My Uncle eta

Last night I was sitting in the warm grass, watching the moon

come out, when Uncle eta, came to call me for dinner. At least that

is what I thought he was doing. Instead he sat next to me and asked

me what I was doing there by myself. I lied to him with a short,

“Nothing.” He didn’t believe me and asked again.

“What are you watching?” Now I was forced to tell him that I was

watching the moon coming out.

“What do you like about the moon?” He continued asking me.

“I don’t know,” I answered. – That was my biggest problem. I

didn’t know. I didn’t know so much. I feared that our beloved goddess

Athena wouldn’t like my ignorance. Would Athena be mad at me if I

am watching the moon. I have noticed many patterns, but I don’t know

so much. I want to be brilliant and intelligent, like Athena and you,” I

finally responded.

My uncle looked at me warmly and replied, “Athena will be

pleased to see your curiosity. It means that you want to learn, did you

know that she is not only the goddess of knowledge and wisdom, but

also courage?” he asked.

I thought about courage, “What does that matter? I am talking

about ignorance and knowledge, not fighting a battle or facing our

foes.” I pressed on.

“Ah, my dear Anna, you always need courage. You must have

the courage to ask, to think, and to try. That courage will lead you to

ask the questions, to open your eyes and really see the beautiful

world around you. Athena loves to see the courage of a young mind

blossom into intelligence.

I sat silently for long time thinking about my uncle’s kind words. I

believed what he said, but knew it to be impossible for me. “Uncle

eta, that is the problem. If you haven’t noticed, I am a girl! I cannot

attend school, at least not here in Alexandria.” I cried. I could feel the

tears coursing down my face as I shared my most secret desire with my

uncle.

Through my tears I emptied my soul painfully, “I want to learn

more about the moon and the stars. I have so many questions! How

far away is the moon? How many stars are in the sky? How big is the

Earth? Does anybody know these answers? I will never know. I am

not allowed to know!” I wailed through my heartbreak.

He looked at me with his deep blue eyes like two oceans,

because they were full of water too at my pain. He sat silently for a

while and finally replied, “I know that you cannot go to school because

you are a girl. It is such a shame that a brilliant and inquisitive mind as

yours is going to get lost in a kitchen merely because belongs to a

girl.”

I could hear the frustration in his voice, and his warm compliment

made me feel a little better. With a smile I thanked him and wrapped

my arms around his neck. He helped me clean my tears and with a firm

voice he queried, “Would you like to be my assistant at the library?

You may have noticed, I am getting old and grumpy and I need

somebody who can read and write for me.”

I was in awe. Being the head of the library of Alexandria was a

great responsibility and he could choose from many people more

intelligent and prepared than me to assist him.

“We would have to make some arrangements first. As you

pointed out, you are still a girl after all. That cannot be changed, but

we can disguise it a little, right?” He winked at me with a knowing smile

on his face.

I slipped inside to ready myself for bed. I went straight to my

My mother’s eyes were aglow with excitement. “Anna, my daughter,

you will have the opportunity that few other women have. We must

take care in our preparations.”

We began to make plans and worked long into the night. I

watched the floor as my long hair fell piece by piece to the floor. I had

so mixed emotions. When my hair was gone, I donned my eldest

brother’s cast-off tunic. I could see my mother’s pleasure at the effect

spread across her face. I ran to the bronze plate to view my reflection.

I did not recognize the young boy who stared back. He looked so

different. “Anna, you are a very handsome boy. Now get some sleep

before the sun makes its return.” my mother instructed.

As the sun made its return visit the next morning, my uncle got

up for breakfast and went straight to his seat at the kitchen table. He

had just begun to sip his fresh cup coffee as I walked into the kitchen.

I watched with a smile as he nearly dropped his drink upon his lap with

surprise. “Agapi, my sister, who is this new boy?” he demanded of my

mother.

With great pride my mother introduced Uncle eta to his new

assistant, me. I ran to his side and began pelting him with details.

“Last night, Mother cut my hair after I told her about your

proposition! What do you think? Do you think it will work?

