Featured Research

from universities, journals, and other organizations

Mathematicians develop new method for describing extremely complicated shapes

Date:
July 30, 2012
Source:
American Institute of Physics (AIP)
Summary:
Building a bridge between topology and fractals may lead to a new way of describing tiny defects in metal or the froth of a breaking wave.

Mathematicians at the Institute for Advanced Study in New Jersey "bridged" topology and fractals and made a discovery that could lead to a new way of describing extremely complicated shapes such as the configuration of the tiniest defects in a metal or even the froth of a breaking wave.

Topology is a powerful branch of mathematics that looks at qualitative geometric properties such as the number of holes a geometric shape contains, while fractals are extremely complicated geometric shapes that appear similarly complicated even when viewed under a microscope of high magnification.

Bridging the topology and fractals, as described in the American Institute of Physics' Journal of Mathematical Physics (JMP), relies upon a recently developed mathematical theory, known as "persistent homology," which takes into account the sizes and number of holes in a geometric shape. The work described in JMP is a proof of concept based on fractals that have already been studied by other methods -- such as the shapes assumed by large polymer molecules as they twist or bend under random thermal fluctuation.

Many geometric structures with fractal-like complexity arise in nature, such as the configuration of defects in a metal or the froth of a breaking wave. Their geometry has important physical effects too, but until now we haven't had a vocabulary rich enough to adequately describe these and other complicated shapes. The mathematicians plan to use the vocabulary provided by persistent homology methods to investigate and describe complicated shapes in a whole new way.


Story Source:

The above story is based on materials provided by American Institute of Physics (AIP). Note: Materials may be edited for content and length.


Journal Reference:

  1. Robert MacPherson, Benjamin Schweinhart. Measuring shape with topology. Journal of Mathematical Physics, 2012; 53 (7): 073516 DOI: 10.1063/1.4737391

Cite This Page:

American Institute of Physics (AIP). "Mathematicians develop new method for describing extremely complicated shapes." ScienceDaily. ScienceDaily, 30 July 2012. <www.sciencedaily.com/releases/2012/07/120730094136.htm>.
American Institute of Physics (AIP). (2012, July 30). Mathematicians develop new method for describing extremely complicated shapes. ScienceDaily. Retrieved September 2, 2014 from www.sciencedaily.com/releases/2012/07/120730094136.htm
American Institute of Physics (AIP). "Mathematicians develop new method for describing extremely complicated shapes." ScienceDaily. www.sciencedaily.com/releases/2012/07/120730094136.htm (accessed September 2, 2014).

Share This




More Computers & Math News

Tuesday, September 2, 2014

Featured Research

from universities, journals, and other organizations


Featured Videos

from AP, Reuters, AFP, and other news services

Google Teases India Event, Possible Android One Reveal

Google Teases India Event, Possible Android One Reveal

Newsy (Sep. 1, 2014) Google has announced a Sept. 15 event in India during which they're expected to reveal their Android One phones. Video provided by Newsy
Powered by NewsLook.com
Google's Self-Driving Car Still Has Many Flaws

Google's Self-Driving Car Still Has Many Flaws

Newsy (Sep. 1, 2014) You've seen a lot of Google's self-driving car, but that doesn't mean it's coming soon. A new report says the vehicle is nowhere near road ready. Video provided by Newsy
Powered by NewsLook.com
Apple's Rumored iWatch Could Cost $400

Apple's Rumored iWatch Could Cost $400

Newsy (Aug. 31, 2014) Apple is expected to charge a premium for its still-rumored wearable device. Video provided by Newsy
Powered by NewsLook.com
Amazon Chases Netflix And HBO With Five New Pilots

Amazon Chases Netflix And HBO With Five New Pilots

Newsy (Aug. 31, 2014) Amazon has released another batch of five pilots, allowing viewers to vote on which shows will get full seasons on the company's streaming service. Video provided by Newsy
Powered by NewsLook.com

Search ScienceDaily

Number of stories in archives: 140,361

Find with keyword(s):
Enter a keyword or phrase to search ScienceDaily for related topics and research stories.

Save/Print:
Share:

Breaking News:
from the past week

In Other News

... from NewsDaily.com

Science News

Health News

Environment News

Technology News



Save/Print:
Share:

Free Subscriptions


Get the latest science news with ScienceDaily's free email newsletters, updated daily and weekly. Or view hourly updated newsfeeds in your RSS reader:

Get Social & Mobile


Keep up to date with the latest news from ScienceDaily via social networks and mobile apps:

Have Feedback?


Tell us what you think of ScienceDaily -- we welcome both positive and negative comments. Have any problems using the site? Questions?
Mobile: iPhone Android Web
Follow: Facebook Twitter Google+
Subscribe: RSS Feeds Email Newsletters
Latest Headlines Health & Medicine Mind & Brain Space & Time Matter & Energy Computers & Math Plants & Animals Earth & Climate Fossils & Ruins