Billiards in the NEWS

[JoeyA]

This news comes on the wings of a sad dirge. Famed mathematician Maryam Mirzakhani dies from cancer at the age of 40.

Mirzakhani collaborated with Alex Eskin, a University of Chicago mathematician "to take on another of the most-vexing problems in the field: the trajectory of a billiards ball around a polygonal table," Stanford News said.

"The challenge began as a thought exercise among physicists a century ago and had yet to be solved."

The duo published a 200-page long paper on the subject in 2014 hailed as "the beginning of a new era" in mathematics, according to Stanford News.

I kind of wish I knew if the billiard mathematical problem and solution could be explained in layman's terms. Maybe, it is just a mathematical problem with little benefit to the layman and that's okay too.

JoeyA

 

[Bob Jewett]

This news comes on the wings of a sad dirge. Famed mathematician Maryam Mirzakhani dies from cancer at the age of 40.

Mirzakhani collaborated with Alex Eskin, a University of Chicago mathematician "to take on another of the most-vexing problems in the field: the trajectory of a billiards ball around a polygonal table," Stanford News said.

"The challenge began as a thought exercise among physicists a century ago and had yet to be solved."

The duo published a 200-page long paper on the subject in 2014 hailed as "the beginning of a new era" in mathematics, according to Stanford News.

I kind of wish I knew if the billiard mathematical problem and solution could be explained in layman's terms. Maybe, it is just a mathematical problem with little benefit to the layman and that's okay too.

JoeyA

The mathematical study of "billiards" does not include friction of any sort, pockets, sticks, spin, or more than one ball. The cushions are ideal reflectors and the single ball has zero diameter. Other than that, it is just like pool.:wink:

 

[mchnhed]

This news comes on the wings of a sad dirge. Famed mathematician Maryam Mirzakhani dies from cancer at the age of 40.

Mirzakhani collaborated with Alex Eskin, a University of Chicago mathematician "to take on another of the most-vexing problems in the field: the trajectory of a billiards ball around a polygonal table," Stanford News said.

Here's a link to that lecture:
Still trying to find it.........

 

[JoeyA]

This news comes on the wings of a sad dirge. Famed mathematician Maryam Mirzakhani dies from cancer at the age of 40.

Mirzakhani collaborated with Alex Eskin, a University of Chicago mathematician "to take on another of the most-vexing problems in the field: the trajectory of a billiards ball around a polygonal table," Stanford News said.

Here's a link to that lecture:
Still trying to find it.........

JoeyA

 

[Bob Jewett]

To give some idea of the sorts of shapes of tables the study applied to, here is a brief excerpt of an article that described Mirzakhani's work. One of her major results is called the "Magic Wand Theorem". The gray areas in the diagram are where the ball is not allowed to go -- the cushions.

 

[skip100]

Sounds like a new subject for the aiming forum. :thumbup:

 

[jay helfert]

To give some idea of the sorts of shapes of tables the study applied to, here is a brief excerpt of an article that described Mirzakhani's work. One of her major results is called the "Magic Wand Theorem". The gray areas in the diagram are where the ball is not allowed to go -- the cushions.

View attachment 464881

I'm trying to figure out how any of this applies to the real world and if it's useful in any way. Kind of looks like a game Mathematicians play with each other, like Candy Crush for geniuses.

 

[Bob Jewett]

I'm trying to figure out how any of this applies to the real world and if it's useful in any way. Kind of looks like a game Mathematicians play with each other, like Candy Crush for geniuses.

The related articles pointed out some connection to chemistry. The billiard stuff is pretty far out there but there are lots of cases of math studies finding application decades or centuries after the first developments.

 

[pocket]

I'm trying to figure out how any of this applies to the real world and if it's useful in any way. Kind of looks like a game Mathematicians play with each other, like Candy Crush for geniuses.

It's not really designed to translate into real world Jay. More of a tool to express concepts.

 

[RussPrince]

The mathematical study of "billiards" does not include friction of any sort, pockets, sticks, spin, or more than one ball. The cushions are ideal reflectors and the single ball has zero diameter. Other than that, it is just like pool.:wink:

So you read the paper? Funny they would leave out all of the variables that affect the very thing they felt it would be worth writing a paper about.... whoda thunk

 

[JoeyA]

I KNEW I would get something out of it!!!

JoeyA

To give some idea of the sorts of shapes of tables the study applied to, here is a brief excerpt of an article that described Mirzakhani's work. One of her major results is called the "Magic Wand Theorem". The gray areas in the diagram are where the ball is not allowed to go -- the cushions.

View attachment 464881

 

[Bob Jewett]

So you read the paper? Funny they would leave out all of the variables that affect the very thing they felt it would be worth writing a paper about.... whoda thunk

In the case of the mathematical study we are talking about, the word "billiards" could have been replaced by the word "reflections" since that is what is going on. The sub-field of advanced mathematics has nothing to do with what Coriolis worked on. It just happens to use a name we are fairly familiar with. In physics, quarks (of which we are all made) can have "charm" but no one ever said, "well, there's a cute one."

 

[tucson9ball]

In other news:
My dog sat today and I gave him a biscuit

 

[MitchAlsup]

The mathematical study of "billiards" does not include friction of any sort, pockets, sticks, spin, or more than one ball. The cushions are ideal reflectors and the single ball has zero diameter. Other than that, it is just like pool.:wink:

Come on, even Dr Dave's stuff has those pieces to the puzzle.