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Chapter 2--Pizza Pi
Chapter 2--Pizza Pi (π)

© 2017 by Jerry L. Croasmun

"3.14159265359 is the beginning of a real, but very large irrational number," Herr Specht said. "We affectionately call this number Pi, which is spelled P I. It is the ratio or comparison of every circle's circumference to its diameter. Pi is a mathematical constant."

"I'm glad you kids are enjoying your pizza. This diner is one of my favorites. The food is always good and the service is excellent. They are consistent much like Pi. You always know what to expect. The value for Pi is the same for every circle both large and small."

"Ben, do you know what this is?" he asked pointing to a strange looking symbol on the placemat.

π

My brother studied it briefly and answered, "No. It looks Greek to me."

We began to laugh at Ben's attempt to be funny, but our demeanor quickly changed to surprise and amazement when our self-appointed professor shook his head in agreement.

"You are a genius, Ben. You might not have realized it, but you are correct. Pi is the 16th out of 24 letters in the Greek alphabet. Alpha to Omega, the first and the last, the beginning and the end." He then drew a letter resembling a capital A, and wrote Alpha below it. Next, he drew something that looked like a horseshoe adding the word Omega.

A            Ω
Alpha     Omega

"Herr Specht, I said, "I just realized the letter P is also the sixteenth letter in the English alphabet."

"Very good. I'm glad you're beginning to recognize the patterns and relationships." He then started drawing and reciting the Greek alphabet. "Alpha, Beta, Gamma, Delta, Epsilon, Zeta, Eta, Theta, Iota, Kappa, Lambda, Mu, Nu, Xi, Omicron, Pi, Rho, Sigma, Tau, Upsilon, Phi, Chi, Psi, Omega."

Α Β Γ Δ E Z H Θ

I Κ Λ M N Ξ O Π

P Σ T Y Φ Χ Ψ Ω

"I saw some buildings with letters like those when we visited the university last fall," I said. "Our tour guide told us they belonged to the fraternities and sororities. What are they?"

"Fraternities used to be exclusively for guys or the brothers and sororities were for the girls or the sisters. Today many are co-educational and accept both genders."

Ben asked, "Are they kind of like a secret club with handshakes, mottoes, colors, and mascots?"

"You're on the right track. Most are social groups primarily with shared interests, values, and goals. The brothers and sisters get together to support one another and usually strive to better their communities. Most have two to four Greek letters as part of their name. Some of my favorites have Pi in them."

"The Delta Sigma Pi (Δ Σ Π) and Pi Sigma Epsilon (Π Σ E) both consist of students studying business and marketing. While the Chi Pi Sigma fraternity (Χ Π Σ) is for students studying law, law enforcement and corrections, along with other criminal justice fields."

"We often use the decimal number 3.14 to represent Pi. March 14th is Pi Day and it is one of my favorite holidays. I always celebrate by eating pie on Pi Day. My favorite is a banana cream pie."

"That's one way to get your daily potassium, Herr Specht," I said. "My favorite is a piece of hot apple pie served with a large scoop of ice cream on top."

"Oh yes. Apple pie, à la mode," said the tiny man.

"What did you say?" Ben asked with a confused look on his face.

"À la mode means served with ice cream."

"Oh, I thought you were speaking German."

"No, à la mode is French along with à la carte, which means to order one item separately from the menu. For example, if I wanted a beef enchilada à la carte, I would order a single enchilada instead of the dinner with the rice and beans."

"There sure are a lot of words and languages mixed in with English. My favorite pie is pumpkin pie à la mode or with lots and lots of whipped cream."

"Your favorite is more like whipped cream with a little pumpkin," I teased.

"Speaking of Pi, are you kids ready for more pizza?"

We each took another slice and continued eating. The cadaverous looking man was beginning to appear more lifelike with each bite.

Between bites he continued, "Pi is equal to the circumference of a circle divided by its diameter. The fraction bar is what helps join the pieces of the Pi pie together. The circumference is the numerator and the diameter is the denominator. Circumference over diameter."

π = circumference/diameter
π = c / d
π = 3.14 ...

My mind was still a little overwhelmed, but I was beginning to understand. The pizza definitely had hit the spot and my stomach and head no longer hurt. The adrenaline rush and excitement made me forget about the black olives.

I bravely added, "Finding the diameter of a circle is easy because we measure the distance across from one edge to another. The circumference is Pi multiplied by the diameter."

Picking up the pen, I began to add to the notes on the placemat.

c = πd
c = 2πr

The man's sunken, green eyes sparkled as he smiled and I could hear the excitement in his voice, "Yes! Yes! Most diners and pizza parlors state the diameter on their menus. So leave your rulers and measuring tapes at home."

"Don't worry. We usually don't carry them," I interrupted.

Without skipping a beat, he continued, "The diameter is two times or twice as big as the radius. Pi is the ratio or comparison of a circle's circumference to its diameter. If you know the diameter of a pizza, you know the radius is one-half that."

d = 2r and r = d/2
r = 1/2(d)

I made an honest effort to pay attention and focus on what had been said, yet I wasn't disappointed when I noticed a school bus parked next to the Unimog. Several fine specimens of human flesh exited the bus and I no longer had an attention problem. A few of the boys stood in front of the former military vehicle and began taking pictures using their cell phones. The antique truck had caught their attention and they held mine.

