Part 1:

1)  Who proved pi is irrational?
	Johann Heinrich Lambert

2) Who proved pi is transcendental?
	Ferdinand von Lindemann

3) Why is 355/113 important and famous?
	It is the best rational approximation of pi with a denominator of 4 digits or fewer being accurate to 6 decimal places. 

Part 2:

1)  11/4 

2 + 3/4

[2,1,3]

2) Let us assume that √2 is a rational number.
So it can be expressed in the form p/q where p, q are co-prime integers and q≠0
√2 = p/q
√2 = p/q
p2/2 = q2
2q² = 4m²
q² is a multiple of 2
q is a multiple of 2
Hence, p, q have a common factor 2. This contradicts our assumption that they are co-primes. Therefore, p/q is not a rational number