An ancient facet of a math problem could have implications for cancer treatment, secure wireless networks, microelectronics and demolitions, according to researchers at the University of Michigan and the University of Connecticut.
The math problem dates back to Sanskrit scrolls, but has only just been exposed by nanotechnology researchers. According to the ancient text we have been missing a version of the famous "packing problem," and its new guise could have big implications on the medical industry as well as computer science and construction industries.
The mathematical equation is called the ‘filing problem’, and it seeks out the best way of filling an object with a particular shape. Contrary to the traditional ‘packing problem’, the discs can overlap. It also differs from the ‘covering problem’, in that the disks can't extend beyond the triangle's boundaries.
Sharon Glotzer, U-M professor of chemical engineering said: "Besides introducing the problem, we also provided a solution in two dimensions.” This is what makes it applicable to treating tumours using fewer shots with radiation beams or speeding up the manufacturing of silicon chips for microprocessors.
Carolyn Phillips explains that the key to finding a solution in any dimension is to find the shape’s skeleton. Ms Phillips is a postdoctoral fellow at Argonne National Laboratory, and said:"Every shape you want to fill has a backbone that goes through the centre of the shape, like a spine.”
The researchers have had their paper published in Physical Review Letters, where they report the rules for how to find the ideal size and spacing of the discs that fill a shape. They hope that this research will help them create 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.
The algorithm is likely to be most suited to nanotechnology, but in biology and medicine, researchers often need models for complex shapes, such as those of proteins.
Miss Phillips said:"You don't want to model every single one of the thousands of atoms that make up this protein.
“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."