Chapter 18 : Euclid's Geometry
"I'll teach you."
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"You'll teach me?"
"Yes, why not?" His eyes had a galaxy of cosmic dreams, like a cascading waterfall of ambrosial amaranthine, that lured my soul in. He was the snake in Adam's garden and I was his inebriated Eve.
"I... I don't mind." I was pulled in his Canis constellation, him being the sirius that outshined my moon.
He curved those plump lips, as red as a cherry and as beautiful as a new rose. He was like Adonis: young, beautiful and could charm anyone. I wasn't his Aphrodite, but he is my Adonis.
"Okay, so let's start with the easiest of the three, should we?" He asked, ushering me to sit on the desk chair while he sat on the bed.
I opened my book and nodded to him. He turned to the fifth chapter of the book, Euclid's Geometry.
"Before we start the chapter, let's know about Euclid. So Euclid is a Greek mathematician who is referred to as the Founder of Geometry and Reasoning.
Although mathematics has been prevailing through every civilization, the Greeks, Egyptians, Roman and Indians laid an emphasis on the reasoning behind the methods used in our practical science.
The Greeks laid a certain emphasis on the construction of stated functioning of methods, which they discovered using deductive reasoning.
Greek mathematician Thales is credited for giving the first known proof. Pythagoras was the first to discover the geometric properties of traingles, precisely right triangle.
But all of these provided no definitions, which was thus concluded by Euclid."
His voice rang in my ears like a drop of honey, that melted on a pancake and soothed the desires of the tongue.
"So, you know who's Euclid now." Said Sunoo.
"Hmm..." I hummed with a rather mesmerized tone.
"Now what's Axioms and Postulates?"
"What?" I asked.
"In geometry, we need not prove everything with a definition because they are the universally accepted truths. These truths were divided in two, axioms and postulates. Axioms are indefinable truths which isn't limited to geometry. It can be used in any subject that involves mathematics.
But Postulates are limited to geometry. These definitions can only be used in geometry, like the congruence theorem."
"Mhm..."
"Let's do it practically." He pulled out three chocolate bars and ordered, "Read the first axiom."
"Things which are equal to the same thing are equal to one another."
"Let's say, this bar is A, this is B, and the last one as C." He showed the bars respectively.
"A and C are of the same size?" He asked. I nodded in response.
"B and C are of the same size?" My response was repeated.
"Now measure C's length." He passed me the chocolate and a measuring scale. It read 15 centimetres.
"15 centimetres." I reported.
"A equals C?"
"Yes."
"B equals C?"
"Yes."
"Then what's the measurement of A and B?"
"15?" I replied with a tint of enquiry.
"Right. It matches the axioms, doesn't it?"
"It does." I spoke with a whispering tone, remembering how my class teacher couldn't get it in my head in 7th grade.
"Now do the first sum of this exercise." He opened a different book and showed me the first chapter. Immediately I panicked, knowing how bad I am at maths.
"Don't worry. No one will judge you. Do it. You can." He gave me a new copy. The uncanny feeling of being able to trust him, erupted in my head, calming my tensed tissues.
"A line CD equal to line AB, has been drawn such that the two lines don't intersect. Line NM perpendicularly disects CD at point O and AB at point P. The ratio of CO to CD is 2:3. If BP is 4 cm, what is the total length of lime CD."
Reading the question felt like someone speaking a foreign language with me which I was undoubtedly unsuccessful at understanding.
"What will you do?" He asked me, resting his biceps on the desk, right next to my trembling hand.
"I... I don't know." I lowered my gaze. I couldn't withstand to face him.
"Don't worry. When two lines don't intersect, what do you call them?" He asked.
"Parallel lines?" I answered in a question.
"Right. Now draw two parallel lines of equal length and name them." I placed the scale and drew two equal lengthed lines and named them as AB and CD.
"NM is perpendicular disector. What is perpendicular?" He said.
"90°?"
"Yep." I drew a line passing through the two parallel lines at point O on CD and at point P on AB.
"Now what information do you know?" He asked.
"NM perpendicular to CD and AB. CD=AB. CO:CD=2:3 and BP=4cm."
"Note them down." I jotted the tip of my pen on the clean sheet.
"What is CO's length?" He asked.
"Umm... 3 minus 4?"
"3? But that's a ratio without any constant value. How's it 3?" He raised his eyebrows.
"Then...?" I asked.
"What's CD's length?" He asked again.
"CO+DO?"
"Right. What is CO without a constant?"
"x? 3x?"
"Read it correctly." He clicked on in pen.
"Read it... 2... 2x! 2x?" I was answering and questioning him at the same time, unaware of my statement.
"Hmm." He hummed
"Then CD=CO+DO, which implies, 3x=2x+4." I wrote the calculation.
"And then?"
"x=4?" I asked, completing the algebraic expression.
"Yup. So what was CD?"
"3 times 4. 12!"
