Upload

Loading icon Loading...

This video is unavailable.

Unexpected connections between three famous old formulas for pi part 4

Sign in to YouTube

Sign in with your Google Account (YouTube, Google+, Gmail, Orkut, Picasa, or Chrome) to like Experimental mathematics's video.

Sign in to YouTube

Sign in with your Google Account (YouTube, Google+, Gmail, Orkut, Picasa, or Chrome) to dislike Experimental mathematics's video.

Sign in to YouTube

Sign in with your Google Account (YouTube, Google+, Gmail, Orkut, Picasa, or Chrome) to add Experimental mathematics's video to your playlist.

Uploaded on Nov 18, 2010

Date: November 11, 2010
Speaker: Tom Osler, Rowan University
Title: Unexpected connections between three famous old formulas for pi
Abstract: In 1593 Vieta produced an infinite product for 2/pi in which the
factors are nested radicals. In 1656 John Wallis published his
"Arithmetica Infinitorum", in which he gave another infinite
product for pi/2. The Wallis product is very different as the
factors are rational numbers. In the same book, Wallis published
a continued fraction for 4/pi which he obtained from Lord
Brouncker. We will show how to morph the Wallis product into
Vieta's product. That this is possible is indeed a surprise. To
obtain this morphing we give a single formula that contains a
parameter "n". When n is zero, the formula produces the Wallis
product. When n = infinity, the formula gives Vieta's product.
As n increases 0, 1, 2, 3, ... we see the gradual transition form
a product of only rational numbers to a product of only nested
radicals. A second formula is given that allows us to morph
Brouncker's continued fraction into the Wallis product. Is there
a morphing between the product of Vieta and Brouncker's
continued fraction?

  • Category

  • License

    Standard YouTube License

Loading icon Loading...

Loading icon Loading...

Loading icon Loading...

The interactive transcript could not be loaded.

Loading icon Loading...

Loading icon Loading...

Ratings have been disabled for this video.
Rating is available when the video has been rented.
This feature is not available right now. Please try again later.

Loading icon Loading...

Loading...
Working...
to add this to Watch Later

Add to