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Richard Green
replied RE:
Counting paths in corridors using circular Pascal arrays
(46 minutes ago)

Drew Armstrong
replied RE:
Counting paths in corridors using circular Pascal arrays
(1 hour ago)

This is what happens when you play the Price is Right™ game Plinko on a cylindrical game board. If you fill in more numbers below the array, the numbers in the n-th row will eventually (for large n) be all (approximately) the same. This corresponds to the Perron-Frobenius eigenvector of the affine Cartan matrix of type A. When you play the usual (nonperiodic) game of Plinko, you are using the affine Cartan matrix of type C.

The Price is Right former biggest Plinko win primetime

The Price is Right former biggest Plinko win primetime

Azlin Bloor
replied RE:
Counting paths in corridors using circular Pascal arrays
(10 hours ago)

+Patrick Honner I'm sure it will, it's for my son. x

Patrick Honner
replied RE:
Counting paths in corridors using circular Pascal arrays
(10 hours ago)

My pleasure, +Richard Green. Hope it helps, +Azlin Bloor!

Azlin Bloor
replied RE:
Counting paths in corridors using circular Pascal arrays
(10 hours ago)

+William Stein thank you, I shall have a look now! x

Azlin Bloor
replied RE:
Counting paths in corridors using circular Pascal arrays
(10 hours ago)

+Patrick Honner thank you so much! Will check it out!

Richard Green
replied RE:
Counting paths in corridors using circular Pascal arrays
(10 hours ago)

Thanks for your input, +Patrick Honner!

William Stein
replied RE:
Counting paths in corridors using circular Pascal arrays
(10 hours ago)

+Patrick Honner Yes, Barry Mazur and I wrote a popular book on RH, which will be published by Cambridge University Press later this year. It's freely available here right now, but won't be soon: http://wstein.org/rh/

Patrick Honner
replied RE:
Counting paths in corridors using circular Pascal arrays
(11 hours ago)

I don't have any good recommendations for you, +Azlin Bloor, however I believe +William Stein is currently working on a *popular mathematics* book on the Riemann Hypothesis.

Also, this +Numberphile video by +Edward Frenkel on the Riemann Hypothesis is excellent--my students loved it!

Riemann Hypothesis - Numberphile

Also, this +Numberphile video by +Edward Frenkel on the Riemann Hypothesis is excellent--my students loved it!

Riemann Hypothesis - Numberphile

Azlin Bloor
replied RE:
Counting paths in corridors using circular Pascal arrays
(11 hours ago)

+Richard Green thank you!

Richard Green
replied RE:
Counting paths in corridors using circular Pascal arrays
(11 hours ago)

Thanks, +Azlin Bloor! I don't know of a suitable book on the Riemann Hypothesis, but there might be one. +Patrick Honner is a mathematics teacher and he might have some ideas, so I'm pinging him.

Azlin Bloor
replied RE:
Counting paths in corridors using circular Pascal arrays
(12 hours ago)

Fascinating as always!

I have a question on a different topic.

Do you know, off the top of your head, any good books on the Riemann Hypothesis?

My 13 year old has been studying it for quite a while (and trying to solve it!), I thought it would be good if he can read up on it too.

Thank you. xx

I have a question on a different topic.

Do you know, off the top of your head, any good books on the Riemann Hypothesis?

My 13 year old has been studying it for quite a while (and trying to solve it!), I thought it would be good if he can read up on it too.

Thank you. xx

Leslie Lina Sigala
replied RE:
Counting paths in corridors using circular Pascal arrays
(12 hours ago)

And this is how I like to start my morning!! Thank you for sharing!

Richard Green
replied RE:
Counting paths in corridors using circular Pascal arrays
(20 hours ago)

Also, I couldn't think of a good way to insert it into the text without messing it up. But thanks!

Debashish Samaddar
replied RE:
Counting paths in corridors using circular Pascal arrays
(20 hours ago)

+Richard Green ah, leaving out deliberately for others to wonder/ponder about. You are most definitely a pedagogue (and I mean that in the nice sense of the word, not the "pedantic" sense).

Richard Green
replied RE:
Counting paths in corridors using circular Pascal arrays
(20 hours ago)

Yes, +Debashish Samaddar, it's because of the cylinder thing. I thought about explaining it in the post, but sometimes I deliberately miss stuff like this out so that people have things to comment about!

“Circular” isn't a very good word. “Cylindrical” or “cyclic” or “periodic” all sound better to me.

“Circular” isn't a very good word. “Cylindrical” or “cyclic” or “periodic” all sound better to me.

Debashish Samaddar
replied RE:
Counting paths in corridors using circular Pascal arrays
(20 hours ago)

Hmm... why can't I imagine the numbers written on a pentagonal prism?

When I think circle I think of an actual geometrical shape. For repeating patterns I think cycle or cyclical.

When I think circle I think of an actual geometrical shape. For repeating patterns I think cycle or cyclical.

Graeme McRae
replied RE:
Counting paths in corridors using circular Pascal arrays
(20 hours ago)

Because every row is a circle. You can think of the collection of rows as being written on a cylinder.

Debashish Samaddar
replied RE:
Counting paths in corridors using circular Pascal arrays
(20 hours ago)

Why is it called "circular"?

Juaquin Anderson
replied RE:
Counting paths in corridors using circular Pascal arrays
(1 day ago)

+Graeme McRae

Sweet! Thanks for checking it.

:-)

That fact became an algorithm that was the enabling technology to make a pattern recognition algorithm feasible for a project I worked on.

I needed a fast accurate low pass filter and subsampling for a continuous stream of high bitrate signal data. The filter had to be accurate with no ringing or phase distortion and fast for high bandwidth.

It was infeasible to do a sliding convolution with a sync function for the real time data, but I used the sync filter as a reference in debuging for my filter. The cpu had slow multipliers in the alu.

The filter I designed did several passes of summing consecutive elements, then a sub sample and scale to reduce the bitrate, then several passes at the reduced rate and sub sampled and scaled again. Continued until the signal was very low bitrate, and because the iteration you carried out converges quickly, I had a very accurate fast approximation to the full sliding window low pass and subsample, with a greatly reduced computation.

Sweet! Thanks for checking it.

:-)

That fact became an algorithm that was the enabling technology to make a pattern recognition algorithm feasible for a project I worked on.

I needed a fast accurate low pass filter and subsampling for a continuous stream of high bitrate signal data. The filter had to be accurate with no ringing or phase distortion and fast for high bandwidth.

It was infeasible to do a sliding convolution with a sync function for the real time data, but I used the sync filter as a reference in debuging for my filter. The cpu had slow multipliers in the alu.

The filter I designed did several passes of summing consecutive elements, then a sub sample and scale to reduce the bitrate, then several passes at the reduced rate and sub sampled and scaled again. Continued until the signal was very low bitrate, and because the iteration you carried out converges quickly, I had a very accurate fast approximation to the full sliding window low pass and subsample, with a greatly reduced computation.

(Pinging +Dana Ernst, who may be interested in the above comment.)