He started to smile and clean the sloshed coffee and bread

strewn across the table from his leap of surprise. “I can tell that you

got your intellect from

your mother. That is

no surprise after all.

She is my younger

sister and often got the

best of me in an

argument or battle of

the wits,” he explained.

“You have the

opportunity that she

never had as a child,” he

continued. “Treasure

your opportunity to

learn. It is a gift,” he concluded admonishing me.

I knew that I would do nearly anything for this chance. I was

filled with anticipation, excitement, questions, and fear. I was sad to

say goodbye to my mother, but excited to begin my new adventure. I

went to my chambers to oversee the final packing before we embarked

told me that he would still call me Anna, but my new name was to be

Anaxagoras like the great astronomer who was the first to explain the

science behind eclipses. “It is fitting that you be named for him, as

your first interest in knowledge was with the sky. You will be called

Anax which will be much easier for you to remember and answer to.”

I had been near the library several times in my life, but I hadn’t

walked inside the different buildings or the patios. My eyes widened

at the incredible luxury. It was beautiful. The architecture was a

tribute to Athena. I could listen to the silence. We entered my uncle’s

office and he pointed to the walls, which were covered with shelves

twice my height full of papyrus. He drew my attention to the

inscription carved over the wall. I read, “The place of the cure of the

soul.”

“I requisitioned that inscription,” he told me, “because I believe

that books can cure any sickness of the soul. It is time to begin to cure

your soul, Anna, and there is no better time than the present. I am

getting old, and it is really hard for me to read especially those small

letters. I need someone who can carry my belongings and that is willing

to help me with reading and writing.

We left his office and began touring the magnificent buildings.

My uncle was true to his word and introduced me to many people.

There were so many. How would I ever begin to remember them all? I

could feel some new emotions begin to brew deep inside as I watched

the interaction of fellow scholars in the library. Their disrespect for

my uncle greatly displeased me. I could taste the blood on my tongue

from biting it so many times. I knew that I must remain silent. This was

neither the time nor the place for my opinions yet. I made a mental

note of all the questions I was longing to ask my uncle for when we

were alone.

As we were exiting one of the buildings, a young man eyed me

up and down. I felt my skin begin to crawl with fear that he had seen

through my guise. He turned to my uncle with a sneer and laughed,

“Old man, you have need of an assistant? Should we call him Gamma

because he will always follow eta?”

I could feel the firm grip of my uncle’s hand upon my shoulder.

Whether he wants to control his own mouth or mine, the pressure was

firm and the message was clear. I kept my mouth closed.

We left the room together and Uncle eta instructed me, “It

does not matter what position you achieve in each individual

challenge. It is the end result that matters. When I competed in the

Pan-Hellenic Games, I placed second in every competition. The end

result was that I was the champion of the Pentathlon.”

My eyes grew wide with surprise, and I could no longer tame my

tongue. “You won the Pentathlon? When? How? Why have I never

heard of this before?” He remained silent and we continued to walk

to his office. My mind was spinning. I was seeing my uncle anew. In

that moment, I finally understood his nickname. I had always been

curious. It had seemed to me that it should have been Epsilon, or

some other letter. eta had never made sense to me before; it made

sense now. It stood for second, like the second letter. Before the

door to his office had even shut I began to bombard him with all my

thoughts and questions.

“To my mother, you are the best, but here everyone treats you

with little or no respect. I understand your nickname now! And you

eyes began to fill with tears.

The silence in the room was heavy as he was lost in his own

thoughts. I waited for eons when he finally began to talk. He looked

directly into my eyes and began to explain.

“I was barely eighteen years old when I competed in the Pan-

Hellenic games; your mother was about your age. I went to represent

Cyrene at the games in Athens. I was naïve; because I had

dominated all five competitions in Cyrene, I thought that I was going

to do the same in Athens and crush every single other competitor. It

was not so. I finished second in every single event.

We started with the long jump. I landed half palm behind the

winner. In the Javelin throw, it happened again. Second. Now I was

tied for first place overall with three events to go.”

