Sir Cumference and the First Round Table
A Math Adventure
Cindy Neuschwander
Illustrated by Wayne Geehan
Long ago in a land known as Camelot, there lived many knights and ladies.
Their ruler was a mighty, but gracious, man named King Arthur. During many
years of peace and good harvest, the people lived happily.
The trouble began when they say the army of their neighbors to the north
gathering at the border. These people, known as Circumscribers, looked as if they
might be preparing to make war. King Arthur called upon his braves and most
trusted knights to plan what to do.
The knights rode as fast as they could to the King’s caste. Sir Cumference live
nearby, so his family came with him. Sir Cumference was married to Lady Di, who
came from the town of Ameter.
They had a son named Radius. Radius was very small and quite young, but
his keen mind and boundless energy more than made up for what he lacked in
height and age.
After the first day of meetings with all the King’s knights, Sir Cumference sat
with Lady Di.
“Oooh,” he groaned, “my throat hurts. I have to shout to be heard at the
other end of that long rectangular table. Everyoe has to shout, and the King is very
upset.”
“Why don’t you fix the table?” suggested Lady Di.
“How can we do that?” Sir Cumference asked.
“Well,” said Lady Di, “you could cut it in half.
Look, here is a drawing of the table.
It has two long sides and two short sides.
If you cut it in half, and put the two halves side-by-side, you will have a table with
four equal sides.”
“Lady Di, what a good idea!” Sir Cumference called for the carpenter, Geo of
Metry. Geo began work immediately.
The next day the new table was ready. Everyone commented on the
wonderful, square shape. However, another problem arose.
At each corner of the table, the knights whispered to each other while someone
else was talking.
Sir Galahad exclaimed, “King Arthur, how can we meet to discuss a solution
when people talk secretely to each other?”
“Sir Galahad is correct,” King Arthur responded. “We have come here to talk
of defending our land against the Circumscribers, not to talk in secrecy.”
After the meeting, King Arthur told Sir Cumference a new table was needed.
That night, Sir Cumference told Lady Di about problems with the square table.
Lady Di thought a moment and then said, “What if we cut the square table
diagonally? We could put the two halves together to make a diamond.”
She drew a diagram and said, “The King could sit at one end, and you could
sit at the opposite end. Everyone would be close enough to hear, but the knights
would not be in and tight corners.”
After seeing the plan, Sir Cumference agreed that it was a good idea. Geo,
the carpenter, said, “In carpentry class they called this shape a parallelogram. I
will have the table ready by the morrow.”
The next day, Sir Lancelot and Sir Gawain were amazed to see a table in the
shape of a parallelogram. The others liked it, but King Arthur was not happy sitting
at the sharp point.
The King let the knights have jousting practice and swordplay while he spoke
with Sir Cumference.
“Sir Cumference, the point of the table sticks into me like a sword! We need
to think about ways to prevent war, but this table makes me feel like fighting! Can
you fix it?”
“I will do my best, Sire,” said Sir Cumference.
That afternoon he stood by the field and watched the others joust. It was a
beautiful day, with blue skies, and flags flapping in the breeze. Sir Gawain’s flag
was blue with a white cross, Sir Lancelot’s flag was green with lions, and Sir Torre’s
flag was green with an eagle. The flags were all similar in shape: they were all
triangles.
“That’s it,” said Sir Cumference, “a triangular table!”
Sir Cumference called Geo and explained. Geo said, “If we cut the
parallelogram table in half, that would leave two triangles. One triangle might be
too small.
So they measured the proposed triangular table, and realized that four
people could not fit on each side. “Geo, let’s think some more, “ said Sir
Cumference, and he went to discuss shapes with Lady Di.
“Yes,” said Lady Di. “The triangles would be too small, so cut off the corners like
this and make an octagon. Look, it will solve the problem.”
When the knights sat at the octagon table, each one wanted a side all to
himself. Eight sides and twelve knights! Who would share a side with another?
They agreed that the King should have a side all to himself, because he was
their leader, but that left seven sides and eleven people.
“Knights, let there be order, “said King Arthur calmly.
We need to remember that we are here for the defense of our land. How
can we talk at this table with its problem of corners and sides? Sir Cumference,
have the carpenter build a table shaped like an egg, and perhaps then we will
behave more like a flock.”
Sir Cumference drew up plans for an oval table for Geo.
“This table is going to be harder to build since it has no straight edges, “said
Geo. “I will begin at once.”
When the knights met again they were all impressed by the oval table. Sir
Lancelot suggested that they raise their goblets and drink a toast.
All of the knights raised their goblets, but there was a great commotion from
the ends of the table.
The knights at the end of the oval table bumped into the King as they raised
their goblets. No one had enough room.
Some of the knights began to argue. Then King Arthur shouted, “STOP! All
leave me until tomorrow, except for Sir Cumference.”
After talking to King Arthur, Sir Cumference returned home discouraged once
again.
Radius piped up, “Father, when I have a problem I cannot solve, I do
something else for a while. Why don’t we go for a ride?”
That afternoon, Sir Cumference, Radius, and Lady Di went riding. No one
said much until Radius shouted, “Father, look! A tree has fallen over!” “So it has,”
observed the knight.
