We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
from Appendices
Ever since I first learned of the Borsuk-Ulam theorem as an undergraduate I wondered if there was a straightforward approach to understanding why it was true. It wasn't until I witnessed the work of youngsters in the Spring of 2008 that I saw it. The following article appeared in the November 2008 issue of FOCUS (volume 28, number 8), the news magazine of the Mathematical Association of America. The proof was also the topic of the October 2008 St. Mark's Institute of Mathematics newsletter.
An Intuitive Approach to the Borsuk-Ulam Theorem
By Alex Bishop, Adam Cimpeanu, Kyle Flood, Bianca Homberg, Steven Homberg, Eric Marriott, Jeffrey Roth, Linus Schultz, William Sherman, Alex Smith, Geoffrey Smith and James Tanton of the St. Mark's Institute of Mathematics.
Each semester I offer extracurricular mathematics courses for math-interested students, ages 11–18, keen to experience mathematics as a creative and organic enterprise. Called research classes, they introduce students to the joys and frustrations of the research experience, of not knowing, of feeling around in the dark, and of finding the fortitude of mind to concentrate on complex issues for sustained periods. (Weeks, not just minutes.) This semester the coauthors of this paper established the classic Borsuk-Ulam Theorem in a way that is slick, intuitive, and accessible. Their success speaks to the joy and value that can be found for all in allowing mathematical creativity to bubble forth, no matter the age and the background experience of the mathematical artists!
To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.
