Method 3 Chart Explanation

Write \(r = k4^m\) where \(k\) is not a multiple of 4.

Recall that 0=R, 1=S, 2=L, and 3=B, and that method 2 says that

• If \(k\) is odd, then \(b_r = 2m \text{ mod } 4\)
• If \(k\) is even, then \(b_r = (2m+1) \text{ mod } 4\)

If \(k\) is odd and \(m = 2p\) is even, then \(b_k = 2(2p) \text {mod } 4 = 4p \text{ mod }4 = 0.\)

If \(k\) is even and \(m = 2p\) is even, then \(b_k = (2(2p)+1) \text {mod } 4 = (4p+1) \text{ mod }4 = 1.\)

If \(k\) is odd and \(m = 2p+1\) is odd, then \(b_k = 2(2p+1) \text {mod } 4 = (4p+2) \text{ mod }4 = 2.\)

If \(k\) is even and \(m = 2p+1\) is odd, then \(b_k = (2(2p+1)+1) \text {mod } 4 = (4p+3) \text{ mod }4 = 3.\)

Individual corner
r = Compute Turn