Now what?”

“I don’t know,” Becca sighed.  “Maybe we’re missing
something.”

They turned each page more slowly, skimming the contents.  Elijah
looked at the top of each page to see if there was a symbol like Uncle Stan’s
mystery book or the book his parents left, but there was nothing that seemed to
be jumping out at them as any kind of information or code or message from
Elijah’s dad.  Elijah’s excitement quickly turned to defeat.  Had he come all
this way to reach a dead end?

“Wait a minute,” Becca said curiously.  “Look here.”

She pointed to a picture that immediately lifted Elijah’s
spirits.  It was the same picture as the drawing in the old book from the Rose
house.  It was a circle with a square inside, perfectly touching four
symmetrical points of the circle.  Inside the drawing were two small words
written in pen: GEOGRAPHY and TANGENT.  Elijah looked at it curiously.

“Geography.  What’s that mean?”

“It’s the study of the earth,” Becca said with a smirk.

“Yes, I know that,” Elijah said.  “I mean why is it written
here?”

“Well, obviously that’s what we have to find out, isn’t it?”

They sat in silence thinking about the possible meanings of the
drawing.  Nothing came to mind.  Becca’s eyes focused on the book as though she
was waiting for it to suddenly produce an answer of its own accord.  Elijah
stared off blankly, looking at a speck on the wall.  It was so little
information to go on.  Elijah half expected there to be pages of information
spelled out for him.  What use was there in a picture, not even a hand-drawn
picture that made no sense, with two words inside?  Plus, he wasn’t sure he
even knew what a tangent was.  What was he supposed to find out?

“Anything?” Elijah asked Becca.

She shook her head.  “I can’t figure out the significance of
this picture.  Clearly, it meant enough for your parents to draw again in the
book.  I thought maybe it was some sort of hieroglyphic or something, but I
don’t know of anything that simple.  What have you come up with?”

“Nothing at all!  Not even your hieroglyphic thing.”

Becca twirled her hair mindlessly, making her look
surprisingly feminine.  Elijah snickered.

“What?” she asked.

“Nothing.  Okay, so this is some sort of math book, but the
word geography is written in here, which isn’t mathematical.  Let’s start
there.  What’s the math concept being taught?”

“Well, since tangent is also written, probably tangent lines
or area or something,” Becca stated.  She looked at the book again.  “A square
inside a circle.  Maybe finding the area of the circle with the square cut
out.”

“Or vice versa,” Elijah recommended.

“Well, there would still be more circle left over.  You can
cut out the entire square but not the entire circle,” she stated.

“So what would that leave you with?” he asked.

“A bunch of circle parts that look like slivers of the
moon,” she said.

Elijah massaged his head and hair.  “This isn’t right. 
We’re looking for cubes, not moons.”

Just then, Becca had a curious look.  “Cubes.”

“Yes, Becca.  Cubes.  Should I have brought Paul with me?”

“No, no.  I mean, we’re looking for cubes and that’s what
this is, right?  The circle could represent the sphere, just like we thought,
and the square could represent the cubes.  That could make sense.”

Elijah frowned.  “Sort of.  But this is just one cube.  If
the circle is supposed to be the sphere, why is there only one cube?  And what
does geography have to do with anything?”

“I’m not there yet,” Becca said, staring at the book.  “But
tangent does.”

“What is a tangent anyway?” Elijah asked.

“It’s a theoretical line touching one point on a curve.”

“Huh?”

Becca didn’t continue.  She seemed to be growing in her
excitement as if she was close to solving a complex math problem, which Elijah
thought wasn’t far from the truth.

She took one of the pencils provided at the head of the
desk.  Then she drew a big U on the desk.

“This curve can be anything.  It can be a sound wave or the
orbit around a planet or a boomerang flight path.  Whatever.”  Then Becca drew
a point on the curve followed by a straight line which touched the curve only
on that point.  “This line is called a tangent, and it touches this point on
the curve.  It’s just a point on the very edge of the curve.”

Elijah was even more confused.

“Take the circle here in the book,” Becca said, her voice
rising with excitement.  “The square intersects with the circle at four
points.  These are points where tangent lines would touch.”  Becca then drew on
the book very lightly.  She drew right angles to the point where the four
corners of the square touched the circle.  Then she drew an X through the
square and out the edges of the circle.

“You said the cubes go inside the sphere, right?” Becca
asked.

“Yeah, that’s what Olivia thought.”

“So let’s say this isn’t one cube.  What if this drawing
represents the four cubes together inside the sphere?  Maybe this picture is
trying to show how they fit inside.  Somehow.  Maybe they are fit inside like
this…”  Becca divided the larger square into four smaller squares.  “…and
intersect on four different points of tangent, which is how you get the sphere
to work!”

Elijah shook his head.  “But my parents weren’t trying to
get the sphere to work.  At least…I don’t think they were.”

