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Calligraphette_Coe
4 hours ago, Heart said:

So my university wrote an article about me and my supervisor :D

 

https://www.sfu.ca/sfunews/stories/2017/sfu-researchers-shine-light-on-antimatter.html

 

(I'm glad they chose flattering pictures of us... ;) )

It's kinda funny, but you look a lot like I've pictured you! It's also a little ironic that this antimatter discussion comes at a time when I've gotten to process build orders again for PET scan support equipment. I have two Coincidence boxes going out next month-- they are really dodgy to set up, though, and I always breathe a little sigh of relief when I get them dialed in to my liking and get detectors from the vendors that are as closely matched as advertised.

 

::::sighs:::: It just kills me when 1/2 my week is siphoned away to do entry level tech work like using a digital calipers to QC a bunch of machined parts and having to troubleshoot the assemblies that the builders get wrong. :(  Having been sick with asthma-like problems for almost a year and having lost a ton or weight now only makes me look more waif-like and feminine, and although that's at least a little easier on the GID, the conservative area where I live and work gives no quarter to those who don't look a certain way.

 

Congrats on the achievement, Heart! I still remember the first time I got quoted and interviewed in a trade magazine ( they chose someone else to model the product for the pics in the article, though),  and it's something you never forget.

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Dodecahedron314

This is the exact kind of good science news I needed today to make me feel a little better even though the world is falling to pieces. Keep on sciencing! 

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16 hours ago, Calligraphette_Coe said:

It's kinda funny, but you look a lot like I've pictured you! It's also a little ironic that this antimatter discussion comes at a time when I've gotten to process build orders again for PET scan support equipment. I have two Coincidence boxes going out next month-- they are really dodgy to set up, though, and I always breathe a little sigh of relief when I get them dialed in to my liking and get detectors from the vendors that are as closely matched as advertised.

 

::::sighs:::: It just kills me when 1/2 my week is siphoned away to do entry level tech work like using a digital calipers to QC a bunch of machined parts and having to troubleshoot the assemblies that the builders get wrong. :(  Having been sick with asthma-like problems for almost a year and having lost a ton or weight now only makes me look more waif-like and feminine, and although that's at least a little easier on the GID, the conservative area where I live and work gives no quarter to those who don't look a certain way.

 

Congrats on the achievement, Heart! I still remember the first time I got quoted and interviewed in a trade magazine ( they chose someone else to model the product for the pics in the article, though),  and it's something you never forget.

Aww, thank you! And I can only imagine that coincidence boxes would be dodgy. Coincidence detection as a whole field is difficult! Installing and calibrating those things can't be easy.... You have all of my respect. In our collaboration, we form mini-groups that specialize in different aspects of the experiment, and I have so much respect for the detector guys, who deal with all that stuff (but our analogue, of course). I just stick to microwaves :P

 

And @Dodecahedron314, I'm glad to be of service! I'm especially glad that my collaboration is super international, so while one government change can affect us, it is less likely to totally ruin us than if we were only based in one country. So, in other words, we shall keep on sciencing, I promise! :cake:

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Hey everyone!

 

My real life things have been ramping up lately. It's all good things, but it all decided to happen at once, so for the next two weeks I won't be around as much as I should to properly moderate. If you have any things that need a moderator or administrator's attention, please poke or PM @Jayce or @Kelly, they would both be happy to help.

 

*goes off to be busy with life*

 

See you guys in two weeks! (Well, probably sporadically between then and now, I'm far too addicted to AVEN to go cold turkey... but you get the idea ;) )

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Don't worry, I'll leave some fun for everyone else I promise ;)

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On 2017-02-11 at 10:22 AM, Jayce said:

Eh. I just caught you posting :P I assume Aven addiction won? 

 

*whispers*

 

....maybe....

 

*wanders back to my simulations*

 

;)

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  • 3 weeks later...

Nice to meet you too @JDB :cake: Welcome to AVEN!

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Time to head home.

 

 

*turns off the lights*

 

enhanced-buzz-26747-1378479000-24.jpg

 

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On 2017-03-09 at 10:17 AM, Kelly said:

In 2012, a MIT professor proposed a "time crystal."  Now, Harvard students made one:

 

http://gizmodo.com/scientists-finally-observed-time-crystals-but-what-the-1793061377

I SAW THAT AND IT MAKES ME SO EXCITED!!! I mean, how cool is this?!?

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*sneaks in a little early*

 

We have 314 replies!  Just in time for...

 

It is Pi Day, and our favorite siblings, Doctors Bart and Lisa, visit each other for their weekly wine and dinner meeting and math discussion.