"Good. Now complete this assignment. I need to use the bathroom. You have 15 minutes. Let's see how many you can do." With that said, he got up and locomoted his body inside that yucky bathroom of his.
There were a total 30 questions, and in order to impress him by keeping upto his expectations, I must complete a minimum 10 sums.
All the questions were based on the first axiom and almost identical. For the first time, I think I'm not that bad after all. I didn't have a teacher is all.
My pen was gliding on the spotless paper as smooth as a professional ice skater dancing.
Little did I know, I was interested in doing mathematics. The way he speaks, the way he touches my heart, feels so unreal that I started finding my paradise in him.
I read the 30th question, unlike the ones I was doing. And it didn't match any of the axioms. It was different, and harder. That was the last question under the HOTS section.
I was disappointed to be unable to complete the worksheet when Sunoo came back and peered over my shoulder to judge my progress.
"Wah, you did all? Great." He said, giving a happy grin.
"I couldn't do the last one." My depressed face was enough to explain how much I wanted to yeet myself out of this world.
"Hmm... I see that. You did all of them correct. It's okay to be unable to do something. Atleast you tried scribbling." He chortled and I huffed in reaction.
"Sorry! Okay, I'll explain you. This question is from quantum physics." He took my unruled copy and measuring scale to draw a figure of cubes, which looked as if they were inside one another.
"In symmetry, two or more objects with equal length and width can never be set in one another.
But in Quantum physics, you can. That is the dimension above 3. You see this figure? These cubes have the same side length. But they fit in one other.
This is the only part in Quantum physics which defies Euclid's Geometry." He said, writing huge calculations.
"When you square root the cube of light's frequency, and root the root three times consecutively, often which is indefinable, you get the perfect 5th dimensional calculation.
That is called shrinking the time. The answer is so minute in the number system, that sometimes it is invalid. That invalid number is the key to the shrinkage of time and dimensions.
Time is the 5th dimension." He said, handing me the copy on which he solved the long calculation: 2nd cube root of 0.632455532.
"And what do you call that theorem?" My brain realised that all this while, he had always told me about shrinking time.
"Tessering. The diagram which I drew is called a Tesseract. In your century, it hasn't yet been proven. But in my time, many scientists have tried this. And went missing.
I was also trying to find the considered invalid number, but unfortunately, my fortune was never related to it." He said. His intimidating orbs showed a wave of nostalgia, wetting his whole heart.
"How would you do that if you could find the number?" I asked him, changing my place from the chair to right next to him on his bed.
"You had to let your body and mind match that invalid state and match your body flow with a frequency higher than the velocity of a beam of light."
"Cool. If you had discovered it, would you also be like Isaac Newton? Or Einstein?" He moved his face away from mine, which was at the proximity of getting inside his.
"Maybe."
"Can't you do it in this time?" I asked.
"I think... I can. But I need assistance. My foster sister and noona had probably found the process already. But I know, the calculation was with her. She gave it to me, in our pendents, that I lost." He heaved a sigh as he mentioned the loss of his sister.
"We can't calculate that again? I'll help you. Addelyn can also. And... And... And maybe Soobin or Yeonjun. We can try to do it again, can't we? And then you can still give your noona the credit."
"Maybe. It would be a cultural reset if we can measure it. You won't need any time machine to travel through time. You won't need a rocket to travel to a different planet or even a different parallel universe." He was excited.
"Wow! Then if you say you're from the future, you'd be able to go back to your time too."
"I'd be able to go back to 3221 even without finding the tesseract theory." He said, as if time travelling was like riding a bicycle to school.
"How will you?"
"Why? What's the date? The time machine was discovered in 2121." He said.
"2121? You mean we'll be having a time machine soon? By the way it's 17th September." I said, checking my phone for the date.
"17? Oh, it hasn't been discovered yet then." He said.
"When will it be?" I asked. His fantasies sounded much logical to me, now that he proved his diagram.
"18th September. A kid discovered it. Probably 15 or so, was his age." He proclaimed.
"15? That's a child. What's his name?"
"Trying to remember. I read that in 7th grade when we were asked to make a model of the first time machine.
I remember reading that the boy was just doing random calculations throughout the month, whose result he used in his science fair project and made the time machine.
It was... Aah! Why don't I remember his name? He was a Japanese kid." He covered his face with his hands.
"It's okay, we'll know tomorrow who it was-"
"Riki Nishimura!" He announced.
"Huh?"
"He discovered the time machine. Yes, that's his name. Riki, Riki Nishimura." He ruffled his own disheveled hair.
"What are you saying? Riki did that?"
"Yeah. That man is credited for discovering the time machine. Genius, he is. I'm still impressed by his brain. For a 15 year old, he's a man of wits."
"You're sure? It's Riki? Riki Nishimura?"
"Hmm! Why are you so surprised?"
"Because I know him."
"You do?"
"Yes! He's my Cousin!"
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Let the story begin...
We gonna have a bundle of things taking place in this book.
And it's just the beginning.
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