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The Art of Summation—An Introduction to Infinite Series

By Tianyu Zhao, VI Form

The Art of Summation—An Introduction to Infinite Series

1. Introduction
No matter if you like math or not, or if you are good at it or not, take a look at this for fun, and see how far you can get. If you are stuck somewhere, skip it and move on. If you think some parts are too easy and obvious for you, just bear with me. Today, I’m graduating from St. Mark’s, and this is probably my last time (maybe even the first time) catching your attention. I promise you’ll discover something deeply mesmerizing about math. Let’s start with some definitions. In mathematics, a series is the sum of a sequence of numbers. Imagine that you are given a sequence, say 1, 2, 3, 4. Then 1 + 2 + 3 + 4 = 10 is a series. Now it’s easy to extend this definition to infinite series, which is simply the sum of an infinite sequence of numbers that never ends like the example above does. An infinite series is convergent if the sum
of its terms is a finite number, and is divergent if the sum reaches infinity.
Infinite series is one of the most beautiful and delicate mathematical objects in my world.

2. Harmonic Series
If you have taken Advanced Calculus BC, you must be familiar with the
p-series:

(more…)

Software Pipeline Connecting Close-Range Photogrammetry and 3D Printing

By Gillian Yue, VI Form

Software Pipeline Connecting Close-Range Photogrammetry and 3D Printing

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Abstract/Introduction

The aim of this project is to make it possible for an average person with no prior knowledge in photogrammetry to 3D-print small objects found in daily lives. My work is to create a software that serves as a pipeline; the software connects the multiple processes that are required to transform the input of of photos of the target object into an output of a 3D printable model file. In other words, what used to be a complicated process of switching between different tools and manually processing the model to make it 3D printable becomes a simple one-click routine where the user can provide the initial group of photos, and then simply sit next to the 3D printer to wait for the object to come out half an hour later. (more…)

“Two Worlds”–Drawing with Color Pencil and Gouache

By Leean Li, V Form

“Two Worlds”–Drawing with Color Pencil and Gouache

Made with color pencil and gouache (a type of paint) on bright orange paper, this drawing is called Two Worlds. It examines pollution, part of my concentration topic for my Studio III portfolio. I approached the subject from a third person perspective. Inside the apartment, a couple sits comfortably, while outside is a polluted world which animals have to escape. The depiction reveals a discrepancy between human and animals’ experience with pollution. We never realize the price the ecosystem paid for us to enjoy our daily conveniences, such as having electricity and running water. Additionally, since our general public regard pollution as distant and irrelevant, we often made little effort to change. Nevertheless, to accept a polluted world is our selfish decision, negligent of not only the future of humanity but also of the entire ecosystem. (more…)

Autism-Vaccine Controversy: Video

By Izzy Kim & Riya Shankar, VI Form and Haley Dion & Laura Drepanos, V Form

Autism-Vaccine Controversy: Video

Editors’ Note: In Advanced Biology, students were encouraged to tell the story that they felt compelled to relate about their Public Health issue (click here for assignment).  In this video, the students integrated a given Case Study with relevant information gathered through independent research. Their integration of the Case Study with additional research reflects an advanced understanding of, and ability to convey, scientific content.

Click on Image for Video

 

Diminishing the Diversity of Devastating Diarrhea

By Geetika Surapaneni, Frances Hornbostel, & Graham Butterfield, III Form with Will Figueroa, V Form

Diminishing the Diversity of Devastating Diarrhea

Please click the image to download/see the poster. Scroll below to see each individual piece.

CLICK ON EACH IMAGE BELOW TO ZOOM TO EACH PIECE OF PROJECT. (more…)

Autonomous Navigation and Decision-Making Process Using Machine and Deep Learning

By Jeongyong Chris Yang, VI Form

 

Autonomous Navigation and Decision-Making Process Using Machine Learning and Deep Learning

Abstract

Please click the image to download/see the poster. Zoom in to read specifics.

Autonomous vehicles are self-driving cars that do not require human drivers. They use sensors that are attached to the vehicle as their vision to detect their environment. After the vehicle detects other objects or signals, computer programming (coding) allows them to react to the situations adaptively. Even though the sensors do not need to be improved, the millions of situations the cars can face on roads create difficulties for people to build a sophisticated computer program that makes the autonomous vehicles completely safe on roads.

First, I decided to build an algorithm pseudocode to help resolve this problem. During this process, I built mazes and followed the instructions based on the algorithm manually to check whether the algorithm is effective. I mainly used three different models for my mazes, each with different difficulty levels to ensure that the algorithm works every time. Then, I decided to record the information (velocity and displacement for both x and y directions) about the vehicle on the map so that the following vehicles can get a picture of the map automatically. However, if the subsequent vehicle detects a different or an altered map with its sensors, the new information will also be recorded on the map. Finally, the final vehicle will follow the path set by the first vehicle, but the map will guide the car with the most efficient path after completely learning and optimizing the possible paths.

To read the full project write-up, CLICK HERE. (more…)