 

They were drinking wine and enjoying dinner. Their classical music station was playing a concerto by the prolific composer and theorist Georg Philipp Telemann, one of their favorite composers.

 

"Happy Pi Day, sis.  Did you know that Albert Einstein was born on Pi Day?"

 

"Indeed, brother; so was Telemann."

 

Lisa brought a nice and heady Northern Rhone wine and they had consumed the natural logarithm of two times the bottle by now.  Bart was cleaning up the dishes from the second course and bringing in the main course, pizza pi.

 

Lisa started the math discussion.  "I found a new way to create the prime numbers from the zeros of the Riemann Zeta function.  It is rather simple and very interesting."

 

"Get real, Lisa.  The wine is already getting to me and I did not want to discuss complex analysis today.  My expertise is in real numbers."

 

Lisa felt dejected.  "Be rational, Bart."

 

Bart smiled, "Yes. Let us just discuss rational numbers today."

 

Lisa smiled, too. "That sounds good. And there is hardly anything more rational than pi."

 

"True. Oh, hey. Hold on. Pi is clearly irrational."

 

"To be infinitely precise, yes. But you will not need the pi to an infinite number of digits to be useful. You can represent pi to a precision as high as you wish with a rational number."

 

Bart began to imagine complex series with zeta functions, binomial coefficients, Legendre symbols and integrals. "Could we keep it simple?"

 

"Of course," she said, opening her laptop.  Let us make a few columns.  In the first, we call it n, will be 1 then 2 then 3 then 4 and so on.  The next column, A, will be the square of the previous number in n.  We skip the first two rows, so from then on, we have 4, 9, 16, and so on.  The next column, B, will be two times that in A, plus one."  She made the columns as such and then gave the computer to Bart.

 

"OK.  What do I do with this?"

 

"The next column will be the numerator and the one after that will be the denominator.  Put 4 and 12 in the first rows of the numerator, then 1 and 4 in the first rows of the denominator.  After that, the numerator will be the number in the A column times the number two spaces up in the numerator column, plus the number in the B column times the number in the numerator column in the space directly above.  We have four times four, plus five times twelve, giving us seventy-six."

 

"OK, sis.  And for the denominator?"

 

"The same thing; so we have four times one, plus five times four, making twenty-four."

 

Bart did so for n up to 14, and that is where the precision maxed for Excel.

 

They drank the rest of the wine (which was OK, as Bart wanted to open a bottle of Sauternes for dessert) and finished the pizza before it got cold.  Then Lisa said, "Now let's get seriously rational, dude.  Divide the numerators by the denominators."

 

They noticed that by n equals 9, it was accurate to five digits past the decimal.  "Three one four one five nine," said Lisa.

 

"You forgot the decimal, smarty pants," corrected her brother.  He then mentioned, "Did you know that 31459 is a prime number?"

 

"Oh, cool."

 

At n equals 14, they were just about correct to ten decimal places.  The Excel sheet looked as such:

 

pi2.jpg

 

"We can continue this on Mathematica," said Lisa.  "We can represent pi as a rational number to just about any degree that you want.  Thus, pi is actually, for all practical purposes, a rational number."

 

"OK, have at it."

 

When they got the accuracy to 39 digits, Bart asked Lisa to read out the number, again without the decimal.

 

She read out, "31415926535897932384626433832795028841."

 

"That, too," said Bart, "is a prime number.  Back to pi, perhaps there must other ways to calculate pi.  How I wish I could calculate pi, sister."

 

"You just did.  The number of letters in each word of your last sentence is three one four one five nine two six, the digits of pi."

 

Bart went to get a bottle of Chateau d'Yquem Sauternes wine while Lisa cleaned the pizza dishes and then started flaming the crème brûlée.

 

Oh, that pizza had a radius of z and a thickness of a.  What was its volume?

 

Spoiler

Pi*z*z*a

 

Bart opened the bottle and poured each a glass.  Glorious!  It had a rich aroma of apricots, honey, lychee, sweetened pineapples, mango, apricot, musk melon, citrus, and burnt brown sugar.

 

Lisa still had Mathematica open on her laptop.  She said, "There are better ways of calculating pi.  The brilliant Indian mathematician Ramanujan developed a method that I will use now."

 

"Oh, I remember Amita Ramanujan from the TV show, NUMB3RS.  She was a math PhD and helped her boyfriend solve crimes."

 

"No," corrected Lisa.  "This one is Srinivasa Ramanujan, a friend of the mathematician G.H. Hardy.  It is this."

