Featured Research

from universities, journals, and other organizations

New twist on ancient math problem could improve medicine, microelectronics

Date:
May 10, 2012
Source:
University of Michigan
Summary:
A hidden facet of a math problem that goes back to Sanskrit scrolls has just been exposed by nanotechnology researchers.

A hidden facet of a math problem that goes back to Sanskrit scrolls has just been exposed by nanotechnology researchers.
Credit: bivainis / Fotolia

A hidden facet of a math problem that goes back to Sanskrit scrolls has just been exposed by nanotechnology researchers at the University of Michigan and the University of Connecticut.

Related Articles


It turns out we've been missing a version of the famous "packing problem," and its new guise could have implications for cancer treatment, secure wireless networks, microelectronics and demolitions, the researchers say.

Called the "filling problem," it seeks the best way to cover the inside of an object with a particular shape, such as filling a triangle with discs of varying sizes. Unlike the traditional packing problem, the discs can overlap. It also differs from the "covering problem" because the discs can't extend beyond the triangle's boundaries.

"Besides introducing the problem, we also provided a solution in two dimensions," said Sharon Glotzer, U-M professor of chemical engineering.

That solution makes it immediately applicable to treating tumors using fewer shots with radiation beams or speeding up the manufacturing of silicon chips for microprocessors.

The key to solutions in any dimension is to find a shape's "skeleton," said Carolyn Phillips, a postdoctoral fellow at Argonne National Laboratory who recently completed her Ph.D. in Glotzer's group and solved the problem as part of her dissertation.

"Every shape you want to fill has a backbone that goes through the center of the shape, like a spine," she said.

For a pentagon, the skeleton looks like a stick-drawing of a starfish. The discs that fill the pentagon best will always have their centers on one of those lines.

Junctions between lines in the skeleton are special points that Glotzer's team refers to as "traps." The pentagon only has one trap, right at its center, but more complicated shapes can contain multiple traps. In most optimal solutions, each trap has a disc centered over it, Phillips said.

Other discs in the pattern change size and move around, depending on how many discs are allowed, but those over the traps are always the same. Phillips suspects that if a design uses enough discs, every trap will have a disc centered over it.

In their paper, published online May 10 in Physical Review Letters, the researchers report the rules for how to find the ideal size and spacing of the discs that fill a shape. In the future, they expect to reveal an algorithm that can take the desired shape and the number of discs, or the shape and percentage of the area to be filled, and spit out the best pattern to fill it.

Extending the approach into three dimensions, Glotzer proposes that it could decide the placement of wireless routers in a building where the signal must not be available to a potential hacker in the parking lot. Alternatively, it could help demolition workers to set off precision explosions, ensuring that the blast covers the desired region but doesn't extend beyond a building's outer walls.

Phillips expects filling solutions to be scientifically useful as well. Glotzer's team developed the new problem by trying to find a way to represent many-sided shapes for their computer models of nanoparticles. In addition to nanotechnology, biology and medicine often need models for complex shapes, such as those of proteins.

"You don't want to model every single one of the thousands of atoms that make up this protein," Phillips said. "You want a minimal model that gives the shape, allowing the proteins to interact in a lock-and-key way, as they do in nature."

The filling approach may prove a perfect fit for a variety of fields.


Story Source:

The above story is based on materials provided by University of Michigan. The original article was written by Katherine McAlpine. Note: Materials may be edited for content and length.


Journal Reference:

  1. Carolyn Phillips, Joshua Anderson, Greg Huber, Sharon Glotzer. Optimal Filling of Shapes. Physical Review Letters, 2012; 108 (19) DOI: 10.1103/PhysRevLett.108.198304

Cite This Page:

University of Michigan. "New twist on ancient math problem could improve medicine, microelectronics." ScienceDaily. ScienceDaily, 10 May 2012. <www.sciencedaily.com/releases/2012/05/120510132715.htm>.
University of Michigan. (2012, May 10). New twist on ancient math problem could improve medicine, microelectronics. ScienceDaily. Retrieved November 28, 2014 from www.sciencedaily.com/releases/2012/05/120510132715.htm
University of Michigan. "New twist on ancient math problem could improve medicine, microelectronics." ScienceDaily. www.sciencedaily.com/releases/2012/05/120510132715.htm (accessed November 28, 2014).

Share This


More From ScienceDaily



More Computers & Math News

Friday, November 28, 2014

Featured Research

from universities, journals, and other organizations


Featured Videos

from AP, Reuters, AFP, and other news services

EU Pushes Google For Worldwide Right To Be Forgotten

EU Pushes Google For Worldwide Right To Be Forgotten

Newsy (Nov. 27, 2014) Privacy regulators recommend Google expand its requested removals to apply to all its web domains. Video provided by Newsy
Powered by NewsLook.com
Predictions Of Tablets' Demise Sound Familiar

Predictions Of Tablets' Demise Sound Familiar

Newsy (Nov. 26, 2014) The tablet's days are numbered, at least according to a recent IDC report. The market-research firm paints a grim outlook for tablets. Video provided by Newsy
Powered by NewsLook.com
Today's Prostheses Are More Capable Than Ever

Today's Prostheses Are More Capable Than Ever

Newsy (Nov. 26, 2014) Advances in prosthetics are making replacement body parts stronger and more lifelike than they’ve ever been. Video provided by Newsy
Powered by NewsLook.com
FCC Forces T-Mobile To Alert Customers Of Data Throttling

FCC Forces T-Mobile To Alert Customers Of Data Throttling

Newsy (Nov. 25, 2014) T-Mobile and the FCC have reached an agreement requiring the company to alert customers when it throttles their data speeds. 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:

Strange & Offbeat Stories


Space & Time

Matter & Energy

Computers & Math

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