He paused for a time reminiscing in the past events. When he

began again, I could see the excitement of the day written across the

lines on his face. “I knew I would win on the disc,” he began, “because

it was my favorite event. I was starting to study math by then, and I

had studied the aerodynamics of the throw in order to get achieve the

best throw ever seen in the game. I broke my personal record, but

again, it wasn’t good enough to get the first place.” Again he paused

lost in thought. “Anna, my dear, fetch me some water. I need to

quench this thirst before I continue.”

I quickly ran across the courtyard to the well and drew a fresh

pitcher of water from the office. When I returned, I demanded to hear

the rest of the story. “Uncle eta,” I began and then I abruptly

stopped myself. “I don’t wish to call you Second!” I exclaimed. “You

are First to me!"

“Let me finish, Anna, and then we will decide,” he gently

admonished me. “The stadia, a foot race of 180 meters, were my

weakest event of the five. I did my best, hoping to stay in the

competition. To my surprise, I placed second again.”

“Why has no one told me of this? Why didn’t I know this? Do

my brothers know?” I interrupted. He did not respond to my outburst

and continued where I interrupted him, “As you can surely guess, I got

the second place again in the final event, the wrestling match.”

I repeated my question, “Why hasn’t anyone ever told me this?”

Uncle eta, hesitated, and began again, “Everyone from my

home expected me to dominate in every event as I had in Cyrene. I

was expected to bring the name of Cyrene to the podium.”

“But you did. You won the competition, right?” I asked.

“Yes,” he sighed, “I did win the competition. However, I was the

first person to win the pentathlon without winning a single event. For

the people in Cyrene it was a shame. From that day on I was called

finished.

“But that is not right.” I nearly yelled at him. “You did win.

Couldn’t anyone see that? How many others before or after you did

the same? Did anyone ever come close to that?”

“Nobody. Cyrene was nobody’s land,” he answered as he

stared at the ceiling.

I wasn’t able to stop there; I bombarded him with my questions.

“What did you do?” I wanted to know everything.

Again he sighed and patiently began to answer, “I moved to

Athens to find my way. At first I tried music. Again, I wasn’t good

enough with any instrument, so I quit. I have been cursed with second

place. Everyone has made fun of that, even now, nearly forty years

later.”

Rising to my feet, with my chest full of pride, I looked my uncle in

the eye and told him, “You are the head of the Library of Alexandria!

That title alone is amazing, without even considering all your duties

and responsibilities in here.”

He nodded, “Yet, it is just a title, and here I am more of an

administrator. With that role, I have a lot of spare time which I have

used wisely to further my investigations.” His eyes began to twinkle

and he shared his excitement with me, “Right now I am in the middle of

a project, and I believe that with this discovery I will get onto the

podium in the first place,” he explained. “And you my dear Anna are

going to help me do it.”

I could barely contain my excitement and cried out with joy when

I was struck with fear again of my ignorance. “How can I help you if I

don’t know anything yet?” I wailed.

“I should say you will help me precisely for that same reason.

You are full of questions and very smart. I will share my thoughts with

you and together we will do it.”

I hardly dared hope that I would be an important part in my

uncle’s project but I did trust his judgment. I asked, “What do you

have in mind? How big is this project?”

With a chuckle, he looked into my eyes and replied, “This

project is the size of the Earth; it is that big of a project”.

That didn’t make any sense to me, but my curiosity was piqued.

“Uncle eta, what exactly are we doing?”

“We are measuring the circumference of Earth. It will be you,

me, and two assistants.” My confusion must have been written all over

my face because he gestured to me to sit down and told me: “I want

you get some sleep. No more questions for tonight. Tomorrow we

leave for Syene.” His command was firm, and left no room for

argument.

I awoke the next morning excited for the next adventure. I knew

that Syene was a long journey by caravan. I had overheard some

caravan travelers discussing the trip. It was a five to six week journey.

My uncle surprised me when he announced that we would be doing

the same trip in three weeks. I was tired already with the thought of

making this trip in half the time! I looked at my uncle, and asked, “Do I

get to ask questions again yet?”