 

She wrote:

 

3554907526d7a18c2c48124688827272.png

 

She typed that into Mathematica.  And while she could use infinity as the upper bound, Mathematica may be too smart, and recognize it as one over pi, and give the answer as "1/π" and when taking the reciprocal, give any amount of digits as asked, without any calculations.  That would be cheating.  So, she first used 1 as the upper bound and took the reciprocal.  Just these two terms gave pi accurate to 14 digits past the decimal.  Her screen showed:

 

pi6.png

 

The "Pi" on the bottom with a capital P was the actual value for comparison.

 

At six terms, she had 53 correct digits past the decimal point.  At 5000 terms it had 39,921 correct digits.  It does take some computing time for Mathematica on a laptop to crunch the numbers; it took a computation time of about 125 seconds for 5000 terms.

 

"That is very interesting, Lisa; thanks.  But we were discussing pi as a rational number."

 

Lisa felt that she had him hooked, and came back with something better.  "OK.  There are likely an infinite amount of ways to produce pi using a ratio.  Here is one."  She wrote this:

 

pi10.jpg

 

"Or"

 

pi11.jpg

 

"But they converge to pi rather slowly.  More clever is this one."

 

π =  Inline112.gif

 

Typing it into Mathematica and taking the first 41 terms, they had a ratio with over a hundred digits each in the numerator and denominator, which gave a number with over 50 correct digits of pi.

 

pi7.png

 

"We could go on as far as you want," said Lisa.  "There are many ways to portray pi as a ratio and you can go on forever for all of them."

 

"But these are not that good, are they?  They need more digits in the numerators and denominators than they give digits of pi."

 

"Oh, there are more complicated methods that do give more digits of pi than the digits in either part of the fractions."  She showed these efficient fractions:

 

image.pngimage.png

125.png

 

"These are better, and they are efficient.  But are there methods that quickly converge to pi?"

 

"Yes."  Lisa wrote:

 

pi3.jpg

 

Where:

 

ff934ad5f124af53365b41ded2438010.png

 

Starting with:

 

62853e30b3cd9190dcdedeed764bc0f4.png

 

"That is a simple ratio, yes, Bart?  It is just the square of a sub n plus b sub n, all over four t sub n."

 

"That is simple, even though it does not produce rational numbers.  I recognize the a terms as an algebraic mean, or average, and the b terms as an harmonic mean.  Brilliant."

 

"Yes.  And indeed, Archimedes used these concepts when calculating pi using polygons thousands of years ago.  But this method is much more outstanding.  It was created in 1975, supposedly independently and simultaneously by Richard Brent and Eugene Salamin.  I guess just like Calculus was supposedly invented independently and simultaneously by Newton and Leibniz."

 

She typed the equations into Mathematica, and asked for the reciprocal.

 

It gave over 100 correct digits with 6 iterations, over 1000 with 9, and over 10,000 with 12 iterations.  14 iterations gave 44,700 correct digits of pi.  It basically doubled the number of correct digits with each iteration.

 

"So, we could go on.  We could calculate pi to a million decimal places."

 

They calculated that they could get a million digits of pi using this method and 19 iterations.  It would take about a half of an hour of computing time.

 

"Shall we, Bart? We can calculate pi to a precision far beyond any practical purpose?  All in thirty minutes."

 

Bart poured another glass.  "Half of an hour for a million digits of pi?  I can get that many in less than five seconds."

 

 

Our puzzle:

 

?!  How?  How could Bart do that?

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The cynic in me whispers: "google it?" I feel like that would be exactly Bart's cheeky personality :P

 

Thank you so much for the story though! I really enjoyed reading it. Do you have plans for baking a pie? I'm quite tired this year, so I think I'm going to go with a simple apple pie, nothing fancy. I have to make it after work after all ;)

 

Is anyone else celebrating pie day? How? Share your festivities :cake:

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6 hours ago, Kelly said:

How could Bart do that?

Way over my head!

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So, how did Bart get a million digits of pi in less than five seconds?

 

There are various ways.  The first is sneaky or creative, and is as follows:

 

Google "million digits pi", then click on a site such as:

 

http://www.eveandersson.com/pi/digits/1000000

 

And then let it download. That whole thing takes a few seconds.

 

But that might be considered to be cheating.  What we really want is to actually calculate a million digits of pi on our laptop in less than five seconds, and Bart can do this.  He had previously downloaded a program called "pifast".  It is available here:

 

http://numbers.computation.free.fr/Constants/PiProgram/download.html

 

To verify if Bart can actually get that many digits in that time, I used it, too.  Here is the top part of the results:

 

Program : PiFast version 4.4, by Xavier Gourdon

Computation of 1000000 digits of Pi

Method used : Chudnovsky

Size of FFT : 128 K

Physical memory used : ~ 7769 K

Disk memory used : ~ 0.00 Meg

------------------------------------------------------------

Computation run information :

 

Start : Sun Mar 05 14:38:41 2017

End   : Sun Mar 05 14:38:43 2017

Duration : 2.09 seconds

============================================================

Total computation time : 2.09 seconds (~ 0.00 hours)

============================================================

Pi with 1000000 digits :

Pi = 3.