"Where is Tahlequah County Schools?" Ben asked reading the sign on the side of the bus.

"I don't know where they're from, but I know where they are now. They're fine and I want them to be mine."

"Sis, sometimes you can be so silly."

Helen Marie escorted the traveling baseball team to another room in the back of diner, which was often reserved for special groups and banquets.

Baseball must had been the magic word because Herr Specht began spouting out numbers and facts. A baseball is just under three inches in diameter and just over nine inches in circumference. Do you kids play any sports?"

"I like to shoot hoops and kick a ball around every now and then," Ben said.

"Hoops?" Herr Specht asked a little confused.

"We both enjoy playing basketball and Ben is getting pretty good at soccer," I said.

"I was quite the athlete back in the day. Did you know, an official NBA basketball is approximately 9.39 inches in diameter and has a circumference of nearly 29 1/2 inches? Whereas, a soccer ball being smaller, has a diameter of about 8 1/2 inches. Its circumference is approximately 26 3/4."

"How do you know these things?" Ben asked. My brother wasn't the only one who was amazed and curious.

"I used to measure things for fun. I now just look at things and guess or estimate their sizes. I've had years and years of practice. Numbers and their relationships still fascinate and excite me."

He pulled a small measuring tape and a quarter dollar coin out of his pocket. Handing both to me, he asked, "What kind of coin is in your hand?"

"I think it is a quarter. Is this a trick question?"

He assured me it wasn't a two-headed coin. "Why do you call it a quarter and how many quarters does it take to make a dollar?"

Before I could answer, Ben blurted out, "Four. Four quarters make a dollar. Everyone should know that. I learned that in elementary school."

The man smiled, but I knew he had more up his magical sleeve.

"Very good. Yes, it is elementary my dear Ben. However, many people forget the relationships and try to eliminate the fractions. Four out of four quarters make one whole dollar. One quarter or twenty-five cents is 1/4 of a dollar."

"Why don't you kids try measuring the diameter of that quarter? You can round your answer to the nearest inch."

"Can I make the quarter disappear and keep it afterwards?" Ben asked.

Herr Specht just looked at Ben.

"Ben, help me out and let's get serious. Remember what mom always said about cutting fabric?"

"Yeah. Measure twice; cut once."

"One inch," we said in unison having taken my mother's advice.

"Yes, you are correct. The diameter of a quarter dollar is more precisely 0.955 inches or just under one inch. When you multiply the one inch diameter by Pi's equivalent of 3.14, you find the circumference of a quarter to be approximately 3 inches."

Ben measured his empty plate and said, "These plates are ten inches from side-to-side."

"Very good. So if a standard dinner plate is 10 inches in diameter, what would the radius and circumference be?"

"The radius is five inches," Ben answered. "Because the radius is the diameter divided by two. Ten divided by two is five."

I loved to see the sparkle in Herr Specht's green eyes when he got excited and knew the lightbulbs in our heads were beginning to illuminate with the knowledge he was attempting to share.

"Very good Ben. The diameter of a circle is indeed equal to two times the radius. But did you know multiplying by one-half is the same as dividing by two?"

"I think I understand," I said. "So, 1/2 of 50 is 25 and that is the same as 50 divided by 2."

"That is an excellent example. Now for the circumference. The circumference of a 10-inch dinner plate would be the diameter multiplied by the value of Pi. 3.14 times 10 is 31.4 inches."

"Speaking of plates," Ben said. "There once was a girl who thought she was too fat. She went on the 'broken plate diet' so she would eat less."

"I've never heard of the 'broken plate diet'," Herr Specht said.

"Me neither. What is it?" I asked.

"It is where you break all of the plates and replace them with smaller ones. The diet was an epic failure because she ended up using more plates."

I wanted to make hissing and booing noises but instead said, "Oh, Benjamin. That is a really bad joke. I hate washing dishes and on more than one occasion have thought about breaking a few myself. My favorite kinds of dishes are the ones we get to throw away."

"We better settle up and pay or we all might end up with dishpan hands," said the frail-looking man.

I looked over at his hands and doubted the skin could shrink or become any tighter around his skeleton-like bones.

"There are two pieces of pizza left. Anyone want another slice?" the man asked.

We both declined and Herr Specht asked, "What do we have left?

"I call them leftovers," Ben answered.

"Out of our original eight slices, how many do we have left?"

"There are 2/8 or two out of the original eight pieces of pizza left," I proudly declared.

I had used a fraction to express my answer and was smiling ear to ear until I heard the wise man begin to say, "Yes, but…"

He said, "Yes, but 2/8 can be reduced or simplified making it 1/4; thus we have 1/4 for leftovers and have shared 3/4 of a delicious pizza pie."

Ben, being a teenager and always needing the last word, jokingly said, "Is that pizza Pi with or without the e? After all, there is a difference. I'll take mine with the e, but hold the anchovies and cockroaches."

"Curiosity killed the cat," they say, so I remained mute as I looked at Ben and held my breath. I wondered if he had just made a Freudian slip or if he had consciously planned his final dialogue.

Our new friend began to laugh and said, “We will save simplifying fractions for another dinner date."