His burst of laughter filled the room as he responded, “You’ve

just asked one. There is no limit on your questions, Anna. It is your

inquisitiveness that I am counting on to help us understand our own

undertaking.” I could still hear him chuckling as he walked from the

room to make ready the preparations for the trip.

When he returned to the office where he had left me poring over

maps of our journey’s path, I demanded more information. “Uncle,

what are we doing?” I asked with exasperation. “So far, I’m just

reading maps!”

“We are calculating the distance between Alexandria and

Syene in a straight line,” he began holding his hand up to signal me to

listen before interrupting. “We are lucky that during the summer

solstice the sun is directly overhead in Syene. If we placed a stick in

the ground, there will be no shadow at all, but here in Alexandria there

will be one. When we return to Alexandria, I will measure the shadow

of the stick here. I have ordered the stick to be placed in the middle of

the main patio of the library so that everyone may be present when I

measure the shadow and calculate the circumference of the Earth.”

I opened my mouth to speak, and he stopped me again with

his hand. “I am sure you have many questions.”

“Yes!” I interrupted quickly before he could stop me again.

“How will measuring the distance from here to Syene and measuring

a shadow tell you the circumference of the Earth?” I demanded.

“It is a difficult answer that requires some mathematical study

first. Watch. Observe. Question. I know that you know your

numbers and how to do the basic operations in arithmetic, but it is

more than just that. The Wonder of Mathematics is not just the

numbers; it is the patterns. The operations and relations between

them make this whole new world of wonders, called Mathematics. We

will build that mathematical foundation on our journey. Then when

you assist me in measuring the stick when we return to Alexandria,

you will have the pleasure of knowing and understanding how we

measured the Earth.”

I couldn’t believe that Uncle eta was going to share his

most glorious moment that he had being waiting for his whole life. I

was anxious to learn so that I could take part in the excitement.

For the rest of the day, we readied ourselves for the trip

gathering different instruments and a couple of boards to write on

during the expedition. The thought of traveling for three weeks

inspired me to pack my checker board too. Surely there would be

some time for entertainment too.

I could feel the excitement in the air as my uncle discussed the

preparations with his assistants and me. We were all filled with anxiety

and nervous tension. “I’m so glad that you will are able to take this

adventure with me and witness our success. It is right that one in my

family should be present when I finally remove the eta curse.”

We left early the next morning. My uncle and I rode in a cart

while the two assistants, and Jason and Anneas rode horses

alongside us. It was their job it was to place stakes every stadia

(approximately 200 yards). In order to keep a straight line they used

long chain measuring two stadia. In the middle was a stake that helped

them keep the line straight.

We will continue to follow the path along the river. Jason and

Anneas will be at the same distance approximately but keeping the

line and reporting to us every night to keep track of the progress.

“Why is it so important to you to keep the exact distance? Why

did you choose Syene and not another major city instead?” I started

to bombard him again with more questions.

Uncle eta replied, “A few years ago, a merchant told me about

this peculiar well in Syene, where you can see the water at the bottom

only once a year, exactly at noon on midsummer’s day. You are

familiar with the summer solstice, aren’t you?”

I nodded my understanding, and he continued. “He came to me

with this information and his basic idea because he tried and tried but

wasn’t able to figure out.” He looked at me with his eyebrows arched

inquisitively and said, “Why do you think this ability to see the bottom

of the well happens just once a year?”

“I don’t know,” I began, “maybe it is a coincidence or something

related to the solstice.” I answered him. But I wasn’t sure.

“It took me a while to figure out the reason, but when I figured it

out, I ran through the patios of the library yelling ‘Eureka.’ I had

figured out a way to become number one.” Uncle eta’s face was

beaming with excitement as he continued, “Last midsummer I went to

Syene to witness the event. My mind was racing on the return

journey to Alexandria, and I began to arrange all the details to

measure the distance between cities. This was too important to leave

in the hands of my assistants. I had to find out myself. I wanted it to

be accurate.”

My uncle’s excitement was contagious, and I could feel the

importance of doing this project well. I wanted it to be his chance to

prove himself. “This is incredible, Uncle eta. But how can you be

sure you will be accurate? How will we know if you are right?”