1415926535 8979323846 2643383279 5028841971 6939937510  : 50

 

It continues for the million digits.  Note that the total computation time is 2.09 seconds.  It can calculate a million digits of pi in two seconds!  How?

 

It used (as mentioned on the third line above) the Chudnovsky algorithm.  It was developed by the Chudnovsky brothers in 1989.  It is:

 

1/π = Inline219.gif

 

I have even used this to calculate a billion digits of pi.  What a beast!

 

Speaking of the beast.  Since this is a math post, the beast has a number, and it is 666.

 

If we add up the first 144 digits past the decimal point of π, we get 666. And 144 is twice 6*(6 + 6).

 

The sum of the numbers from 1 to 6*6 is 666.


The squares of the first seven primes equal the beast:


666 = 22 + 32 + 52 + 72 + 112 + 132 + 172

The cubes of a triangular shape of one to six equals the beast:

666 = 13 + 23 + 33 + 43 + 53 + 63 + 53 + 43 + 33 + 23 + 13

 

And:

 

666 = 6 + 6 + 6 + 63 + 63 + 63

 

Euler's totient function Phi (which counts the positive integers up to a given integer n that are relatively prime to n) of 666 gives the following:

 

Phi(666)=6*6*6.

 

Phi is also used as a symbol for the Golden Ratio.   666 is the Sine of the Beast because it negates the golden ratio:

 

Phi/2 + sin(666) = 0, to eight decimal places, when 666 is in degrees.  And if we add the first 146 digits of the Golden Ratio, we get 666.

 

Further, using degrees, Phi is annihilated by 666:

 

Phi + sin(666) + cos(6*6*6) = 0

 

If we invert the Sine of the Beast (flip it around), we get 999, which is the Cosine of the Beast.

 

Keeping it in degrees, cos(666) = 0.999.  Switching to radians, cos(0.666) is...

 

tumblr_m3x648wxbj1ru99qvo1_500.png

 

...cos(0.666) = 0.999 as well!

 

Anyway...

 

72fa7b8588dda861dc31e4b7511a57f4.jpg

Happy Pi Day.

 

Capture.png

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ChillaKilla

How is this a riddle it doesn't even have a clever answer TT-TT

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The answer was that Bart used the Chudnovsky algorithm for calculating a million digits of pi in a few seconds (Bart says that he can get that many in "less than five seconds"; I showed that it can be calculated on a home computer in two seconds).

 

The Chudnovsky algorithm is very clever.  Bart stomped his sister on this one.  He had her strung out to dry from the beginning.  He was devious. :twisted:

 

Happy Pi Day, all! :) 

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ChillaKilla

NERDS

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ChillaKilla
Just now, CakeSpadeAce said:

Does anyone else celebrate Tau Day or am I the only one?

 

(there's way less opportunity for puns on Tau Day but it's still cool xD)

What day is that?

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ChillaKilla
Just now, CakeSpadeAce said:

June 28 

 

Why?

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ChillaKilla
12 minutes ago, CakeSpadeAce said:

Because Tau is 2 Pi and 3.14 * 2 is 6.28, which is June 28th in calendar form.

I see!

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Still way over my head!

 

And thanks, @ChillaKilla, for asking those questions! :) I didn't know either. Celebrating May, the 4th, is more my speed (I could do that in 12 parsecs). :P

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On 2017-03-14 at 8:58 AM, ChillaKilla said:

NERDS

And proud of it ;)

 

And Dave, May the 4th be with you too! I celebrate that day with excessive puns every year. In fact, I think I might celebrate more nerd holidays than religious ones... :P

 

On 2017-03-14 at 9:06 AM, CakeSpadeAce said:

Does anyone else celebrate Tau Day or am I the only one?

 

(there's way less opportunity for puns on Tau Day but it's still cool xD)

I do! I usually make two pies ^_^ Though to be fair, I sometimes forget about tau day. For some reason pie day just sits so much more prominently in my memory... Though I admit, tau is pretty genius. It's like h-bar; we found h first, and then decided that in a lot of circumstances, h/(2*pi) is actually the more useful constant, so we named that h-bar. And though we discovered pi first, tau = 2*pi is in many ways the more useful or more intuitive constant...:

 

An intro to why tau might be better than pi, and a debate into which is better:

 

 

 

 

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