140-year-old math problem solved by researcher
March 3, 2008A 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.
Citation: 'Schwarz-Christoffel mappings to unbounded multiply connected polygonal regions,' Math. Proc. Camb. Phil. Soc. (2007), 142, 319.
Source: Imperial College London
-
Nanotube growth theory experimentally confirmed
Jan 30, 2012 |
4.9 / 5 (10) |
1
-
Latest gadgets give diets, workouts a high-tech boost
Jan 20, 2012 |
5 / 5 (1) |
0
-
Seeing the world of nanotechnology from a single-molecule perspective
Aug 22, 2011 |
5 / 5 (1) |
0
-
Space shuttle's science brought payoffs to Earth
Jul 18, 2011 |
5 / 5 (4) |
2
-
Centuries-old math formula helps map galaxy clusters
Jun 09, 2011 |
4.5 / 5 (4) |
3
-
Engineers build first sub-10-nm carbon nanotube transistor
Feb 01, 2012 |
4.9 / 5 (33) |
30
-
Something old, something new: Evolution and the structural divergence of duplicate genes
Jan 31, 2012 |
4.6 / 5 (7) |
1
-
The hidden nanoworld of ice crystals: Revealing the dynamic behavior of quasi-liquid layers
Jan 30, 2012 |
5 / 5 (4) |
1
-
Stock market network reveals investor clustering
Jan 27, 2012 |
3.9 / 5 (23) |
8
-
Of microchemistry and molecules: Electronic microfluidic device synthesizes biocompatible probes
Jan 26, 2012 |
5 / 5 (2) |
0
-
Probability Question - Chances Of Meeting Again
1 hour ago
-
Young Diagrams
8 hours ago
-
transforming from polar to parametric functions
8 hours ago
-
Validity of proof method -- error in book?
9 hours ago
-
Finding intersections
Feb 11, 2012
-
Interpreting a function based on it's equation.
Feb 11, 2012
- More from Physics Forums - General Math
More news stories
A frank discussion of the power law and linking correlation to causation
(PhysOrg.com) -- Michael Stumpf a mathematics professor at Imperial College in London, and Mason Porter a lecturer at Oxford have teamed together to write and publish a perspective piece in Science regarding the in ...
US workers are 'giving away the store,' costing firms billions
Nearly 70 percent of the nation's service employees give away free goods and services from hamburgers to cable TV costing companies billions of dollars a year, according to a groundbreaking study.
Other Sciences / Economics & Business
Feb 09, 2012 |
3 / 5 (5) |
11
Employers feel no love for unscrupulous practice of 'service sweethearting'
A new study led by two Florida State University marketing professors finds that some frontline service employees who are rewarded for hikes in customer loyalty and satisfaction also may engage in "service ...
Other Sciences / Economics & Business
Feb 10, 2012 |
3.3 / 5 (3) |
10
New insights into how to correct false knowledge
The abundance of false information available on the Internet, in movies and on TV has created a big challenge for educators.
Other Sciences / Social Sciences
Feb 07, 2012 |
4.9 / 5 (7) |
9
|
Neanderthal demise due to many influences, including cultural changes: study
As an ice age crept upon them thousands of years ago, Neanderthals and modern human ancestors expanded their territory ranges across Asia and Europe to adapt to the changing environment.
Other Sciences / Archaeology & Fossils
Feb 07, 2012 |
4.4 / 5 (5) |
8
|
Japan's Fukushima reactor may be reheating: operator
Temperature readings at one of the crippled Fukushima nuclear reactors have risen above Japan's stringent new safety standard but there was no immediate danger, its operator said Sunday.
Scientists discover molecular secrets of 2,000-year-old Chinese herbal remedy
For roughly two thousand years, Chinese herbalists have treated Malaria using a root extract, commonly known as Chang Shan, from a type of hydrangea that grows in Tibet and Nepal. More recent studies suggest that halofuginone, ...
New method to examine batteries -- MRI from the inside
There is an ever-increasing need for advanced batteries for portable electronics, such as phones, cameras, and music players, but also to power electric vehicles and to facilitate the distribution and storage of energy derived ...
Google might launch Drive for cloud storage soon
(PhysOrg.com) -- Google's next big move, according to the Wall Street Journal, is a cloud storage service called Drive. Hardly first to the plate, Google is simply catching up to introducing its cloud reposi ...
A mitosis mystery solved: How chromosomes align perfectly in a dividing cell
Although the process of mitotic cell division has been studied intensely for more than 50 years, Whitehead Institute researchers have only now solved the mystery of how cells correctly align their chromosomes during symmetric ...
Lab study raises questions over nano-particle impact
Tests involving chickens have raised questions about the impact on health from engineered nano-particles, the ultra-fine grains commonly used in drugs and processed foods, scientists said on Sunday.
Mar 03, 2008
Rank: not rated yet
Mar 03, 2008
Rank: not rated yet