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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:
A Tale of Three Species: The Man, the Woman, and the Communist in ‘Some Like It Hot’
By Lulu Eastman, VI Form
A Tale of Three Species: The Man, the Woman, and the Communist in ‘Some Like It Hot’
The 1950s were a time of deep cultural turmoil in the United States. In the era of the Cold War and the Red Scare, an environment of tension and confusion emerged due to uncertainty in the home and society as a whole. The Cold War era, clouded by an intense and deeply ingrained fear of communism, had Americans desperately seeking a standard of comfort or normalcy to turn to, and they found it in gender roles. Unease cornered women into their positions as housewives, and men were solidified as the family providers. Some Like It Hot, a 1959 film, was released amid a time of tension in American society, when gender roles and family life were strongly influenced by a Cold War-induced climate of fear and conformity. (more…)
From The Writers’ Room: Extracurricular, An Original TV Series
By Riya Shankar, Lulu Eastman, Lillian Stout, Cooper Giblin, Tony Banson, Nick Hallal, Sophie Haugen, Sada Nichols-Worley, Ben Hunnewell, and Jimmy Tobin, VI Form
From The Writers’ Room: Extracurricular, An Original TV Series
(Above title sequence scene: music composed and played by Riya Shankar & Sophie Haugen)
Check out Extracurricular’s fan website here: https://extracurricular.squarespace.com
Yin and Yang: The Interdependence of Dr. Martin Luther King Jr. and Malcolm X
By Isabelle Titcomb, VI Form
Yin and Yang: The Interdependence of Dr. Martin Luther King Jr. and Malcolm X
Sixth form Isabelle Titcomb spent a semester this year in History Fellowship class conducting research on the relationship between MLK and Malcolm X — two of the most influential leaders in African American history whose words still have a lingering influence.
A Study of Fullerenes
By Jovin Ho, VI Form
A Study of Fullerenes
A fullerene is an allotrope of carbon which denotes a series of carbon molecules that form a multitude of different shapes including hollow spheres (Buckminsterfullerenes) or cylindrical tubes (carbon nanotubes). Buckminsterfullerenes (or Buckyballs) were the first type of Fullerene whose structure was determined. In 1980, Sumio Iijima examined an electron microscope image, and found a cluster of carbon molecules which formed the core of a “bucky onion.”[1]Buckyballs are a chemical compound with the formula C60 and comprises of carbon atoms arranged in a hollow cage-like ball shape (truncated icosahedron) – not dissimilar to a soccer ball – and made up of twelve pentagons and twenty hexagons. The existence of the Buckyball had originally been predicted in 1970 by Eji Osawa after observing the structure of corannulene (C20H10) molecule which appeared to be a fragment of the full soccer ball shape that Buckyballs take. (more…)
Macroeconomics: “Easy Key” Product for Campus Safety and Convenience
By Colin Boylan and Jonathan Noel, VI Form
Macroeconomics: “Easy Key” Product for Campus Safety and Convenience
Editor’s Note: As a final project in Macroeconomics, students had to find an issue within St. Mark’s and the world and then find the solution to it by “creating” a product. They had to find the costs associated with making the startup business, pitch the idea to Mr. Rob Calagione, and ask the venture capitalist for money in exchange for royalty.
On American educational campuses and specifically the St. Mark’s campus, campus safety and individual convenience are issues. All campus buildings are now being locked for safety reasons, but unfortunately, this is leaving students and faculty locked out of the buildings as well. Yes, key cards are a solution. However key cards are easily forgotten or lost, are likely to be broken, and are simply outdated. Our product, Easy Key, addresses both issues by providing students with a convenient way to access locked buildings in addition to allowing students to pay for school products. (more…)
Software Pipeline Connecting Close-Range Photogrammetry and 3D Printing
By Gillian Yue, VI Form
Software Pipeline Connecting Close-Range Photogrammetry and 3D Printing
Click on Image to View Full Poster
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…)
DACA’s Uncertain Future
By Lauren Menjivar, VI Form
DACA’s Uncertain Future
On September 5, 2017, Attorney General Jeff Sessions announced on behalf of the Trump Administration that it would rescind DACA after ten state attorneys general threatened to sue the administration if it didn’t end the program. Deferred Action for Childhood Arrivals, or DACA, is a program that allows DREAMers (Development, Relief, Education for Alien Minors) to avoid deportation for two years and make them eligible for a work permit. By ending DACA, 800,000 recipients are at a loss in their ability to work and live in the U.S., and they risk deportation. As a result, a debate on DACA has ensued on its value in American society after five years since the Obama Administration began the program. (more…)
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