Expression 24: "y" Subscript, "p" 2 , Baseline left parenthesis, "t" , right parenthesis equals "x" Subscript, "y" , Baseline "X" left parenthesis, StartFraction, 2 pi Over "n" , EndFraction floor left parenthesis, "t" , right parenthesis , 2 pi mod left parenthesis, "t" , 1 , right parenthesis , right parenthesis plus "y" Subscript, "y" , Baseline "Y" left parenthesis, StartFraction, 2 pi Over "n" , EndFraction floor left parenthesis, "t" , right parenthesis , 2 pi mod left parenthesis, "t" , 1 , right parenthesis , right parenthesis plus "z" Subscript, "y" , Baseline "Z" left parenthesis, StartFraction, 2 pi Over "n" , EndFraction floor left parenthesis, "t" , right parenthesis , 2 pi mod left parenthesis, "t" , 1 , right parenthesis , right parenthesisyp2t=xyX2πnfloort,2πmodt,1+yyY2πnfloort,2πmodt,1+zyZ2πnfloort,2πmodt,1
24
Expression 25: "x" Subscript, "p" 3 , Baseline left parenthesis, "t" , right parenthesis equals "x" Subscript, "x" , Baseline "X" Subscript, 2 , Baseline left parenthesis, 2 pi mod left parenthesis, "t" , 1 , right parenthesis , StartFraction, 2 pi Over "n" Subscript, 1 , Baseline , EndFraction floor left parenthesis, "t" , right parenthesis , right parenthesis plus "y" Subscript, "x" , Baseline "Y" Subscript, 2 , Baseline left parenthesis, 2 pi mod left parenthesis, "t" , 1 , right parenthesis , StartFraction, 2 pi Over "n" Subscript, 1 , Baseline , EndFraction floor left parenthesis, "t" , right parenthesis , right parenthesis plus "z" Subscript, "x" , Baseline "Z" Subscript, 2 , Baseline left parenthesis, 2 pi mod left parenthesis, "t" , 1 , right parenthesis , StartFraction, 2 pi Over "n" Subscript, 1 , Baseline , EndFraction floor left parenthesis, "t" , right parenthesis , right parenthesis left brace, "t" less than or equal to "n" Subscript, 1 , Baseline , right bracexp3t=xxX22πmodt,1,2πn1floort+yxY22πmodt,1,2πn1floort+zxZ22πmodt,1,2πn1floortt≤n1
25
Expression 26: "y" Subscript, "p" 3 , Baseline left parenthesis, "t" , right parenthesis equals "x" Subscript, "y" , Baseline "X" Subscript, 2 , Baseline left parenthesis, 2 pi mod left parenthesis, "t" , 1 , right parenthesis , StartFraction, 2 pi Over "n" Subscript, 1 , Baseline , EndFraction floor left parenthesis, "t" , right parenthesis , right parenthesis plus "y" Subscript, "y" , Baseline "Y" Subscript, 2 , Baseline left parenthesis, 2 pi mod left parenthesis, "t" , 1 , right parenthesis , StartFraction, 2 pi Over "n" Subscript, 1 , Baseline , EndFraction floor left parenthesis, "t" , right parenthesis , right parenthesis plus "z" Subscript, "y" , Baseline "Z" Subscript, 2 , Baseline left parenthesis, 2 pi mod left parenthesis, "t" , 1 , right parenthesis , StartFraction, 2 pi Over "n" Subscript, 1 , Baseline , EndFraction floor left parenthesis, "t" , right parenthesis , right parenthesisyp3t=xyX22πmodt,1,2πn1floort+yyY22πmodt,1,2πn1floort+zyZ22πmodt,1,2πn1floort
26
Expression 27: "x" Subscript, "p" 4 , Baseline left parenthesis, "t" , right parenthesis equals "x" Subscript, "x" , Baseline "X" Subscript, 2 , Baseline left parenthesis, StartFraction, 2 pi Over "n" Subscript, 1 , Baseline , EndFraction floor left parenthesis, "t" , right parenthesis , 2 pi mod left parenthesis, "t" , 1 , right parenthesis , right parenthesis plus "y" Subscript, "x" , Baseline "Y" Subscript, 2 , Baseline left parenthesis, StartFraction, 2 pi Over "n" Subscript, 1 , Baseline , EndFraction floor left parenthesis, "t" , right parenthesis , 2 pi mod left parenthesis, "t" , 1 , right parenthesis , right parenthesis plus "z" Subscript, "x" , Baseline "Z" Subscript, 2 , Baseline left parenthesis, StartFraction, 2 pi Over "n" Subscript, 1 , Baseline , EndFraction floor left parenthesis, "t" , right parenthesis , 2 pi mod left parenthesis, "t" , 1 , right parenthesis , right parenthesis left brace, "t" less than or equal to "n" Subscript, 1 , Baseline plus 1 , right bracexp4t=xxX22πn1floort,2πmodt,1+yxY22πn1floort,2πmodt,1+zxZ22πn1floort,2πmodt,1t≤n1+1
27
