III: Eclipsing Boundaries

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Lisa's decision to settle into the back row of Mr. Francisco's math class was a strategic one, a calculated move to blend seamlessly into the background while absorbing the unfolding dynamics of her new environment. As the teacher embarked on the day's lesson, Lisa maintained a composed exterior, her mind already dissecting the complexities of the mathematical problems being presented.

In a departure from the typical first-day formalities, Mr. Francisco dove headfirst into a rigorous discussion, probing the class to engage with a level of intensity that belied the usual introductory banter. For Lisa, this was nothing out of the ordinary. Raised in an environment where academic excellence was the norm, she had long since acclimated to the relentless pursuit of knowledge.

As the class delved into a particularly intricate math problem, Lisa observed with detached interest, her keen intellect already racing ahead to the solution. While her classmates furrowed their brows in frustration, she remained outwardly calm, confident in her ability to unravel even the most convoluted of equations.

When Mr. Francisco called upon the students to offer their insights, Lisa chose to bide her time, allowing others the opportunity to grapple with the problem before stepping into the spotlight herself. With each passing moment, her anticipation grew, a quiet excitement bubbling beneath the surface as she awaited her moment to shine.

"Miss Lisa right?, you can go out if you will just sleep in my class. But if you can answer the question on the board, I may allow you to sleep in class until the signal for your next subject rings " Lisa didn't realize that Mr. Francisco was already in front of her.

Without a word, she rose from her seat and made her way to the front of the class, her movements purposeful and deliberate. As she picked up the marker and began to solve the problem, a hush fell over the room, broken only by the soft scratch of chalk against the blackboard.

For Lisa, the act of solving the problem was akin to a dance, a fluid and graceful motion guided by an innate understanding of mathematical principles. With each stroke of the marker, she breathed life into the equation, transforming abstract symbols into concrete solutions with effortless precision.

As she neared the end of her solution, a sense of quiet satisfaction washed over her, a testament to the years of dedication and hard work that had brought her to this moment. With a final flourish, she set down the marker and turned to face her classmates, her expression serene and composed.

"explain" Mr. Francicsco unconciously commanded as he where even out of words how Lisa flawlessly solve the mathemathical problem because of this kind of proposition is one of the most difficult problems and a year ago he read an article about the youngest person who was able to solve this problem, and he thinks that Lisa may have read it too so that she solved the problem but for him it is impossible for Lisa to be an expert after only reading or watching it.

"Collatz Conjecture: It's all about that function f (n), shown above, which takes even numbers and cuts them in half, while odd numbers get tripled and then added to 1. Take any natural number, apply f, then apply f again and again. You eventually land on 1, for every number we've ever checked. The Conjecture is that this is true for all natural numbers (positive integers from 1 through infinity). Conjecture lives in the math discipline known as Dynamical Systems, or the study of situations that change over time in semi-predictable ways. It looks like a simple, innocuous question, but that's what makes it special. Why is such a basic question so hard to answer? It serves as a benchmark for our understanding; once we solve it, then we can proceed onto much more complicated matters. "

For a moment, the room was silent, the weight of Lisa's accomplishment hanging heavy in the air. Then, as if released from a spell, the class erupted into applause, their admiration for her talent and intellect palpable in the air. Even Mr. Francisco, usually reserved and stoic, couldn't help but offer a nod of approval.

As the bell rang, signaling the end of the first class, Lisa gathered her belongings and made her way out into the hallway, a sense of quiet satisfaction settling over her. Yet, even as she navigated the crowded corridors, she couldn't shake the feeling of being watched, the curious glances of her classmates following her every move.

It was then that she was approached by her bodyguard, a silent sentinel at her side.

Miss, your grandfather is reminding you of his order, and asking if you're willing to take care of it yourself or will he just send someone to do it for you?" the body guard told her.

"I'm going myself. Please tell grandpa " the body guard nodded and left.

 With a brief exchange of words, he relayed a message from her grandfather, a reminder of an impending task that required her attention. With a nod of acknowledgment, Lisa assured him that she would handle it herself, her mind already racing ahead to the challenge that lay before her.

Her next class was physics, and as she entered the room, she found herself face to face with the girl she had encountered earlier that morning - Jennie, if she recalled correctly. Despite the earlier altercation, Lisa approached the situation with a sense of calm detachment, her focus unwavering as she settled into her seat at the back of the room.

As the teacher launched into a discussion about the color of the sky, Lisa listened with quiet interest, her mind already churning with thoughts and ideas. When the teacher turned to the class for answers

"Blue maam" someone proudly answers...

"obviously mister park" his classmates laughed.

"The sky looks blue but really it is made up of all the colors of the rainbow. Each of these colors has a different wavelength. Some of these are smoother while others are choppy. Blue light waves travel in short, choppy waves. Like each of the other colors, blue light waves are scattered and reflected as they enter Earth's atmosphere and collide with gases and other particles. Because the color blue has the shortest wavelength, it collides with nearly everything in its path and is scattered about the sky. This is why the sky appears blue. " the classmates applauded and others whistled for the excellent answer given by Jennie.

 Lisa remained silent, her thoughts drifting to the various factors that influenced the hues of the heavens above.

Yet, when the teacher's gaze fell upon her, she found herself drawn into the spotlight once more, her presence demanded by the curiosity of her peers. With a measured tone, she offered her insights into the complexities of atmospheric science, her words a testament to the depth of her understanding and the breadth of her knowledge.

"Can you share with us Miss Lisa what you're up to and written in your paper?" the teacher curiously asked Lisa.

"Nothing important maam" Lisa replied back

"Then would you care explain your idea as to what color the sky has?"

"The sky has no true color. While most of the time it is blue, sometimes it is not. It can often be pale blue, gray, or even white. The reason for this is pollution. Deep blue sky, this color means the sky is very clean. This often occurs when a cold front brings clean air from the north, or when clean air from the ocean moves onto land. Medium blue sky, this color means there is lots of water vapor in the sky. It can also suggest the presence of sulfur from coal-burning operations. Lastly, it may be caused by the chemical emissions of plants and trees, such as those found in The Smokey Mountains of North Carolina and Tennessee. Pale or milky-white sky, this color indicates considerable air pollution from coal-burning power plants or chemical power plants. This condition often occurs in the summer when the air is still. There are also natural causes, such as volcanic activity or ocean plankton. Gray or dark gray, Smoke from forest fires or agricultural burns can cause the sky to appear this color. Brown or brownish orange, Emissions from cars and trucks can cause a layer of this color to form over the horizon. The main component of this kind of pollution is nitrogen dioxide. "

As the class drew to a close, Lisa gathered her belongings and prepared to move on to her next subject, a sense of quiet satisfaction settling over her once more. Despite the challenges that lay ahead, she faced them with a sense of calm determination, secure in the knowledge that she possessed the intellect and the resilience to overcome whatever obstacles came her way.

For Lisa, the journey was just beginning, and with each passing day, she grew more confident in her ability to navigate the complexities of the world around her. With her intellect as her guide and her determination as her fuel, she was prepared to face whatever challenges lay ahead, secure in the knowledge that she was destined for greatness.

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