“Math is the science of patterns. We live in a world of patterns,

and what we do with the language of mathematics, is describe those

patterns. All of these patterns can be expressed through

relationships and functions.” He looked at me and could read the

expression on my face of complete confusion. My understanding was

equal to zero.

“I know it is hard to grasp at first, but you will get it with a couple

examples, and there are full examples everywhere we look. We’ll see

them if we remain alert.” He stopped on this last word and changed

the subject for one much more tangible, dinner.

Early the next morning after cleaning everything, my uncle

began my education again. Over a sip of his coffee, he asked,

“Where did we stop last night?”

“About the patterns.” I answered him. “Last night I was thinking

about patterns. Do you mean the kinds of patterns that my mother

uses when she is making our clothing?” Truthfully I did not think that

is what he had been talking about, but they were the only patterns I

knew at that moment.

My uncle drained his coffee and began gathering our supplies

to continue south. When we were on our way again he answered my

question. “The patterns you mentioned are one example. Some are

really basic, while others are more complicated. You put them over

the fabric, cut them, and put them together following an order and you

get a simple tunic or a more complicated one. At the end it is just

clothing. It is the process all together that is important, because you

can’t put together the pieces together and then cut, or cut and then

mark the pattern. You have to follow a specific order, that order is

what creates the pattern.”

“I got it. I don’t have to learn math, just to create complicated

tunics, so I can be familiar with more complicated patterns, right?” I

answered him with a grin in my face and he knew that I was just teasing.

Uncle eta began to explain how everything follows a pattern.

The seasons follow a specific pattern. We know that after spring

comes the summer; then it is autumn followed by winter, and then we

are back to spring again. Everything has cycles. Some are easy to

understand because we can see them, but others are more

complicated or complex. He explained using trees. They grow from a

small, simple seed. After many years, they are able to give fruit, and in

the middle of the fruit are the seeds to start the process again. I

realized that there really were patterns everywhere ready to be

discovered.

“Do you enjoy listening to music?” my uncle asked me. “Artists,

painters, sculptors, and musicians follow patterns as well,” he

continued.

“Musicians follow patterns too?” I asked incredulously. I had

never thought about that.

“How do they make it music instead of noise? How is it that all

of their songs are different?” he inquired. “Music has cycles. You

have noticed that they start and finish a song, and it sounds pleasant

to the ear.”

“But which kind of patterns do they follow?” I interrupted. I

loved to listen to music and had never thought of it as a pattern.

“Let’s consider the Lyre. Each cord has a specific length, and

there is a direct relationship between them. Pythagoras was the first

to come to this conclusion. When I went to Athens to learn music,

they started to teach me math at the music school.”

I looked at my uncle with disbelief, “To become a musician you

have to learn mathematics first and then you can start to learn music?”

“You need to understand how the music flows and the

relationship between notes and scales. It is much more complicated

than just learning how to play a specific instrument. The idea is learn

how to create music rather than noise. You must know how to follow a

rhythmic array of notes, find a new pattern, or song, and to blend

sounds that are pleasing to the ear within that rhythm. You see, music

is a kind of math. It is a pattern.

I thought about that for a while and began humming one of my

favorite melodies. My uncle joined me and we harmonized together

beautifully. “That was my first mathematical test, Uncle eta,” I said

laughingly when we finished our song.

“Patterns are everywhere. You have to learn to see them. Now

that you know them, you will be able to see them more clearly.

Observation is one of the key ingredients to see patterns. When you

are observing something, pay close attention. Did it have any

repetitions? Did it have any changes? If you change one thing, does

the pattern change too? Like your heart beat.”

“Patterns aren’t always the same? They can be changed too?” I

asked him.

“Yes, and sometimes the change of the pattern is a pattern

itself,” he grinned at me.

“Let me see if I am right. What we are doing is analyzing a

pattern of the well, the one that you can see the bottom once a year.

Am I right?”

“Eventually, yes, even though I believe I have already solved the

well’s mysterious pattern.” He gave me a wink, and I knew that he was

going to tell me the mystery later. Even if I tried to ask, he would just

ask me more questions to make me figure it out on my own. I closed my

mouth and decided to let him to do the talking for now.

