Pi Day

[EricJ]

41 minutes ago, aviatoreb said:

However, since the rational numbers are dense in the set of real numbers that equals the set of rationals union the set of irrationals, then it follows that all approximately rational people in fact include all the irrational people.

QED!   

[DonMuncy]

You guys are making my head hurt. 

[aviatoreb]

30 minutes ago, DonMuncy said:

You guys are making my head hurt. 

The 1897 Pi Bill tried to simplify Pi by legislative action to set Pi=3.2.  Which would be simpler.  But thanks to a testimonial by a math prof from Purdue…

anyway pi day is simpler in Indiana!

[aviatoreb]

I said Pi is my second favorite number.  No one is going to ask me what is my favorite number?

 

[Fly Boomer]

e

[EricJ]

37 minutes ago, Fly Boomer said:

e

Was gonna be my guess, too.

Or maybe Planck's constant. 

[aviatoreb]

All good.

But my favorite is (1+sqrt(5)/2 =aproximately 1.618....

The golden mean.  It has all kinds of lovely properties - it is intimately wrapped up with resonance - e.g. why we see gaps in say Saturns bands, or plasma confinement (KAM theory), it is the most diophantine number meaning difficult to estimate by fractions of small numerators and divisors. It has a continued fraction representation

often written gamma

gamma=1+1/(1+1/(1+1/(1+/...) a continued fraction (infinitely deep fraction.

And the artists like it because the greeks said it was the most balanced lovely ratio to the human eye.

Alas - you can't easily make a date of 1.62

And I decided against making that my tail number since a) it is less well known and b) I liked the pun of "pi plane" as if it is a biplane but with an irrational number of wings.

[carusoam]

3.14 X 2.718 = Pie 

All of the mathematically inclined spelling bee participants eat this up!

irrational spelling humor only…

Best regards, 

-a-

[Andy95W]

The Golden Mean...

[aviatoreb]

Here is where I first learned of the golden ratio - in kindergarten!  And yes - it did make an important appearance in my PhD thesis which include elements of KAM theory and celestial mechanics.  So you can say its run a long course in my life - and thus my favorite number - since it is also the most amazing magical number for the number of different amazing things it touches from pure mathematics, to physics, to art.  What's not to love?  As Donald Duck.

 

[Andy95W]

Erik, I’m embarrassed to admit that the Donald Duck video helped my understanding. 

If I ever meet you in person, you’ll have to explain gamma=1+1/(1+1/(1+1/(1+/...)

[aviatoreb]

6 minutes ago, Andy95W said:

Erik, I’m embarrassed to admit that the Donald Duck video helped my understanding. 

If I ever meet you in person, you’ll have to explain gamma=1+1/(1+1/(1+1/(1+/...)

I will be happy to!

But meanwhile - perhaps the standard keyboard ascii way of writing isn't good for conveying something simple, which is a limit of simple fractions all piled up as I include a screen clip below.

And here is a link explaining it.  https://www.theproblemsite.com/reference/mathematics/the-golden-ratio/continued-fraction

[carusoam]

Ahhhhhh

So Fibonacci-esque….  
 

numbers, nature, and investing…. All in one….

Best regards,

-a-

[EricJ]

[Hank]

On 3/16/2022 at 10:55 PM, Andy95W said:

The Golden Mean...

And here are my Golden Mean dividers!