Expresión 75: "y" equals left parenthesis, "c" minus left parenthesis, "e" Superscript, "i" pi Superscript, "x" , Baseline , Baseline , right parenthesis minus "d" , right parenthesis Superscript, "x" , Baseliney=c−eiπx−dx
75
"x"x
negative left parenthesis, "c" minus left parenthesis, "e" Superscript, "i" pi Superscript, "x" , Baseline , Baseline , right parenthesis minus "d" , right parenthesis Superscript, "x" , Baseline−c−eiπx−dx
left parenthesis, "c" minus left parenthesis, "e" Superscript, "i" pi Superscript, "x" , Baseline , Baseline , right parenthesis minus "d" , right parenthesis Superscript, "x" , Baselinec−eiπx−dx
negative 2−2
negative 2.2−2.2
negative 2.4−2.4
negative 2.6−2.6
negative 2.8−2.8
negative 2.9 6−2.96
negative 1.9−1.9
54 más filas
negative 13−13
negative 14−14
negative 15−15
negative 16−16
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Every expression coming up are all coming from the joint expression. what is special about these lines is that they disappear then reappear at specific points. possibly proving that lines act as both a line and point. also switches poles after disappearing. All o's are negative equations; all x's are positive.
77
control line void set Master rip
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78
Expresión 80: "y" equals left parenthesis, "c" minus left parenthesis, "e" Superscript, "i" pi Superscript, "x" , Baseline , Baseline , right parenthesis minus "d" , right parenthesis Superscript, pi Superscript, "x" , Baseline , Baseline "x"y=c−eiπx−dπxx
80
Expresión 81: "y" equals negative left parenthesis, "c" minus left parenthesis, "e" Superscript, "i" pi Superscript, "x" , Baseline , Baseline , right parenthesis minus "d" , right parenthesis Superscript, pi Superscript, "x" , Baseline , Baseline "x"y=−c−eiπx−dπxx
81
"x"x
left parenthesis, "c" minus left parenthesis, "e" Superscript, "i" pi Superscript, "x" , Baseline , Baseline , right parenthesis minus "d" , right parenthesis Superscript, pi Superscript, "x" , Baseline , Baseline "x"c−eiπx−dπxx
negative left parenthesis, "c" minus left parenthesis, "e" Superscript, "i" pi Superscript, "x" , Baseline , Baseline , right parenthesis minus "d" , right parenthesis Superscript, pi Superscript, "x" , Baseline , Baseline "x"−c−eiπx−dπxx
negative 30.8 8 1 0 9−30.88109
00
82
Control line void sets
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83
Expresión 92: "y" equals StartFraction, left parenthesis, "c" minus left parenthesis, "e" Superscript, "i" pi Superscript, "x" , Baseline , Baseline , right parenthesis minus "d" , right parenthesis Superscript, pi Superscript, "x" , Baseline , Baseline Over "e" Superscript, "i" pi , Baseline , EndFractiony=c−eiπx−dπxeiπ
92
Expresión 93: "y" equals negative StartFraction, left parenthesis, "c" minus left parenthesis, "e" Superscript, "i" pi Superscript, "x" , Baseline , Baseline , right parenthesis minus "d" , right parenthesis Superscript, pi Superscript, "x" , Baseline , Baseline Over "e" Superscript, "i" pi , Baseline , EndFractiony=−c−eiπx−dπxeiπ
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"x"x
StartFraction, left parenthesis, "c" minus left parenthesis, "e" Superscript, "i" pi Superscript, "x" , Baseline , Baseline , right parenthesis minus "d" , right parenthesis Superscript, pi Superscript, "x" , Baseline , Baseline Over "e" Superscript, "i" pi , Baseline , EndFractionc−eiπx−dπxeiπ
negative StartFraction, left parenthesis, "c" minus left parenthesis, "e" Superscript, "i" pi Superscript, "x" , Baseline , Baseline , right parenthesis minus "d" , right parenthesis Superscript, pi Superscript, "x" , Baseline , Baseline Over "e" Superscript, "i" pi , Baseline , EndFraction−c−eiπx−dπxeiπ
