Poles and Polars
by Maxwell Zen
An introduction to poles and polars, a powerful concept in geometry that can solve many complex problems with just a couple key observations.
From the Editor
At Math and CS Research, we aim to inform and entertain the public about mathematics and computer science, one paper at a time. The year 2020 has been marked by a pandemic that has uprooted all our lives but we have only been more committed to our mission. While schools adapted to online learning, businesses suspended operations, and many others shifted to remote work, we have been tirelessly at work on the edition you now read.
In this edition, we bring to you a view of the stock market through computer science, math in language, new robot dogs, a history of geometry, and a generalization of friends meeting. We have also attached photos of mathematics in the real world, a special puzzle, and an examination of the mental health of students in the time of COVID-19. I hope that the work of a group of high school students may reveal a part of the beauty of mathematics and computer science I know and love, even if it is just a small part of it.
When I scribble away at my paper, exploring the properties of different numbers, I become enthralled by the scenes that fold before my eyes. That is precisely the feeling that drives many of the mathematicians and computer scientists at this publication. By welcoming diverse articles, I hope that we may impart a little part of our joy to you, the reader. Whether you are another math or computer science fanatic, or simply exploring a new interest, we hope you uncover a part of the complex and boundless secrets of math and computer science.
Finally, I would like to thank everyone who made the publication of this edition possible:
- To Jerry, thank you for leading all our non-writing and writing departments, contributors, and editors to their full potential. Your heartfelt leadership, deep care for mathematics and computer science, and great knowledge in the fields keeps this publication running everyday. Your guidance to every contributor and unique friendship creates the close community our contributors love.
- To Mario, thank you for working to ensure the flawless publication of Math and CS Research. The writers of this publication are grateful for your immaculate attention to detail and deep knowledge of math and computer science.
- To Theo, Alvin, and Vincent, thank you for your dedication in ensuring the quality of the articles of this publication. Your guides and edits allow the depth of writing few high school students can be expected to achieve.
- To Jennifer, Andrea, and Ezra, thank you for connecting to our readers in every way you can. Whether it be through art and photos, or business relations, you help us reveal another side of mathematics and computer science.
- To all the contributors of Math and CS Research, thank you for bringing the value and beauty of mathematics and computer science to the public, one paper at a time. Despite the pandemic and a new virtual setting, you remained selflessly determined to share your joy with others in these hard times.
Informing readers, one paper at a time.
Math and CS Research is a nonprofit mathematics and computer science publication written and produced entirely by students. The publication has four writing departments: math, CS, puzzles, features; and five non-writing departments: art, photo, literary, layout, business, photo.
Math and CS Research aims to inform and entertain students through a variety of different articles about mathematics and computer science. The publication encourages conversation and interest by providing editors, writers, and readers with a platform to express and exchange ideas in mathematics and computer science. Articles and other published material may range in topics including: applied mathematics, problem solving, math research, computer science, features, and puzzles.
The publication strives to uphold professional standards of mathematical excellence and create interest in deeper math exploration. Every article is reviewed and edited multiple times by a literary editor, departmental editor, associate editor, and Editor-in-Chief for accuracy, clarity, originality, and relevance. Accepted articles are expected to be innovative in thought and ideas. We have previously published articles ranging in topics from the election cycle forecasts to COVID-19 to conditional probability.