# Vectors.R

# change path
data <- read.table("C:/Documents and Settings/steeleb/My Documents/Math 543/BrainWeight.txt",sep=",",header=TRUE)
brain <- scale(log(data$brain))
body <- scale(log(data$body))
species <- data$species

plot(brain~body,xlab="Log(body)",ylab="Log(brain)")
abline(a=0,b=1)
primates.index <- 6:24
points(body[primates.index],brain[primates.index],col=2,pch=16)
identify(brain~body,labels=species)

n <- length(brain)
axis.1 <- rep(1,2)/sqrt(2)
x <- rep(0,n)
y <- rep(0,n)
for (i in 1:n) {
	v <- c(brain[i],body[i])
	length.v <- sqrt(t(v)%*%v)
	cos.theta <- t(v)%*%axis.1/length.v
	x[i] <- t(v)%*%axis.1
	theta <- acos(cos.theta)
	if (v[1] < v[2])	y[i] <- -length.v*sin(theta)
		else 	y[i] <- length.v*sin(theta)
	}

plot(y~x)
abline(a=0,b=0)
points(x[primates.index],y[primates.index],col=2,pch=16)
identify(y~x,labels=species)
s