negative 2−2
negative 1−1
00
11
2.52.5
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Expresión 95: "y" equals negative left parenthesis, left parenthesis, "c" minus left parenthesis, "e" Superscript, "i" pi Superscript, "x" , Baseline , Baseline , right parenthesis minus "d" , right parenthesis Superscript, pi Superscript, "x" , Baseline , Baseline , right parenthesisy=−c−eiπx−dπx
95
Expresión 96: "y" equals left parenthesis, "c" minus left parenthesis, "e" Superscript, "i" pi Superscript, "x" , Baseline , Baseline , right parenthesis minus "d" , right parenthesis Superscript, pi Superscript, "x" , Baseline , Baseliney=c−eiπx−dπx
96
"x"x
negative left parenthesis, left parenthesis, "c" minus left parenthesis, "e" Superscript, "i" pi Superscript, "x" , Baseline , Baseline , right parenthesis minus "d" , right parenthesis Superscript, pi Superscript, "x" , Baseline , Baseline , right parenthesis−c−eiπx−dπx
left parenthesis, "c" minus left parenthesis, "e" Superscript, "i" pi Superscript, "x" , Baseline , Baseline , right parenthesis minus "d" , right parenthesis Superscript, pi Superscript, "x" , Baseline , Baselinec−eiπx−dπx
negative 30.8 8 1 0 9−30.88109
00
97
Wave sets
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98
Division sets
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106
Expresión 107: "y" equals StartFraction, left parenthesis, 1 minus left parenthesis, "e" Superscript, "i" pi Superscript, "x" , Baseline , Baseline , right parenthesis minus 1 , right parenthesis Superscript, pi Superscript, "x" , Baseline , Baseline Over pi , EndFractiony=1−eiπx−1πxπ
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Expresión 108: "y" equals negative StartFraction, left parenthesis, 1 minus left parenthesis, "e" Superscript, "i" pi Superscript, "x" , Baseline , Baseline , right parenthesis minus 1 , right parenthesis Superscript, pi Superscript, "x" , Baseline , Baseline Over pi , EndFractiony=−1−eiπx−1πxπ
108
"x"x
StartFraction, left parenthesis, 1 minus left parenthesis, "e" Superscript, "i" pi Superscript, "x" , Baseline , Baseline , right parenthesis minus 1 , right parenthesis Superscript, pi Superscript, "x" , Baseline , Baseline Over pi , EndFraction1−eiπx−1πxπ
negative StartFraction, left parenthesis, 1 minus left parenthesis, "e" Superscript, "i" pi Superscript, "x" , Baseline , Baseline , right parenthesis minus 1 , right parenthesis Superscript, pi Superscript, "x" , Baseline , Baseline Over pi , EndFraction−1−eiπx−1πxπ
negative 2−2
negative 1−1
00
11
22
109
Expresión 110: "y" equals StartFraction, left parenthesis, 1 minus left parenthesis, "e" Superscript, "i" pi Superscript, "x" , Baseline , Baseline , right parenthesis minus 1 , right parenthesis Superscript, pi Superscript, "x" , Baseline , Baseline Over "e" , EndFractiony=1−eiπx−1πxe
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Expresión 111: "y" equals negative StartFraction, left parenthesis, 1 minus left parenthesis, "e" Superscript, "i" pi Superscript, "x" , Baseline , Baseline , right parenthesis minus 1 , right parenthesis Superscript, pi Superscript, "x" , Baseline , Baseline Over "e" , EndFractiony=−1−eiπx−1πxe
111
"x"x
StartFraction, left parenthesis, 1 minus left parenthesis, "e" Superscript, "i" pi Superscript, "x" , Baseline , Baseline , right parenthesis minus 1 , right parenthesis Superscript, pi Superscript, "x" , Baseline , Baseline Over "e" , EndFraction1−eiπx−1πxe
