Featured Research

from universities, journals, and other organizations

140-year-old Math Problem Solved

Date:
March 4, 2008
Source:
Imperial College London
Summary:
A problem which has defeated mathematicians for almost 140 years has now been solved. The breakthrough is in an area of mathematics known as conformal mapping, a key theoretical tool used by mathematicians, engineers and scientists to translate information from a complicated shape to a simpler circular shape so that it is easier to analyze. Key additions have been made to the Schwarz-Christoffel formula.

A problem which has defeated mathematicians for almost 140 years has been solved by a researcher at Imperial College London. Professor Darren Crowdy, Chair in Applied Mathematics, has made the breakthrough in an area of mathematics known as conformal mapping, a key theoretical tool used by mathematicians, engineers and scientists to translate information from a complicated shape to a simpler circular shape so that it is easier to analyse.

This theoretical tool has a long history and has uses in a large number of fields including modelling airflow patterns over intricate wing shapes in aeronautics. It is also currently being used in neuroscience to visualise the complicated structure of the grey matter in the human brain.

A formula, now known as the Schwarz-Christoffel formula, was developed by two mathematicians in the mid-19th century to enable them to carry out this kind of mapping. However, for 140 years there has been a deficiency in this formula: it only worked for shapes that did not contain any holes or irregularities.

Now Professor Crowdy has made additions to the famous Schwarz-Christoffel formula which mean it can be used for these more complicated shapes. He explains the significance of his work, saying:

"This formula is an essential piece of mathematical kit which is used the world over. Now, with my additions to it, it can be used in far more complex scenarios than before. In industry, for example, this mapping tool was previously inadequate if a piece of metal or other material was not uniform all over - for instance, if it contained parts of a different material, or had holes."

Professor Crowdy's work has overcome these obstacles and he says he hopes it will open up many new opportunities for this kind of conformal mapping to be used in diverse applications.

"With my extensions to this formula, you can take account of these differences and map them onto a simple disk shape for analysis in the same way as you can with less complex shapes without any of the holes," he added.

Professor Crowdy's improvements to the Schwarz-Christoffel formula were published in the March-June 2007 issue of Mathematical Proceedings of the Cambridge Philosophical Society.

Journal reference: 'Schwarz-Christoffel mappings to unbounded multiply connected polygonal regions,' Math. Proc. Camb. Phil. Soc. (2007), 142, 319.


Story Source:

The above story is based on materials provided by Imperial College London. Note: Materials may be edited for content and length.


Cite This Page:

Imperial College London. "140-year-old Math Problem Solved." ScienceDaily. ScienceDaily, 4 March 2008. <www.sciencedaily.com/releases/2008/03/080303110214.htm>.
Imperial College London. (2008, March 4). 140-year-old Math Problem Solved. ScienceDaily. Retrieved April 17, 2014 from www.sciencedaily.com/releases/2008/03/080303110214.htm
Imperial College London. "140-year-old Math Problem Solved." ScienceDaily. www.sciencedaily.com/releases/2008/03/080303110214.htm (accessed April 17, 2014).

Share This



More Computers & Math News

Thursday, April 17, 2014

Featured Research

from universities, journals, and other organizations


Featured Videos

from AP, Reuters, AFP, and other news services

German Researchers Crack Samsung's Fingerprint Scanner

German Researchers Crack Samsung's Fingerprint Scanner

Newsy (Apr. 16, 2014) German researchers have used a fake fingerprint made from glue to bypass the fingerprint security system on Samsung's new Galaxy S5 smartphone. Video provided by Newsy
Powered by NewsLook.com
Twitter, Apple Social Data Purchases Likely to Spur More Mergers and Acquisitions

Twitter, Apple Social Data Purchases Likely to Spur More Mergers and Acquisitions

TheStreet (Apr. 16, 2014) The social media data space is likely to see more mergers and acquisitions following Twitter Inc.'s acquisition of tweet analyzer Gnip Inc. on Tuesday and Apples Inc.'s purchase of Topsy Labs Inc. back in December. One firm in particular, the U.K.'s DataSift Inc., could be on the list of potential buyers. Among other social media startups that could be ripe for picking is Banjo, whose mobile app provides aggregated content by topic and location. Banjo could also be a good fit for Twitter. Video provided by TheStreet
Powered by NewsLook.com
Bitcoin Exchange Mt. Gox to Liquidate After Rebuilding Rejected

Bitcoin Exchange Mt. Gox to Liquidate After Rebuilding Rejected

TheStreet (Apr. 16, 2014) Bitcoin exchange Mt. Gox has agreed to liquidate after a Japanese court rejected its plans to rebuild, according to a report by the Wall Street Journal. Mt. Gox filed for bankruptcy protection in February after announcing about 850,000 bitcoins, worth around $454 million at today's rates, may have been stolen by hackers. It has since recovered 200,000 of the missing bitcoins. The court put Mt. Gox's assets under a provisional administrator's control until bankruptcy proceedings begin. Video provided by TheStreet
Powered by NewsLook.com
BlackBerry: The Crash That Launched 1,000 Startups

BlackBerry: The Crash That Launched 1,000 Startups

Reuters - Business Video Online (Apr. 16, 2014) Tech startups in BlackBerry's hometown of Waterloo, Ontario, are tapping talent from the struggling smartphone company and filling the void left in the region by its meltdown. Reuters correspondent Euan Rocha visits the region that could become Canada's Silicon Valley. Video provided by Reuters
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