“Let’s move forward and start to understand more about it.

Today we will switch positions. You will be the teacher, and I will ask

the questions. You are in charge, so you have to decide what we are

learning today.” he proposed.

Sounds like fun. We changed the pattern of teaching already,” I

added excitedly.

“Ah, yes, the pattern of teaching has chanted, but the learning

is the same. It is a different pattern that produces the same result. I

am glad you noticed.” He complemented me.

I thought about what I should teach my uncle. He already knew

much more than I did about everything. “I don’t know what I should

teach you, Uncle, but we can try with numbers. Sometimes I feel like

they are magical when you can see through them and see how they are

related special they are”

and then added, “Numbers are special. In many ways they are like

people; everyone is unique and different. Learning to identify their

differences is really a talent.”

“That’s something I know about. I can classify things. But I

have never thought about classifying numbers. They are all different.

The only thing they have in common is that they are numbers.” I

offered, although I knew I was about to learn otherwise.

“If you want to classify numbers, there are many different ways

to do it. You use counting numbers every day. But there are integers

which add negative numbers. Sometimes numbers don’t have exact

values, but they are still consistent. These are irrational numbers.

We can also define numbers as perfect numbers and non-perfect

too.”

“What’s wrong with the non-perfect numbers?” I interrupted

immediately.

“There is nothing wrong with them; it is just that they don’t fit

the pattern.” He answered.

“What is the pattern for the perfect number?” I asked him trying

to figure out what he was talking about.

“Well in mathematics, a perfect number is the one that the sum

of all its whole number factors, except for the number itself, equals the

number.” His eyes met mine, and he continued, “You know that 28 it

has as a factors 1, 2, 4, 7, and 14, right?”

“Yes, you count the 1, but not 28, because that is the same

number” I responded, to show him that I was following him.

He began the calculations explaining, “Let’s see, we have 1 and

2 makes 3, plus 7 is 10; 4 and 14 are 18.”

“And 18 plus 10 is 28!” I finished excitedly. “It works.

That’s amazing! Does it work for every number?” I asked quickly

trying to figure out another number in my head.

“Well,

it works for the

perfect numbers

obviously but not

for the non-

perfect. As of

today we only

know just four

perfect numbers,

the first is six.”

He started, but I

interrupted.

“Because 1+2+3 makes 6,” I finished.

He smiled at me and continued, “Exactly, the next is 496, and

then there are 8,128.” He finished.

“Just four perfect numbers?” I was disappointed, I knew that

math was an exact science; it should have more perfect numbers, not

just four.

“Because there are just four, my favorite numbers are prime

numbers, probably because they always want to be number one. What

do you know about prime numbers?” He tried, testing my knowledge

about numbers.

“Those are the ones who can be divided evenly by themselves

and one only. I tried to memorize them, but I know just a few of them. I

don’t know any pattern or formula to find them. The first few are: 2,

3, 5, 7, 11, 13, 17 and 19,” I answered him trying my best to sound

educated.

“Well, those are all that you need to know to discover if a

number is a prime or not. Actually with the numbers that you already

know you can find all of the prime numbers from 2 through 400.”

“Really, that’s all?” I asked. “How did you figure out? Do you

have a formula or a pattern?”

down a little. One question at the time! Yes, that is all you need, just

the first few prime numbers. With those you can find all the rest of

primes. There is no formula, nor a distinct pattern. However, with

several patterns, I have been working on a technique to separate

prime from non-prime numbers.” He proudly announced.

“Show me,” I demanded.

“It is not a formula, but a technique that allows you to separate

them. I called it “The Sieve,” because it works in the same manner.

You separate one kind from the other.”

He was getting really excited because he had been working on

this project for quite some time. It was the first time he had shown

someone else. I was going to be the first to see it!

“Give me the checker board, and I will give you a really quick

example.” He ordered and began to write on his slate:

“Sift the Two's and

Sift the Three's,

The Sieve of

Eratosthenes.