“Don’t you see, Father? There’s your table!”
Lady Di got off her horse for a closer look. She stood on her tiptoes and
stretched her arm up as high as it could go. Her finger tips just met the upper
edge of the trunk.
“It should be big enough,” she said. “This part is as tall as I can reach, and
the wood seems to be of good enough quality.”
Sir Cumference summoned Geo to cut a cross-section of the trunk to make
into a tabletop.
“Leave the bark on the outside edge,” he told Geo, “I like its rough feel.”
Geo and his helper sawed through the huge tree trunk. Then they hoisted
the heavy slab into an oxcart, and off they went to Geo’s workshop. Geo worked
all night building the new table.
When the knights met the next day, the table was finished. Everyone was
content. No one shouted or whispered. No one felt cornered or trapped. No one
was poked in the stomach, and no one felt squished.
Everyone had an equal position around the table. As they talked, they
decided the best plan was to try to make peace with their neighbors. King Arthur
was so pleased that he announced they would celebrate that night.
Soon, everyone was enjoying the music, dancing, and banquet. Suddenly,
the music stopped. A messenger rushed in and handed a sealed parchment to
King Arthur. The King read it and smiled.
“Ladies, knights, and guests, I have excellent news. The Circumscribers are
not planning an attack. The want only to measure the area of their kingdom.
There will be peace in the land!”
“Hooray!” Everyone cheered ‘til the King held up his hand for silence.
“To honor these knights who gathered at this table to same our kingdom, let
them henceforth be known as the Knights of the Round Table.
“Let us thank Sir Cumference and Lady Di, and their son Radius. They made
this round table possible.” Everyone cheered again.
“Furthermore, because Lady Di of Ameter has a reach that is equal to the distance
across the table, we will name this measurement for her. We will call it the
diameter.”
“I am proud of Radius, too,” added King Arthur. “Someday he will become a
fine knight. He may be small but he has tall ideas.” Everyone nodded and clapped.
“Let us call this small measurement from the center of the circle to its edge the
radius.”
“Finally, let us not forget our clever Sir Cumference. Since it was his idea to
leave the bark on the outside edge of our table, we will name the outside edge of
any circle after him. Let us call it the circumference.”
Sir Cumference bowed to the King as everyone rose from their seats and
began cheering and whistling and stomping their feet. It was the happiest
celebration that anyone could remember.
Sir Cumference and the Dragon of Pi
A Math Adventure
By Cindy Neuschwander
Illustrated by Wayne Geehan
Sir Cumference and his son, Radius sat in the shade of a tree, enjoying a
delicious midday meal. Partway through the lunch, Sir Cumference grabbed his
stomach and doubled over in pain.
“Ooooh, my belly!” he wailed. “It feels like fire! Radius! Run to the castle.
Find the good doctor and get me a cure.”
Radius ran to the castle and up a winding staircase to the doctor’s workroom.
The doctor was out. Radius entered the mysterious place full of plants and
potions.
“What shall I do?” he wondered. “Father is in great pain. I’ve got to bring
him something.”
Radius looked at several bottles. “Hmmm,” he murmured. “This says ‘Fire
Belly.’ Father has a fire in his belly. Maybe this will cure it.”
Radius picked up the bottle and hurried back to Sir Cumference.
The knight gratefully took the bottle and gulped the liquid down. KABOOM!
Sir Cumference disappeared and a dragon now sat on the grass.
“AHHHHHH!” screamed Radius. “Where is my father?”
“H-h-here,” hissed the dragon, flames slithering out of its mouth. “H-h-help
me,” it pleaded, and belched puffs of smoke into the sky. “I f-f-feel beastly!” Its
arms pedaled wildly as its tail thrashed back and forth.
“Don’t worry, Father! I’ll get help,” Radius called over his shoulder as he ran back
toward the castle.
The guards on watch had also seen the big explosion. When the smoke
cleared, they saw the dragon and alerted everyone in the castle to the danger.
Plans were made. Messengers were sent across the countryside to ask nearby
knights to come vanquish the fire-breathing beast.
“Mother, Mother!” called out Radius as he hurried into the castle.
“There you are!” his mother answered his mother, Lady Di of Ameter, looking
relieved. “Come inside quickly! A dragon has been spotted nearby.”
“I know,” Radius answered. “It’s Father!” Radius told his mother what had
happened.
“We must find another portion that will change your father back into himself.
I’ll go look for the doctor,” she said. “We don’t have much time. The knights plan
to slay the dragon tomorrow morning.”
Radius ran back to the doctor’s workroom. He looked at drawings and notes.
He peeked inside boxes and bags. He searched through book after book.
Finally, he spotted a curious-looking container with a set of spoons and a
poem. It might be a cure.
The Circle’s Measure
Measure the middle and circle around,
Divide so a number can be found.
Every circle, great and smallThe number is the same for all.
It’s also the dose, so be clever,
Or a dragon he will stay…
forever.
“Measure the middle and circle around…,” thought Radius. “I’ll bet Geo of
Metry can help! Carpenters measure things everyday.
