Expression 11: "R" equals StartFraction, "r" Subscript, 1 , Baseline Over 2 , EndFraction left parenthesis, left parenthesis, negative 1 , right parenthesis Superscript, "T" , Baseline minus 1 , right parenthesis minus StartFraction, "r" Subscript, 2 , Baseline Over 2 , EndFraction left parenthesis, left parenthesis, negative 1 , right parenthesis Superscript, "T" , Baseline plus 1 , right parenthesisR=r12−1T−1−r22−1T+1
equals=
negative 3.1 5−3.15
negative 1.1 6−1.16
negative 3.1 5−3.15
negative 1.1 6−1.16
negative 3.1 5−3.15
negative 1.1 6−1.16
negative 3.1 5−3.15
negative 1.1 6−1.16
negative 3.1 5−3.15
negative 1.1 6−1.16
negative 3.1 5−3.15
11
Points are generated in the anti-clockwise direction, so imagine first 10 points on the circumference of a circle. The angular gap between each point is π/n. Try replacing the 1s below with something else.
12
Hidden Label: left parenthesis, "R" cos left parenthesis, left parenthesis, 1 , right parenthesis StartFraction, "T" pi Over "n" , EndFraction plus StartFraction, pi Over 2 , EndFraction plus theta Subscript, 1 , Baseline , right parenthesis , "R" sin left parenthesis, left parenthesis, 1 , right parenthesis StartFraction, "T" pi Over "n" , EndFraction plus StartFraction, pi Over 2 , EndFraction plus theta Subscript, 1 , Baseline , right parenthesis , right parenthesisRcos1Tπn+π2+θ1,Rsin1Tπn+π2+θ1
Label
13
These are just to put sliders on the graph to adjust the parameters. Desmos doesn’t like complex numbers so when the x-coordinate of the red dot is negative, the purples kinda just vanish.
14
Hidden Label: left parenthesis, StartFraction, 4 "n" Over 7 , EndFraction minus 26 sevenths , 1 plus 0 "w" , right parenthesis4n7−267,1+0w
Label
15
Hidden Label: left parenthesis, 4 fifths "r" Subscript, 1 , Baseline minus 2 , 0 plus 0 "w" , right parenthesis45r1−2,0+0w
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16
Hidden Label: left parenthesis, 4 fifths "r" Subscript, 2 , Baseline minus 2 , negative 1 plus 0 "w" , right parenthesis45r2−2,−1+0w