Chi Square Random Variables are Sums of Squares of Independent Normals. These actually have a Gamma Distribution. Because these are SUMS, they are approximately normal for large number of terms. We develop this theory now.
S2: Proof that Sums of Squares of Normals is Chi Square
S3: Cochran's Theorem by Induction
S5: Application -- Is there significant difference between male and female responses?
NOTE: The Chi-Square Distribution with K degrees of freedom is a SPECIAL CASE of the Gamma Distribution. It is obtained by setting the shape parameter p=K/2 and the scale parameter lambda equal to 1/2.