negative StartFraction, left parenthesis, 1 minus left parenthesis, "e" Superscript, "i" pi Superscript, "x" , Baseline , Baseline , right parenthesis minus 1 , right parenthesis Superscript, pi Superscript, "x" , Baseline , Baseline Over "e" , EndFraction−1−eiπx−1πxe
negative 2−2
negative 1−1
00
11
22
112
Expresión 113: "y" equals StartFraction, left parenthesis, 1 minus left parenthesis, "e" Superscript, "i" pi Superscript, "x" , Baseline , Baseline , right parenthesis minus 1 , right parenthesis Superscript, pi Superscript, "x" , Baseline , Baseline Over "e" Superscript, "i" pi , Baseline , EndFractiony=1−eiπx−1πxeiπ
113
Expresión 114: "y" equals negative StartFraction, left parenthesis, 1 minus left parenthesis, "e" Superscript, "i" pi Superscript, "x" , Baseline , Baseline , right parenthesis minus 1 , right parenthesis Superscript, pi Superscript, "x" , Baseline , Baseline Over "e" Superscript, "i" pi , Baseline , EndFractiony=−1−eiπx−1πxeiπ
114
"x"x
StartFraction, left parenthesis, 1 minus left parenthesis, "e" Superscript, "i" pi Superscript, "x" , Baseline , Baseline , right parenthesis minus 1 , right parenthesis Superscript, pi Superscript, "x" , Baseline , Baseline Over "e" Superscript, "i" pi , Baseline , EndFraction1−eiπx−1πxeiπ
negative StartFraction, left parenthesis, 1 minus left parenthesis, "e" Superscript, "i" pi Superscript, "x" , Baseline , Baseline , right parenthesis minus 1 , right parenthesis Superscript, pi Superscript, "x" , Baseline , Baseline Over "e" Superscript, "i" pi , Baseline , EndFraction−1−eiπx−1πxeiπ
negative 2−2
negative 1−1
00
11
22
115
Expresión 116: "y" equals StartFraction, left parenthesis, 1 minus left parenthesis, "e" Superscript, "i" pi Superscript, "x" , Baseline , Baseline , right parenthesis minus 1 , right parenthesis Superscript, pi Superscript, "x" , Baseline , Baseline Over "i" , EndFractiony=1−eiπx−1πxi
116
Expresión 117: "y" equals StartFraction, left parenthesis, 1 minus left parenthesis, "e" Superscript, "i" pi Superscript, "x" , Baseline , Baseline , right parenthesis minus 1 , right parenthesis Superscript, pi Superscript, "x" , Baseline , Baseline Over "i" , EndFractiony=1−eiπx−1πxi
117
"x"x
StartFraction, left parenthesis, 1 minus left parenthesis, "e" Superscript, "i" pi Superscript, "x" , Baseline , Baseline , right parenthesis minus 1 , right parenthesis Superscript, pi Superscript, "x" , Baseline , Baseline Over "i" , EndFraction1−eiπx−1πxi
StartFraction, left parenthesis, 1 minus left parenthesis, "e" Superscript, "i" pi Superscript, "x" , Baseline , Baseline , right parenthesis minus 1 , right parenthesis Superscript, pi Superscript, "x" , Baseline , Baseline Over "i" , EndFraction1−eiπx−1πxi
00
11
22
118
when going negative this expression expands at a considerable pace.when hitting zero it returns to mid control line.
119
Experimental sets
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120
More experimental sets
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139
Cycloid
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147
Expresión 148: left parenthesis, left parenthesis, "c" minus left parenthesis, "e" Superscript, "i" pi Superscript, "t" , Baseline , Baseline , right parenthesis minus "d" , right parenthesis minus sin left parenthesis, left parenthesis, "c" minus left parenthesis, "e" Superscript, "i" pi Superscript, "t" , Baseline , Baseline , right parenthesis minus "d" , right parenthesis , right parenthesis , 1 minus cos left parenthesis, left parenthesis, "c" minus left parenthesis, "e" Superscript, "i" pi Superscript, "t" , Baseline , Baseline , right parenthesis minus "d" , right parenthesis , right parenthesis , right parenthesisc−eiπt−d−sinc−eiπt−d,1−cosc−eiπt−d