When the multiples sublime,

The numbers that remain

are Prime.”

“Can you repeat it please?” I begged. I was still thinking about

Sifting the Twos.

“I will tell you what to do, but one step at a time. Number your

checkerboard from 1 to 64,” he instructed.

I did what he said and showed him my finished product.

“Now cross out all of the multiples of two.”

I followed his directions and noticed my first pattern. “They all

form vertical lines!” I exclaimed, offering my own “Eureka” with the

discovery.

Uncle eta’s chuckle was warm and I felt pride in my observation

as he gave the next instruction.

“Now mark all of the multiples of the number three. When you

finish that, do the same for the multiples of five and seven.”

The numbers that remain are the prime numbers through 64.”

Then after we filter our first 64 numbers out of the matrix,

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59 and 61 are

prime numbers,” he concluded.

“Uncle eta! That is wonderful, have you already taught all of

that in Alexandria?” I was impressed with his discovery.

“No, I haven’t yet; it is so simple that they will laugh at me, like

they always do,” he responded sadly.

“Well, you have to tell them, or somebody else will figure it out

too. And then he will get all the credit.” I decided to help him present

this discovery to his peers. “I will help you to polish it more, we have a

couple weeks to get back and you can kill two birds with one stone,” I

vowed, imagining the pride of my mother with him and with me for

pushing him to finish it.

When we arrived in Syene, I was surprised by the well. It was

almost like an oasis around the well that provided water for the people

there and the travelers. A few minutes after us, we were able to see

Jason and Anneas in the distance. We walked to the well to wait for

them. We were anxious to discover the distance from Alexandria to

Syene. I was able to see how nervous and excited my uncle was; he

wasn’t able to keep himself standing still even for a second.

On their last day, Jason and Anneas covered 119 Stadion in

total. My Uncle took note of the distance and added it to the rest of

the days of the trip.

Because it was almost time for lunch, we ate and immediately

began to travel back to Alexandria. He gave some final instructions

to Jason and Anneas—a few places to double check and made plans

to meet back with them in Alexandria. We would be travelling straight.

Neither of us wanted to wait to get home and share the discovery.

During our first week of the return trip, my uncle was occupied

making his calculations for his project. He put me in charge of

discovering how the different arrays change the pattern.

The first thing that I noticed was the change in the pattern of

vertical rows. Because 9 is a multiple of 3, the columns starting with 3,

6 and 9 made vertical rows, and the multiples of 2 looked just like my

checkerboard! The rest of the multiples of 5 and 7 created diagonal

patterns.

I excitedly tried other arrays. After several days of creating the

arrays and finding the patterns, I was able to really see it for first time.

By repeating the numbers I was able to feel the flow of the pattern

and see the changes between the arrays. I saw music and I

understood why musician have to learn math.

I finally interrupted Uncle eta’s quiet concentration with my

excitement. “I have to show you this!” I exclaimed. “When I change the

number of columns in the array, it produces a different set of patterns.

It’s like a musical instrument. When you change the tension of the

cords it produces a different set of sounds. I’m making mathematical

music!” I concluded.

“You are right, and so wise to have seen that pattern. Athena is

surely smiling upon you today,” he complimented.

When we finally arrived in Alexandria it was the same morning of

the mid-summer equinox, a large gathering of mathematicians and

philosophers were already waiting our return. I could hear the

rumblings of doubt and skepticism. They were expecting to see my

uncle’s experiment fail.

I could feel my heart racing and forced it to calm down—to

change the pattern. Not only was I feeling nervous and excited, I was

feeling anger toward the crowd’s attitude. They obviously didn’t

know who they were ridiculing! I felt a hand on my shoulder and one of

my uncle’s fellow mathematicians spoke to me. “Anna,” he began

making my heart beat anew. I was supposed to be Anax! He

continued, “I am a friend of your mother and your uncle. I know your

uncle well, and I trust him. Today will be his shining glory. I am glad to

see you had a safe return from your trip.”

I mumbled a quick, “Thank you, sir,” and felt some relief that

there was one other in the crowd that was looking forward to Uncle

eta’s success!

