(photo credit: )
Many natural objects such as flowers are "pre-programmed" to develop into delicate, beautiful and intricately shaped forms. Hebrew University physicists have managed to duplicate this process by starting with plain, flat surfaces.
Dr. Eran Sharon and coworkers Yael Klein and Efi Efrati at the HU's Racah Institute of Physics have succeeded in programming polymer sheets to bend and wrinkle by themselves into prescribed structures. Their work has just been described in Science.
They made flat discs of a soft gel that, when warmed gently, curved into domes, saddles and even sombrero shapes. Such shape control in a soft material could have applications ranging from optics to biomedicine. The sheets change shape because the gel - a web of cross-linked polymers - shrinks at temperatures above 33ÂºC to an amount determined by the local polymer density. When the density varies across the disc, the sheet buckles to relieve the pressure of uneven shrinkage. The researchers worked out what shrinkage patterns would produce the structures they wanted, then used an automated mixing system to produce "cocktails" of gels with the right properties.
The principle on which this is based is derived from differential geometry - the same principle used by Albert Einstein in his development of the general theory of relativity. This principle, by the way, is the one that gives us the curves in potato chips. The ability to create pre-planned, spontaneously formed objects, say the Jerusalem researchers, can have far-reaching effects for various manufacturing processes, or for creating structures that have to meet specific climatic conditions.
"Our work enables the creation of highly complex structures," says Sharon "which sometimes would be difficult to manufacture through regular industrial means." It also provides greater understanding of the ways in which complex structures such as flowers develop in nature, he added.
MATH LAB IN YOUR POCKET
A new University of Haifa development promises to make young people addicted to cellular phones appreciate how important mathematics can be. Prof. Michal Yerushalmy of the Institute for Educational Alternatives, together with Arik Weizman and Zohar Shavit of the computer sciences department, have developed a program that is installed on Java-enabled models of cellular phones and turns them into computers that can carry out a wide variety of mathematical applications, from elementary-school geometry to high-school differential mathematics. It can be downloaded free via www.math4mobile.com and requires a minimum screen resolution of 128 x 96 and recommended resolution of 176 x 208. Advice on using the program can be obtained via the Web site.
The program draws on material from the school curriculum but allows the use of graphs, solution of equations, calculation of derivatives, quadrilaterals, graphs and other functions on the cellular phone screen.
"I believe that mathematics must be taught by creating and not by rote learning," says Yerushalmi. "Just as there are physics and biology labs, there should be [easily accessible] math labs. Today, there are too few math labs in high schools, but now it can be accessed via cell phones. Pupils must understand how to reach formulas through situations that happen in daily life."
For example, if you are a 16-year-old waiting at a bus stop, trying to prepare for the pre-calculus exam, you take out your cellular phone, open the Math4Mobile Book and start learning. You can explore concepts and test your understanding by doing quizzes that your teacher stored on the class site. You are already on the bus when your friend calls and asks for help with an exercise. You exchange messages, attaching the diagrams you worked on and compare your attempts at solving the problem. When you feel ready, you send the exercises to your teacher. In the meantime you have arrived home. You check your teacher's comments on your PC and continue working from there.
University of Haifa students have completed a preliminary study of the program, photographing daily events such as the speed with which different-sized cups fill with water from a faucet, or the distance of a bus from the station. They were then instructed by Dr. Galit Botzer, who conducted the research, to turn their video clips into a mathematical model using the applications available on their cell phone.
"It was important for us to see whether or not the students actually use their phone as a medium for communication to help solve the problem. We found that they did indeed use text messaging to send one another information, questions and comments at different times and from different places. Our next step is to engage in more intensive research, and to develop additional, unique applications for cellular phones," said Botzer.
MATH STEREOTYPES UNDERMINE GIRLS
The stereotype that boys are better at math than girls might undermine girls' math performance, according to a study by Prof. Sian Beilock at the University of California-Santa Barbara and Prof. Allen McConnell of Miami University in Ohio. In addition, University of Chicago researchers also showed that stereotyping can hinder success in other academic areas because mental abilities do not immediately rebound after being compromised by anxiety.
If a girl takes the verbal portion of a standardized test after taking the mathematics portion, she may not do as well on the verbal portion as she would have if she had not been recently struggling with math-related anxiety, said Beilock. "Likewise, our work suggests that if a girl has a math class first thing in the morning and experiences math-related worries in this class, these worries may carry implications for her performance in the class she attends next," added Beilock, whose study appeared in the Journal of Experimental Psychology.