**Problem Solving**

### Poles and Polars

*by Maxwell Zen*| April 2021

An introduction to poles and polars. Along the way, many important theorems, such as La Hire's Theorem, Pascal's Theorem, and the Fundamental Theorem of Poles and Polars, will be introduced in order to further explore this interesting topic.

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### Conic Sections

*by Josiah Moltz*| April 2021

Introduction to conic sections. A cone is a figure in which a circular base tapers to a single point. A Hyperbola comes when a plane splits a cone into 4 different sections.

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### Harmonic Geometry

*by John Gupta-She*| April 2021

Harmonic, or projective, geometry is a special way of looking at ratios in a geometric figure. Many difficult problems can be solved with only the two most important constructions.

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### Complex Numbers

*by Hunter Pesin*| March 2021

Some properties of complex numbers entail how arithmetic in its polar form is conducted, its geometric connection, and how complex numbers behave like binomials.

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### A Combinatorial Identity

*by Declan Stacy*| March 2021

Let S be the set of n-tuples A=(a_1, a_2, ..., a_n) such that a_i >=0. A summation question and solution.

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### Marbles

*by Declan Stacy*| Feb 2021

Johnny has a bag of marbles with n red marbles and n blue marbles. What is the probability that he goes through the entire bag before stopping?

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### Calculating a Fixed Distance

*by Benjamin Gallai, Khizer Shahid*| June 2020

An alternate derivation of a well known sum from Calculus.

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### Conditional Probability

*by Declan Stacy*| June 2020

An introduction to conditional probability and the most important theorems relating to it. At the end, there are interesting problems to try and solutions.

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### Conditional Probability Problem Set

*by Declan Stacy*| June 2020

Solutions to the Conditional Probability Problem Set

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### Generating Functions

*by Khizer Shahid, Benjamin Gallai*| June 2020

Using Generating Functions to Compute Infinite Series.

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