Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:


Getting a handle on minimal surfaces


The top image is a traditional helicoid. The bottom one has a hole in it that would become a handle if the shape were completely untwisted into a flat surface.

IU mathematician helps solve old problem that may have new applications

A twisted soap bubble with a handle?

If you find that hard to visualize, it’s understandable. Experts had thought for more than 200 years that such a structure was not even mathematically possible. But no longer.

In a paper published in the Nov. 15 issue of Proceedings of the National Academy of Sciences, mathematicians Matthias Weber of Indiana University, David Hoffman of Stanford University, and Michael Wolf of Rice University presented a proof of the existence of a new minimal surface they call a genus one helicoid.

"This proof tells us that our intuition was not quite right about what is possible and what is not possible," Weber said. "Probably one reason it was not discovered sooner is that no one imagined that something like this could exist."

A helicoid is what results when one of the simplest shapes -- a flat plane -- is twisted an infinite number of times. If the helicoid is vertical, its shape resembles a spiral parking ramp.

The new surface looks much like this traditional helicoid with an extra feature: a handle such as one finds on a coffee mug. It turns out that on one "floor" of the parking ramp there is an additional column -- the handle.

All minimal surfaces have something important in common: a minimal surface area.

"A minimal surface is formed when the pressure on both sides of a surface is the same," Weber explained. "’For example, when you dip a bent coat hanger into soapy water, the soap bubble that forms on the hanger is a minimal surface." These soap bubbles can have various shapes, depending on the shape of the coat hanger, but in every case the bubble is trying to minimize surface tension, he said. This happens when the bubble has the smallest possible surface area.

At every point, a minimal surface is either flat or shaped like a saddle or a potato chip.

Minimal surfaces are proving to be important at the molecular level. "Minimal surfaces actually occur in nature at the nanoscale as interfaces between certain substances," Weber said. An example is some copolymers that are plastics used to make new kinds of fabrics. When these copolymers are mixed, there are interfaces between them that are minimal surfaces. Knowing what these interfaces look like can help in determining what the chemical properties of the mixture will be.

Minimal surfaces are extremely stable as physical objects, Weber pointed out, and this can be an advantage in many kinds of structures. He has heard from architects who have seen computerized illustrations of some of his minimal surfaces and are intrigued by the possibility of adapting them to structures, both interior and exterior. He has exchanged information about minimal surfaces with some architects and is exploring ways to collaborate with them.

Calendars are another use for this work, highlighting the aesthetic qualities of minimal surfaces. These aesthetic qualities are on vivid display in Weber’s computer gallery of minimal surfaces at, which shows minimal-surface objects set in imaginary landscapes.

"The images in the gallery are not intended as illustrations of mathematical facts," Weber said. "They more than fulfill their purpose if people see them and can feel some of the intriguing enchantment that a mathematician feels when exploring the mathematical objects."

In a second gallery at the pictures do illustrate mathematical facts. "This is the most comprehensive collection of minimal surfaces available," Weber said. "Users can download programs that recreate the surfaces, allowing them to conduct numerical and visual experiments."

A detailed article about the helicoid discovered by Weber and his co-workers can be found in the Dec. 17 issue of Science News at

The mathematicians’ complete proof is more than 100 pages long. The abstract of their report in Proceedings of the National Academy of Sciences is available at

Weber can be reached at 812-855-8724 or

Matthias Weber | EurekAlert!
Further information:

More articles from Physics and Astronomy:

nachricht Move over, lasers: Scientists can now create holograms from neutrons, too
21.10.2016 | National Institute of Standards and Technology (NIST)

nachricht Finding the lightest superdeformed triaxial atomic nucleus
20.10.2016 | The Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences

All articles from Physics and Astronomy >>>

The most recent press releases about innovation >>>

Die letzten 5 Focus-News des innovations-reports im Überblick:

Im Focus: New 3-D wiring technique brings scalable quantum computers closer to reality

Researchers from the Institute for Quantum Computing (IQC) at the University of Waterloo led the development of a new extensible wiring technique capable of controlling superconducting quantum bits, representing a significant step towards to the realization of a scalable quantum computer.

"The quantum socket is a wiring method that uses three-dimensional wires based on spring-loaded pins to address individual qubits," said Jeremy Béjanin, a PhD...

Im Focus: Scientists develop a semiconductor nanocomposite material that moves in response to light

In a paper in Scientific Reports, a research team at Worcester Polytechnic Institute describes a novel light-activated phenomenon that could become the basis for applications as diverse as microscopic robotic grippers and more efficient solar cells.

A research team at Worcester Polytechnic Institute (WPI) has developed a revolutionary, light-activated semiconductor nanocomposite material that can be used...

Im Focus: Diamonds aren't forever: Sandia, Harvard team create first quantum computer bridge

By forcefully embedding two silicon atoms in a diamond matrix, Sandia researchers have demonstrated for the first time on a single chip all the components needed to create a quantum bridge to link quantum computers together.

"People have already built small quantum computers," says Sandia researcher Ryan Camacho. "Maybe the first useful one won't be a single giant quantum computer...

Im Focus: New Products - Highlights of COMPAMED 2016

COMPAMED has become the leading international marketplace for suppliers of medical manufacturing. The trade fair, which takes place every November and is co-located to MEDICA in Dusseldorf, has been steadily growing over the past years and shows that medical technology remains a rapidly growing market.

In 2016, the joint pavilion by the IVAM Microtechnology Network, the Product Market “High-tech for Medical Devices”, will be located in Hall 8a again and will...

Im Focus: Ultra-thin ferroelectric material for next-generation electronics

'Ferroelectric' materials can switch between different states of electrical polarization in response to an external electric field. This flexibility means they show promise for many applications, for example in electronic devices and computer memory. Current ferroelectric materials are highly valued for their thermal and chemical stability and rapid electro-mechanical responses, but creating a material that is scalable down to the tiny sizes needed for technologies like silicon-based semiconductors (Si-based CMOS) has proven challenging.

Now, Hiroshi Funakubo and co-workers at the Tokyo Institute of Technology, in collaboration with researchers across Japan, have conducted experiments to...

All Focus news of the innovation-report >>>



Event News

#IC2S2: When Social Science meets Computer Science - GESIS will host the IC2S2 conference 2017

14.10.2016 | Event News

Agricultural Trade Developments and Potentials in Central Asia and the South Caucasus

14.10.2016 | Event News

World Health Summit – Day Three: A Call to Action

12.10.2016 | Event News

Latest News

Resolving the mystery of preeclampsia

21.10.2016 | Health and Medicine

Stanford researchers create new special-purpose computer that may someday save us billions

21.10.2016 | Information Technology

From ancient fossils to future cars

21.10.2016 | Materials Sciences

More VideoLinks >>>