Expression 28: "y" Subscript, "p" 4 , Baseline left parenthesis, "t" , right parenthesis equals "x" Subscript, "y" , Baseline "X" Subscript, 2 , Baseline left parenthesis, StartFraction, 2 pi Over "n" Subscript, 1 , Baseline , EndFraction floor left parenthesis, "t" , right parenthesis , 2 pi mod left parenthesis, "t" , 1 , right parenthesis , right parenthesis plus "y" Subscript, "y" , Baseline "Y" Subscript, 2 , Baseline left parenthesis, StartFraction, 2 pi Over "n" Subscript, 1 , Baseline , EndFraction floor left parenthesis, "t" , right parenthesis , 2 pi mod left parenthesis, "t" , 1 , right parenthesis , right parenthesis plus "z" Subscript, "y" , Baseline "Z" Subscript, 2 , Baseline left parenthesis, StartFraction, 2 pi Over "n" Subscript, 1 , Baseline , EndFraction floor left parenthesis, "t" , right parenthesis , 2 pi mod left parenthesis, "t" , 1 , right parenthesis , right parenthesisyp4t=xyX22πn1floort,2πmodt,1+yyY22πn1floort,2πmodt,1+zyZ22πn1floort,2πmodt,1
28
Expression 29:
29
fondnoire1.jpg
Change Image
Center:
center: left parenthesis, 0 , 0 , right parenthesis0,0
Width:
width: 36.7 336.73
Angle:
angle: 00
Height:
height: 20.2 520.25
Opacity:
opacity: 11
30
logo.gif
Change Image
Center:
center: left parenthesis, negative 12.2 6 , negative 4.6 , right parenthesis−12.26,−4.6
Width:
width: 1.31.3
Angle:
angle: 00
Height:
height: 1.31.3
Opacity:
opacity: 11
31
Expression 32: "X" Subscript, 2 , Baseline left parenthesis, "u" , "v" , right parenthesis equals "R" cosine left parenthesis, "v" , right parenthesis left parenthesis, sin "u" , right parenthesisX2u,v=Rcosvsinu
32
Expression 33: "Y" Subscript, 2 , Baseline left parenthesis, "u" , "v" , right parenthesis equals "R" sine left parenthesis, "v" , right parenthesis left parenthesis, sin "u" , right parenthesisY2u,v=Rsinvsinu
33
Expression 34: "Z" Subscript, 2 , Baseline left parenthesis, "u" , "v" , right parenthesis equals "R" cosine ( "u" ) plus "R"Z2u,v=Rcos(u)+R
34
Expression 35: "n" Subscript, 1 , Baseline equals 16n1=16
negative 10−10
100100
35
Expression 36: left parenthesis, "x" Subscript, "p" 4 , Baseline left parenthesis, "t" , right parenthesis , "y" Subscript, "p" 4 , Baseline left parenthesis, "t" , right parenthesis , right parenthesisxp4t,yp4t
domain t Minimum: 00
less than or equal to "t" less than or equal to≤t≤
domain t Maximum: 100100
36
Expression 37: left parenthesis, "x" Subscript, "p" 3 , Baseline left parenthesis, "t" , right parenthesis , "y" Subscript, "p" 3 , Baseline left parenthesis, "t" , right parenthesis , right parenthesisxp3t,yp3t
domain t Minimum: 00
less than or equal to "t" less than or equal to≤t≤
domain t Maximum: 100100
37
Hidden Label: "O" equals left parenthesis, "x" Subscript, 0 , Baseline , "y" Subscript, 0 , Baseline , right parenthesisO=x0,y0
Label
equals=
left parenthesis, negative 21.6 4 , 3.2 1 , right parenthesis−21.64,3.21
Hidden Label: "X" Subscript, 20 , Baseline equals left parenthesis, "x" Subscript, 0 , Baseline plus "x" Subscript, "x" , Baseline , "y" Subscript, 0 , Baseline plus "y" Subscript, "x" , Baseline , right parenthesisX20=x0+xx,y0+yx
Label
equals=
left parenthesis, negative 20.6 5 0 7 5 7 9 , 3.2 1 , right parenthesis−20.6507579,3.21
41
Hidden Label: "Y" Subscript, 20 , Baseline equals left parenthesis, "x" Subscript, 0 , Baseline plus "y" Subscript, "x" , Baseline , "y" Subscript, 0 , Baseline plus "y" Subscript, "y" , Baseline , right parenthesisY20=x0+yx,y0+yy
Label
equals=
left parenthesis, negative 21.6 4 , 3.8 2 3 7 4 5 7 5 , right parenthesis−21.64,3.82374575
42
Hidden Label: "Z" Subscript, 20 , Baseline equals left parenthesis, "x" Subscript, 0 , Baseline plus "z" Subscript, "x" , Baseline , "y" Subscript, 0 , Baseline plus "z" Subscript, "x" , Baseline , right parenthesisZ20=x0+zx,y0+zx
Expression 47: "a" Subscript, 50 , Baseline equals sine left parenthesis, StartFraction, "a" Subscript, 20 , Baseline Over "b" Subscript, 20 , Baseline , EndFraction , right parenthesisa50=sina20b20
equals=
0.9 9 9 1 5 9 0 2 1 7 2 90.999159021729
47
Expression 48: "b" Subscript, 50 , Baseline equals sine left parenthesis, StartFraction, "a" Subscript, 20 , Baseline Over "c" Subscript, 20 , Baseline , EndFraction , right parenthesisb50=sina20c20