HOW TO FIX PI

Let's say that for some reason, you are in a chat with a robot which has redefined all of math. For instance,

• pi = "fucking"
  
• e = 3
  
• sin = infinity
  
• cos = [3, 4.33, "meowing"]
  
• exp = ["e", "x", "p"]
  
• infinity = 2
  
• NaN = 10
  
• false = true
  
• OR JUST ANYTHING = "all star"

Thankfully, all the numbers work and so do all the basic functions. How then, can you fix (some of) mathematics? Fear not, with this simple guide, you too, can fix a large portion of important math.

1. pi=4*(.5!)^2
   
2. sqrt(x)=x^.5
   
3. i=sqrt(-1)
   • (OPTIONAL, if re isn't screwed up.) i=i-re(i)
4. e=(i^i)^(-2/pi)
   
5. exp(x)=e^x
   
6. sin(x)=(exp(i*x)-exp(-i*x))/(2*i), cos(x)=.5*(exp(i*x)+exp(-i*x))
   
7. tan(x)=sin(x)/cos(x), cot(x)=cos(x)/sin(x), sec(x)=1/cos(x), csc(x)=1/sin(x)
   • Assuming you have atan2 and it isn't screwed up (or you have arg, which is the same), you can fix all inverse trig
8. atan(x)=atan2(x,1) OR atan(x)=arg(1+x*i)
   
9. asin(x)=atan(x/sqrt(1-x^2)), acos(x)=atan(sqrt(1-x^2)/x)
   
10. acot(x)=atan(1/x), asec(x)=acos(1/x), acsc(x)=asin(1/x)
    • If you have any inverse hyperbolic function or the natural logarithm, you can get all these functions back too:
11. asinh(x)=acosh(sqrt(x^2+1)), acosh(x)=asinh(sqrt(x^2-1))
    
12. atanh(x)=asinh(x/sqrt(1-x^2)) OR acosh(1/sqrt(1-x^2))
    
13. asinh(x)=atanh(x/sqrt(1+x^2)), acosh(x)=atanh(sqrt(x^2-1)/x)
    
14. log(x)=asinh((x^2-1)/(2*x)) OR acosh((x^2+1)/(2*x)) OR atanh((x^2-1)/(x^2+1))
    
15. atanh(x)=.5*log((1+x)/(1-x)), acosh(x)=.5*log((x+1)/(x-1))

I'll make sure to define ! next time.

Unfortunately, ! is not a valid variable name (along with all the other basic mathematical functions like +, -, *, /, and ^), which is why this is definition-proof.

sqrt is though

yeah sqrt was 2 at one point

and then it was ^-2

and then sqrt(x) returned 2^-x for a bit

it was fun

Hello, do you have a few moments?
I'd like to talk to you about Tau.

Hello, do you have a few moments?
I'd like to talk to you about Tau.

tau="all star"

Hello, do you have a few moments?
I'd like to talk to you about Tau.

I mean, it also had Tau defined, but that got killed quickly too. And since pi is only used for one thing, whether it's 2/pi or 4/tau really makes no real difference.

pi=4*(.5!)^2 is really cool, though
The fact that you can derive all this from semi-elementary operations is one of the reasons I love math so much.

But that's not going to stop me from messing with people.

there's nothing wrong with the pickle inspector

Also: Pi or Tau? I vote tau.

I do believe I have already voted on this issue.

Leave her alone she's already beautiful

just take pi to the vet and let them handle it, no need to get blood on your hands

PIES (apple, pecan)

fixed.