Easy as Pi? (1 Viewer)

[Jeff Gatie]

Yup, I'll give you that one. I personally thought of squeezing a middle finger joke in there someplce, but my comic timing is off today.

 

[BrianW]

[Holds up one finger]

I missed it by THAT much!

 

[PeterK]

there would still be a pattern that emerges though wouldn't there? no matter what number system you use? hmm, i'll look into this.


I've memorized pi before, our calculus teacher in grade 12 said he would raise our mark 1% for every 100 decimal places we memorized to a max of 300. I was lazy so I only did 60. I can still do about 30 today and have those stuck in my head forever!

 

[Haggai]

Depends on what you mean by "pattern"...as per Brian Perry's post #32, if you used our regular base 10 system and got to a 1-million-long string of digits in pi that contained nothing but 1s and 0s, that would be extremely surprising. If pi really does have a random distribution of how frequently different digits show up in its decimal expansion (and if I understand things right, this is NOT known to be true, but most people who study this topic think it is true, even though nobody's been able to prove it), one would expect any million-long string of digits in its expansion to have about 100,000 0s, 100,000 1s, 100,000 2s, ... , and 100,000 9s. Likewise, if you do the expansion in binary, having a million consecutive 1s would be very surprising. One would be much more inclined to expect about 500,000 0s, and 500,000 1s.

 

[Christ Reynolds]

but some numbers are not able to be expressed (exactly) in binary. haggai (or anyone else who knows), can a decimal irrational number be expressed in any other base? my guess would be no.

CJ

 

[Holadem]

Yes they can. Any base can be used to accurate express a number.

--
H

 

[BrianW]

I think it depends on the kind of "message" contained in pi. For a "message" contained in pi to reveal itself regardless of number base, it would have to be something that could be discerned within the context of mathematics itself, like a pattern using a series of prime numbers, perfect squares, or something similar, rather than an abstract and arbitrary contrivance, like the emergence of a stick figure with a smiley face when the digits are arranged in a grid.

Man, I haven't thought about the difference between transcendental and irrational numbers in over twenty years. Since I have taken all the same college math courses as required to get an undergraduate degree in math, I find it a rather shameful admission that I had forgotten the definition of transcendental numbers until I read this thread. Thanks for a great discussion.

 

[Jeff Gatie]

If the Laws of Physics are different in another part of the universe and Pi equals 5 when you are there, are transporters actually possible? Is Hydrogen a positive ROEI? Is there global warming? Is it really three licks to get to the center of a Tootsie Pop?


The world may never know...

 

[Christ Reynolds]

you can express irrational numbers in any base?

when i took intro to digital logic, i remember there were some terminal decimal numbers that resulted in non-terminal binary numbers. i'll have to see if i can find my papers from that class, but the conversions did not work out perfectly.

CJ

 

[Haggai]

That's right, but non-terminal numbers can still be rational (like 1/3 = 0.3333...) in any base. It's true that a terminating number in one base can be non-terminating in another, but you can always do the conversion, even if you're dealing with an irrational number.