Featured Research

from universities, journals, and other organizations

Soap films help to solve mathematical problems

Date:
January 27, 2011
Source:
FECYT - Spanish Foundation for Science and Technology
Summary:
Soap bubbles and films have always fascinated children and adults, but they can also serve to solve complex mathematical calculations. This is shown by a study carried out by two professors who have succeeded in solving classic problems using just such an innovative procedure.

Soap films help to solve mathematical problems.
Credit: Criado et al.

Soap bubbles and films have always fascinated children and adults, but they can also serve to solve complex mathematical calculations. This is shown by a study carried out by two professors at the University of Málaga, who have succeeded in solving classic problems using just such an innovative procedure.

"With the aid of soap films we have solved variational mathematical problems, which appear in the formulation of many physical problems," explains Carlos Criado, professor at the University of Málaga. Together with his colleague Nieves Álamo, he has just published his work in the American Journal of Physics.

Soap films always adopt the shape which minimises their elastic energy, and therefore their area, so that they turn out to be ideal in the calculus of variations, "where we look for a function that minimises a certain quantity (depending on the function)," adds the researcher.

"Of course there are other ways to solve variational problems, but it turns out to be surprising, fun and educative to obtain soap films in the shape of brachistochrones, catenaries and semicircles," Criado emphasises.

The professor offers the example of the famous problem of the brachistochrone curve. What shape must a wire be in order that a ball travels down it from one end to the other (at a different height) as rapidly as possible? The answer is the brachistochrone (from the Greek brachistos, the shortest, and cronos, time), the curve of fastest descent.

New methods for old problems

The mathematician Johann Bernoulli found the answer centuries ago when he realised that it was a cycloid (the curve described by a point on a circle rolling along a line). That was the origin of the calculus of variations, which was also used in other classic problems, like that of the catenary (the shape of a chain suspended by its endpoints) and the isoperimetric curve (a curve which maximises the area it encloses).

The study shows that these calculations may be related to Plateau's problem, that is, to find the shape adopted by a soap film under certain boundary restrictions. Besides, the researchers show how to design the experiments, constraining the soap films between two surfaces in such a way as to obtain the appropriate curves.

Other Spanish researchers, like Isabel Fernández, of the University of Seville, and Pablo Mira, of the Polytechnic University of Cartagena, have succeeded in finding for the first time the solution to specific mathematical problems (the Bernstein problem in the Heisenberg space) with the help of soap films.


Story Source:

The above story is based on materials provided by FECYT - Spanish Foundation for Science and Technology. Note: Materials may be edited for content and length.


Journal Reference:

  1. C. Criado, N. Alamo. Solving the brachistochrone and other variational problems with soap films. American Journal of Physics, 2010; 78 (12): 1400 DOI: 10.1119/1.3483276

Cite This Page:

FECYT - Spanish Foundation for Science and Technology. "Soap films help to solve mathematical problems." ScienceDaily. ScienceDaily, 27 January 2011. <www.sciencedaily.com/releases/2011/01/110125123235.htm>.
FECYT - Spanish Foundation for Science and Technology. (2011, January 27). Soap films help to solve mathematical problems. ScienceDaily. Retrieved April 24, 2014 from www.sciencedaily.com/releases/2011/01/110125123235.htm
FECYT - Spanish Foundation for Science and Technology. "Soap films help to solve mathematical problems." ScienceDaily. www.sciencedaily.com/releases/2011/01/110125123235.htm (accessed April 24, 2014).

Share This



More Computers & Math News

Thursday, April 24, 2014

Featured Research

from universities, journals, and other organizations


Featured Videos

from AP, Reuters, AFP, and other news services

Monkeys Are Better At Math Than We Thought, Study Shows

Monkeys Are Better At Math Than We Thought, Study Shows

Newsy (Apr. 23, 2014) — A Harvard University study suggests monkeys can use symbols to perform basic math calculations. Video provided by Newsy
Powered by NewsLook.com
High Court to Hear Dispute of TV Over Internet

High Court to Hear Dispute of TV Over Internet

AP (Apr. 22, 2014) — The future of Aereo, an online service that provides over-the-air TV channels, hinges on a battle with broadcasters that goes before the U.S. Supreme Court on Tuesday. (April 22) Video provided by AP
Powered by NewsLook.com
Aereo Takes on Broadcast TV Titans in Supreme Court Today

Aereo Takes on Broadcast TV Titans in Supreme Court Today

TheStreet (Apr. 22, 2014) — Aereo heads to the Supreme Court today to fight for its right to stream broadcast TV over the Internet -- against broadcasters who say the start-up infringes upon copyright law. TheStreet Deputy Managing Editor Leon Lazaroff explains the importance of the case in the TV industry and details what the outcome of it could mean for broadcasters and for cloud storage services -- as Aereo allows its subscribers to not just watch live TV shows but also store content to a DVR in the cloud. Video provided by TheStreet
Powered by NewsLook.com
Lytro Introduces 'Illum,' A Professional Light-Field Camera

Lytro Introduces 'Illum,' A Professional Light-Field Camera

Newsy (Apr. 22, 2014) — The light-field photography engineers at Lytro unveiled their next innovation: a professional DSLR-like camera called "Illum." 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