What if Pi is rational?

Things I wonder about- Pi is an irrational number. However, there is, in principle, a small but nonzero chance that everyone who has proven Pis irrationality was wrong, and that Pi is, in fact, rational.

If this were to be the case, I wonder what the implications would be? Not much on a day to day basis right now, we use it to great practical effect under the assumption it is irrational and get the right answer(or at least something usefully close). But I wonder what would be impacted in more pure mathematics and number theory, and if there might be something humans might get into some day where this would have significant practical implications?

I suppose the implications would depend at least on part on where in the proofs people have gone wrong. This could potentially have implications beyond pi and its uses.

Now I’m not as crazy as this might make me seem- I’m pretty well satisfied that Pi is irrational.  While I have no idea what the proof is and might not understand the math involved anyways, it’s been treated as irrational for so long that if it wasn’t, *someone* would have noticed by now. I just wonder about weird things sometimes.

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Education plans

I need to get my CompSci degree.  At least an AS degree in it.

Now, my math grades from my AS in General Studies were bad.  It’s not that I didn’t understand the math- my procedural skills were at or near the top of the class pretty much every time.  My attention to detail, though, hurt my grades badly.  I’d write down x^2 when it was supposed to be x^3, not because I miscalculated, but just a copying error.  It would be x^3 on the first line, and just end up x^2 on the next.  I need to fix that.

So, my short term plan is use some online resources to brush up on my math skills through Calculus 1.  Going through Algebra and Pre Calculus on Khan Academy.  I’m signed up for a Geometry course on edX, and a self paced Calculus 1 on Coursera.

Once all that is done, it will be time to start at OTC.  I will probably just have to take CompSci courses and a few math courses, with all the general ed stuff taken care of with my General Studies degree.  So a year or so.  Maybe less if I take advantage of winter and maybe summer terms.

Then I might look at a job in the field, or doing my own business with the knowledge, or perhaps moving on to a 4 year degree. I’ll see how that goes.

Perfect numbers in Python

Euclid algorithm for Greatest common Denominator, SML

fun gcd (x,y) = 
    if y = 0 then x 
    else gcd(y, x mod y)

I’ve wondered how to easily do this in code, without having to brute force it.  Turns out Euclid worked out the algorithm over 2,000 years ago.

Even if you aren’t a programmer, you can probably follow this code if you understand that “x mod y” gives you the remainder of x divided by y.  Then you need to understand recursion, but you’ll need to understand recursion first.

I don’t recall ever learning this technique in school.  It would have made some operations on fractions easier.