Expression 4: left parenthesis, "X" left parenthesis, "t" , right parenthesis plus StartFraction, 1 Over "N" , EndFraction "r" left parenthesis, "X" left parenthesis, "t" , right parenthesis , "Y" left parenthesis, "t" , right parenthesis , right parenthesis cos left parenthesis, 2 pi "t" , right parenthesis , positive "Y" left parenthesis, "t" , right parenthesis plus StartFraction, 1 Over "N" , EndFraction "r" left parenthesis, "X" left parenthesis, "t" , right parenthesis , "Y" left parenthesis, "t" , right parenthesis , right parenthesis sin left parenthesis, 2 pi "t" , right parenthesis , right parenthesisXt+1NrXt,Ytcos2πt,+Yt+1NrXt,Ytsin2πt
domain t Minimum: 00
less than or equal to "t" less than or equal to≤t≤
domain t Maximum: "N" squaredN2
4
Expression 5: "X" left parenthesis, "t" , right parenthesis equals StartFraction, 2 Over "N" , EndFraction mod left parenthesis, floor left parenthesis, "t" , right parenthesis , "N" , right parenthesis minus 1Xt=2Nmodfloort,N−1
5
Expression 6: "Y" left parenthesis, "t" , right parenthesis equals StartFraction, 2 Over "N" , EndFraction floor left parenthesis, StartFraction, "t" Over "N" , EndFraction , right parenthesis minus 1Yt=2NfloortN−1
6
Expression 7: "l" left parenthesis, "x" , "y" , right parenthesis equals StartRoot, "x" squared plus "y" squared , EndRootlx,y=x2+y2