attendance quiz

q1. who proved PI is irrational?
Johann Heinrich Lambert

q2. who proved that pi is transcendental
Ferdinand von Lindemann

q3. Prove that sqrt(3) is irrational
if sqrt(3) is rational then it can be repreented as a/b where a and b
hve no common factors

a^2=3b^2
if b is even, then a is also even in which case a/b is not in simplest form
if b is odd then a is also odd therefore:
a=2n+1
b= 2m+1
(2n+1)^2=3(2m+1)^2
4n^2+4n+1=12m^2+12m+3
4n^2+4n=12m^2+12m+2
2n^2+2n=6m^2+6m+1
2(n^2+n) = 2(3m^2+3m) + 1
since (n^2+n) is an int, then the left hand side is even. Since (3m^2+3m) is an
integer, the right hand side is odd. This is a controdiction and our
hypothesis is false.


Next attendance question: why is htis rational number important and famous?
I didn't get this one very well

Part II:
1. Convert the fraction 11/4
into a simple continued fraction.

11/4 = 2+3/4=2+1/(4/3) = 2+1/(1+1/3) -> [2,1,3]