My uncle motioned for me to follow and we went straight into the

library. My mother was waiting for us and wrapped me in her arms. “I

am so glad you are home safely. Today is a great day for your uncle,”

she exclaimed.

“I am so glad that you are here and able to witness this too. He

is your brother, and he is brilliant. He can see beyond,” I began to

explain. My mother knew what I was talking about, because he had

taught her as well.

“Let’s get closer I don’t want to miss anything, it is time for him to

measure the shadow,” instructed my mother as she dragged me by the

arm to the first row with her. We watched Anneas to measure shadow

cast in the middle of the library followed very closely by my uncle who

was supervising every movement. Any mistake would require a full

year until the next mid-summer to rectify.

“23½ daktyloi ” Anneas said solemnly. He looked at me and

winked knowing how important this moment was for my uncle. The

column was 12 pouls tall [ 192 daktyloi]. Then Anneas measured the

distance between the top of the column and the length of the shadow.

“It is 193½ daktyloi,” he announced.

My uncle wrote down the measurements, and using one of the

boards from the trip he got the angle and calculated the measure of

the earth.

The crowd was growing impatient. I could hear the rumblings

throughout the crowd as they began to mock him. He was so

absorbed in his calculations that he did not hear them. At long last,

he stepped in front of the crowd. “Thank you for joining me here

today to witness the completion of my journey,” he began. “I have

much gratitude for all those who supported me during this quest. It

allowed for my success here today,” he continued. His voice was loud

and confident, and I was proud to be part of the event. “I would like to

give special thanks to my niece, Anna. Without her questions and

desire for learning, all of this would be for nothing.”

I could feel many eyes on me and the crowd’s mumbling grew

louder. “His niece? I thought that was his nephew.”

I was in awe. He had not only publicly told them that I helped

him, he had acknowledged that I was Anna. Not Anax. He told them

that I was his niece! My mind was still spinning when he began again.

“The angle of elevation of the sun was 1/50th of a circle (7°12')

south of the zenith. With the assumptions that Earth is a perfect

sphere (360°), and that Alexandria was due north of Syene, we

concluded that the distance from Alexandria to Syene must

therefore be 1/50 [7°12'/360°] of the total circumference of the

Earth.”

Everyone began to talk at once. They were astonished by the

simplicity of his method. He hadn’t used big formulas or anything

fancy, just his brilliant mind. Some of them were still skeptical, and

without determining the validity of his statement, began to mock him.

At that moment, I lost my temper. I would not allow them to ruin

his moment. I stood in front of everyone, and looking directly to them

began to speak. “Some concepts may be hard to grasp at the

beginning, but with patience, I was willing to teach them so that one

day maybe they could understand it.”

The crowd burst into applause and those who had mocked my

uncle quickly quieted and began to leave the crowd. My uncle looked

at me and winked while embracing my mother. Because everyone was

still watching intently, I continued talking. That is not all, My uncle has

determined a method for finding prime numbers. It is called ‘The

Sieve of Eratosthenes’, because that is HIS name, and not eta like

some of you like to call him.” I announced proudly.

I continued the lesson and recited the verses showing them first

my checker board with the 8x8 array. I was asked many questions and

answered each of them with confidence. I brought out the 9x9 array

and then my favorite one, a 20x20 array with all the primes from 2

through 397 that I had created on our way back to Alexandria.

The mathematicians were in awe of both techniques and

impressed with how well prepared he got me with only few weeks of

teaching.

I concluded my impromptu lecture with, “Math is the science of

patterns. We live in a world of patterns, and what we do with the

language of mathematics, is describe those patterns. All of these

patterns can be expressed through relationships and functions.”

The crowd stood and applauded chanting, “Eratosthenes!

Eratosthenes! Eratosthenes!” Not a single person shouted, “eta.”

I could see the tears welling up in my mother’s eyes, and my uncle’s

face beamed with pride. No one was prouder than I at that moment. I

took hold of my uncle’s hand and my mother’s hand, and as we left the

library, I told them, “The library truly is ‘The place of the cure of the

soul’.”