Mathematical Moments From The American Mathematical Society

Lydia Bourouiba talks about surface tension and the transmission of disease

Colin Adams talks about knot theory

Michael Trick talks about creating schedules for leagues.

Despite the considerable variety among cities, researchers have identified common mathematical properties that hold around the world, regardless of a city.s population, location or even time.

Nazareth Bedrossian talks about using math to reposition the International Space Station.

Nazareth Bedrossian explains more about math's role in maneuvering spacecraft and why he's a consumer of mathematical results.

Despite the considerable variety among cities, researchers have identified common mathematical properties that hold around the world, regardless of a city.s population, location or even time.

Van Wedeen talks about the geometry of the brain's communication pathways.

Muthu Alagappan explains how topology and analytics are bringing a new look to basketball.

James Sethian and Frank Morgan talk about their research investigating bubbles.

James Sethian and Frank Morgan talk about their research investigating bubbles.

James Sethian and Frank Morgan talk about their research investigating bubbles.

James Sethian and Frank Morgan talk about their research investigating bubbles.

Many of today.s most striking buildings are nontraditional freeform shapes. A new field of mathematics, discrete differential geometry, makes it possible to construct these complex shapes that begin as designers. digital creations. Since it.s impossible to fashion a large structure out of a single piece of glass or metal, the design is realized using smaller pieces that best fit the original smooth surface. Triangles would appear to be a natural choice to represent a shape, but it turns out that using quadrilaterals.which would seem to be more difficult.saves material and money and makes the structure easier to build. One of the primary goals of researchers is to create an efficient, streamlined process that integrates design and construction parameters so that early on architects can assess the feasibility of a given idea. Currently, implementing a plan involves extensive (and often expensive) interplay on computers between subdivision.breaking up the entire structure into manageable manufacturable pieces.a

Many of today.s most striking buildings are nontraditional freeform shapes. A new field of mathematics, discrete differential geometry, makes it possible to construct these complex shapes that begin as designers. digital creations. Since it.s impossible to fashion a large structure out of a single piece of glass or metal, the design is realized using smaller pieces that best fit the original smooth surface. Triangles would appear to be a natural choice to represent a shape, but it turns out that using quadrilaterals.which would seem to be more difficult.saves material and money and makes the structure easier to build. One of the primary goals of researchers is to create an efficient, streamlined process that integrates design and construction parameters so that early on architects can assess the feasibility of a given idea. Currently, implementing a plan involves extensive (and often expensive) interplay on computers between subdivision.breaking up the entire structure into manageable manufacturable pieces.a

Imagine trying to describe the circulation and temperatures across the vast expanse of our oceans. Good models of our oceans not only benefit fishermen on our coasts but farmers inland as well. Until recently, there were neither adequate tools nor enough data to construct models. Now with new data and new mathematics, short-range climate forecasting for example, of an upcoming El Nino is possible.There is still much work to be done in long-term climate forecasting, however, and we only barely understand the oceans. Existing equations describe ocean dynamics, but solutions to the equations are currently out of reach. No computer can accommodate the data required to approximate a good solution to these equations. Researchers therefore make simplifying assumptions in order to solve the equations. New data are used to test the accuracy of models derived from these assumptions. This research is essential because we cannot understand our climate until we understand the oceans. For More Information: What.s Happening

Facebook has over 700 million users with almost 70 billion connections. The hard part isn.t people making friends; rather it.s Facebook.s computers storing and accessing relevant data, including information about friends of friends. The latter is important for recommendations to users (People You May Know). Much of this work involves computer science, but mathematics also plays a significant role. Subjects such as linear programming and graph theory help cut in half the time needed to determine a person.s friends of friends and reduce network traffic on Facebook.s machines by about two-thirds. What.s not to like? The probability of people being friends tends to decrease as the distance between them increases. This makes sense in the physical world, but it.s true in the digital world as well. Yet, despite this, the enormous network of Facebook users is an example of a small-world network. The average distance between Facebook users the number of friend-links to connect people is less than five. And even though

Facebook has over 700 million users with almost 70 billion connections. The hard part isn.t people making friends; rather it.s Facebook.s computers storing and accessing relevant data, including information about friends of friends. The latter is important for recommendations to users (People You May Know). Much of this work involves computer science, but mathematics also plays a significant role. Subjects such as linear programming and graph theory help cut in half the time needed to determine a person.s friends of friends and reduce network traffic on Facebook.s machines by about two-thirds. What.s not to like? The probability of people being friends tends to decrease as the distance between them increases. This makes sense in the physical world, but it.s true in the digital world as well. Yet, despite this, the enormous network of Facebook users is an example of a small-world network. The average distance between Facebook users the number of friend-links to connect people is less than five. And even though

There.s more mathematics involved in juggling than just trying to make sure that the number of balls (or chainsaws) that hits the ground stays at zero. Subjects such as combinatorics and abstract algebra help jugglers answer important questions, such as whether a particular juggling pattern can actually be juggled. For example, can balls be juggled so that the time period that each ball stays aloft alternates between five counts and one? The answer is Yes. Math also tells you that the number of balls needed for such a juggling pattern is the average of the counts, in this case three. Once a pattern is shown to be juggleable and the number of balls needed is known, equations of motion determine the speed with which each ball must be thrown and the maximum height it will attain. Obviously the harder a juggler throws, the faster and higher an object will go. Unfortunately hang time increases proportionally to the square root of the height, so the difficulty of keeping many objects in the air increases very quic

There.s more mathematics involved in juggling than just trying to make sure that the number of balls (or chainsaws) that hits the ground stays at zero. Subjects such as combinatorics and abstract algebra help jugglers answer important questions, such as whether a particular juggling pattern can actually be juggled. For example, can balls be juggled so that the time period that each ball stays aloft alternates between five counts and one? The answer is Yes. Math also tells you that the number of balls needed for such a juggling pattern is the average of the counts, in this case three. Once a pattern is shown to be juggleable and the number of balls needed is known, equations of motion determine the speed with which each ball must be thrown and the maximum height it will attain. Obviously the harder a juggler throws, the faster and higher an object will go. Unfortunately hang time increases proportionally to the square root of the height, so the difficulty of keeping many objects in the air increases very quic