Becca’s excitement tapered off.  “Well, at least it makes
sense.”

“But it gives us no information to
finding
the
cubes,” Elijah argued.  “What good is all this if we don’t know where the cubes
are.”

Elijah and Becca sat again in silence when the door to the
archive room burst open and the librarian came in, looking grumpier than ever. 
Becca quickly tore the page out of the book, being careful not to make a noise,
and hid it in Adam’s pants pocket before the librarian made it to them.

“I think you’ve had enough time in here,” the librarian
said, giving Becca a very curt look.  “I’ll take that.”  She took the book from
Becca—after which Becca stuck out her tongue at her— and escorted them back
into the library.

Elijah sat down at one of the empty tables in the back where
no other students were around.  Becca took out the torn page and they huddled
together to look at it again.

“Hold on,” Elijah said suddenly.  He looked at the paper
again and thought through his idea before he said anything else.  “Geography.”

“Yes?”

“Assuming that was written as a message, geography could be
exactly the direction we’re looking for.”

Becca looked confused.  “I don’t follow.”

“This drawing could be a representation of the sphere,
right?” Elijah began.

“That’s what it looks like,” Becca said.

“What if the sphere…or at least the drawing…is actually a
representation of Earth?  Olivia said at one point that the early Magi were
very mathematical.  That they had a systematic approach to things.  Look at
this.”  Elijah pointed to the drawing again.  “If you put a square inside a
circle…or in this case four squares together inside a circle…it touches the
circle at four different points, right?”

“Tangents, yes,” Becca said.

Elijah shrugged.  “Sure, call them whatever you want.  But
the point is, there are only four points where it touches the circle.  If you
assume the circle is Earth, it could be that those are the locations we’re
looking for.”

Becca picked up the page so she could look at it closer. 
“So you’re saying you think these tangent points are actually locations?  Here
on Earth?”

“Yes,” Elijah answered.  “Only the trouble is, where are
they?”

“What do you mean?”

“I mean this is a circle with no reference points.  There’s
not a map showing where these points line up.  I wouldn’t know where to start.”

“I thought you said you already had one cube,” Becca stated.

Elijah lit up.  “Sure!  Oh, man, where did Olivia say the
first cube was found?”  Elijah pounded his fist on the table which echoed
loudly around the room, causing everyone, including the librarian, who already
had her eye on the two of them, to turn and look.  Elijah lowered his voice
when he spoke again.  “Grrr.  I can’t remember.  Wait.  Was it Morocco?  Or
maybe M-M-Malaysia?  It started with an M.”

Just then, Becca looked up at the clock.  “C’mon!” she
said.  “Paul and Adam will be coming in for a rescue operation if we don’t
leave.”

“But we’re so close!” Elijah pleaded.

“We have libraries in Savenridge too, you know.”

“Fine,” Elijah agreed reluctantly.

They got up and left quietly.  Becca and the librarian had a
glaring match as Becca left the room.  Elijah shooed her out as quickly as he
could so there wasn’t an all-out brawl between them.

Paul was on edge when they finally met in the forest.

“I was about to scour the place for you!” he scolded.

“Oh, knock it off you big baby,” Becca said.

Paul only grunted as they took off toward the cave.

“So what did you guys find out?” Paul asked on the way.

“We need to go to the library when we get back to
Savenridge,” Elijah said.

“Are you kidding?!?” Paul shouted.  “What did you guys just
do in there for the last couple hours?”

“We thought it would be good to take a little trip down here
to make you all huffy,” Becca said.  “Calm down, we’ll explain when we get back
to camp.”

Hannah and Isaac had most everything packed and ready to go
by the time everyone arrived.  It startled Elijah seeing so little of their
camp left.

“Where is everything?” Elijah asked.

“Isaac went out to get some more firewood while you guys
were away and said he heard some voices,” Hannah explained.

“I don’t doubt that,” Paul joked.

“They were real!” Isaac said.  “But they were far away.”

Hannah continued.  “We didn’t know what the plan was, so we
thought we would pack everything up in case we needed to make a quick getaway. 
Then, if we were going to leave tonight we would have everything ready.  If
not, we could easily unpack everything again.  Did you guys find it?”

“Yes,” Elijah answered.  “But it’s complicated.  We’re going
to have to do a little more research when we get back, but I think we have a
lead.”

“Like what?” Hannah asked.

“Seriously,” Paul interjected.  “Can you finally spill it?”

“We found a book with the same drawing as my parents made in
the book we looked at with Phinneas.  Olivia even asked me about the drawing
before she left.  Becca has it if you want to look at it.”

Becca took out the page and passed it around for everyone to
look.

“We think that the circle represents the sphere,” Elijah
continued as they looked over the page, “and that the square represents the
cubes all fitting together inside the sphere.  And even more than that, we
think that all four points of the square are really reference points to places
on Earth.  Kind of like the sphere is a small version of Earth.”