Soap films help to solve mathematical problems (2/2/2011)
 | | Soap films help to solve mathematical problems. - 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, speaking to SINC. 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 emphasizes.
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.
Note: This story has been adapted from a news release issued by the FECYT - Spanish Foundation for Science and Technology
Post Comments:
| 
Subscribe
Tiny water creepy crawlies from South Korea and the Russian Far East
NASA satellite data helps pinpoint glaciers' role in sea level rise
Weather on the outer planets only goes so deep
Shattering the endurance record for small electric UAV
But what does it do?
Artificial forest for solar water-splitting
Sea level influenced tropical climate during the last ice age
World's smallest droplets
Using clay to grow bone
Grammar errors? The brain detects them even when you are unaware
Principles of locomotion in confined spaces could help robot teams work underground
Researchers perform fastest measurements ever made of ion channel proteins
Ultraresponsive magnetic nanoscavengers for next generation water purification
Do potatoes grow on vines? A review of the wild relatives of some favorite food plants
New discovery of ancient diet shatters conventional ideas of how agriculture emerged
Carnivorous plant throws out 'junk' DNA
Untangling the tree of life
More effective, cheaper concrete manufactured with ash from olive residue biomass
New quantitative analysis for open source software projects
High-volume Bitcoin exchanges less likely to fail, but more likely breached, says study
Computer scientists develop video game that teaches how to program in Java
Do palm trees hold the key to immortality?
Researchers show how we can do math problems unconsciously
Keep moving and have fun
New strategy for fingerprint visualization developed at Hebrew University
Children's bicycle helmets shown to be effective in impact and crush tests
How Usain Bolt can run faster -- effortlessly
Enhancing cognition in older adults also changes personality
Moth-inspired nanostructures take the color out of thin films
Robotic insects make first controlled flight
Seahorse's armor gives engineers insight into robotics designs
Insect-inspired camera captures wide field of view with no distortion, according to CU-Boulder study
Bed of needles
Not slippery when wet: Geckos adhere to surfaces submerged underwater
Cry me a river of possibility: Scientists design new adaptive material inspired by tears
Robot ants successfully mimic real colony behavior
Researchers unveil large robotic jellyfish that one day could patrol oceans
Sometimes, the rubber meets the road when you don't want it to