Geo was with his brother Sym when Radius arrived at their workshop. They
were looking at a wheel Sym had made.
“No matter where you look around the circle, the spokes go across the
middle and cut the circle exactly in half,” Sym said.
“Such a lovely design,” complimented Geo.
When Radius heard “across the middle” and “around the circle,” he had an
idea. He needed to go back and reread the poem.
“Goodbye!” he called as he rushed out.
As he ran through the kitchen, he saw his cousin, Lady Fingers. She was
baking pies.
She measured strips of dough into equal lengths with a span of her fingers.
“Help me finish the last pie, please,” she pleaded.
Radius thought about Sym’s wheel. He arranged the strips on the pie like the
spokes. There were three strips left over. He draped them around the rim of the
pie pan.
“One, two, three strips go almost all the way around the edge. Pinky, may I
have a little more dough?” asked Radius. Pinky was Lady Finger’s nickname.
Lady Fingers handed him another strip of dough. Radius folded it in half,
but half was longer than he needed. He folded it in quarters, but even a quarter of
a piece was too long. He folded it in eights, and an eighth was almost right.
Almost, but not exactly. “Pinky, I’ve got to get going,” said Radius.
“Farewell!”
Radius knew the magic number was more than three, but exactly how much more
did it take to make a whole circle?
Back in the workshop, Radius found Geo’s measuring tape—a long strip of
cloth marked in inches. He measured 49 inches across the middle of a wheel and
1
154 inches around the outside edge. “154 divided by 49 is 3 ,” he figured out.
7
Radius measured big wheels and small wheels. Every time, the distance
1
around was 3 times the distance across. He stuffed the measuring tape into his
7
pocket and ran off to the doctor’s room.
As Radius ran around a corner, he saw his mother coming toward him.
“There you are!” Lady Di cried. “I cannot find the doctor anywhere. What are we
going to do?”
“It’s alright, Mother. I know what to do.” He showed her how he figured out
the magic number.
He measured an onion slice, a basket, a bowl, and a round cheese. “This
makes sense,”
Lady Di drew some diagrams to show the measurements. “This makes sense,
“This makes sense,” she said. Good work. I’ll go and tell your father while you get
the medicine. Don’t forget we have only until morning.
Radius went back to the doctor’s workroom to get the medicine. “I think I
understand these directions,” he said out loud. “But if I measure the wrong dose,
Father will remain a dragon forever!”
I must be sure I am right,” said Radius. He sat down to reread the poem. As
he read, his eyelids slowly closed. Soon, he was fast asleep.
When Radius awoke, the sun was rising. “Oh, no, I must hurry,” he said. He
grabbed the medicine and headed toward the woods. The smoke and flames led
him right to Sir Cumference the dragon.
The sleeping dragon was lying in a circle with its tail in its mouth. Just then, it
opened one eye and hissed, “H-h-hello, S-s-son.”
“Father, you’re a circle, too, but such a big circle!” Radius looked at the
dragon doubtfully. Could the distance around the dragon circle really be three and
one seventh times the distance across it?
Just then, they heard the blaring of trumpets. “Hurry, Radius!” Lady Di said.
“The knights are coming!”
“Mother!” Radius said. “Hold this part of the tape while I measure across the
middle of the dragon circle.”
Sir Cumference cried out, “Why are you measuring my diameter?” As he
spoke, his fiery breath burned the measuring tape so that Radius could barely read
the numbers. It looked like seven feet, but was it?
Together, Radius and Lady Di measured 22 feet around the outside of the
dragon circle. Sir Cumference whimpered, “Must you measure my circumference
NOW?” Radius quickly divided 22 by 7. The circumference of the circle divided by
the diameter was three and one seventh!
Now the knights were surrounding them with swords drawn. “Radius! Lady
Di! We’ve come to save you!” they shouted. It was now or “dragon forever.”
Radius gave the creature three and a seventh spoonfuls.
KABOOM-FAROOM! A big explosion shook the forest. When the smoke
cleared, a hearty, human Sir Cumference stood in their midst.
Sir Cumference leaned over and hugged his son. “Thank you, Radius but how
did you do it?” Radius explained about the pie and the measurements.
Sir Cumference and the knights listened with amazement. Cheering, they
swept Radius up on their shoulders and returned to the castle.
“Pies! Let’s eat some pies!” shouted Sir Cumference. “Radius saved my life
because of a pie.”
At the celebration, Radius held up a pie and explained what he had
discovered. “I found out that the outside edge of a circle, called the
circumference, is three and one seventh times as long as the diameter, which is
the measure across the middle. It’s true for any circle.
“I say we honor this new discovery,” said Sir Cumference. “From now on, pie
with an e will be for eating. Pi without an e will be the name of this number for all
things round!”
Geo and Sym stepped forward and gave Radius a present. “This is a drawing
compass. May it lead you to other great discoveries about circles!” they said.
And Radius had the seat of honor for the entire Pi Celebration which lasted
three days, three hours, and twenty-four minutes.
Pi is an interesting number. We often represent it with the 16th letter of the
alphabet, π. It is usually expressed as a decimal number 3.14159… The part to the
right of the decimal point is about a seventh.