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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:

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Calculus: Optimization Problem for Derivatives

By Haley Dion, V Form

Calculus: Optimization Problem for Derivatives

Editor’s Note: In Advanced Calculus, students spend considerable time studying derivatives (rates of change) and their applications.   This problem is an “optimization” problem that asks students to calculate the best or optimal value relative to a particular situation.   Students need to first interpret the meaning of the problem (which involves particular rates of change) and model the situation with a function.    

In this problem, George wants to minimize the time it takes for him to get home.  Haley applied her understanding of derivatives to determine the exact spot on the shore where George should leave his rowboat before running home.

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Math Modeling: Protein Bars Ranking Project

By Helynna Lin and Tommy MacNeil, VI Form

Math Modeling: Protein Bars Ranking Project

Click HERE to read Tommy and Helynna’s math modeling writeup report and analysis of which protein bars are the best. They considered nutrition facts and developed a formula that “scored” each bar on its ability to help someone effectively gain muscle mass.

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Non-Euclidean Geometry

By Gabriel Xu, VI Form

Non-Euclidean Geometry

What if math students no longer had to study similar triangles because they simply don’t exist?

What if you could draw as many lines parallel as you want to a given line from only one point?

What if angle-angle-angle was enough to prove congruence of triangles?

Would these changes to our known geometric system finally make it easier, or would they  further contribute to its fascinatingly intricate nature?

Studying Non-Euclidean Geometry aims to answer these questions. (more…)

Math Modeling: Using Math for Flight Path Safety

By Kate Sotir, Cooper Sarafin, Anderson Fan, Shep Green, VI Form and Mo Liu, V Form

Math Modeling: Using Math for Flight Path Safety

Part 1:

The problem at hand is to create a model, a rating system, that would inform potential flyers of the safety of a particular flight. Our solution includes a mathematical equation that gives us a number between 1 and 100, depending on the inputs. Although the values themselves indicate the safety level of flights, we do not want to our audience to read into the numbers: a flight with a safety index of 63 should not be considered a more dangerous flight than a flight with a safety index of 67. Therefore, to make our model directly presentable to our audience, we classified the possible outcomes into ratings. A safety index ranges from 1 to 20 would have a rating of ★, from 20 to 40 would have ★★, 40 to 60 would be ★★★, 60 to  80 ★★★★, and finally, 80 to 100 would have the highest rating of ★★★★★, and flights that fall under this rating would be the safest choice based on our model. (more…)

Competing in the FIRST Robotics Challenge

By Kate Sotir, VI Form

Competing in the FIRST Robotics Challenge

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Working in the basement level of the STEM building, using lots of power tools, and occasionally throwing out words like “kickoff,” “drivetrain,” or “STEAMworks,” we are FIRST team 3566, also known as Gone Fishin’.

Gone Fishin’ competes in the FIRST Robotics Competition. FIRST stands for “For Inspiration and Recognition of Science and Technology.” The robotics competition, open to any high school student, was created in order to promote the STEM fields and offer a competitive yet collaborative atmosphere for robotics. In the FIRST Robotics Competition (FRC), teams are given a challenge, in the form of a game, and then have six weeks to build a 120 pound, $10,000 robot to meet this challenge. After those six weeks are up, teams compete in various regional events. The ultimate goal is to go to the world championship, held in St. Louis, where around 800 teams gather to play the game. (more…)