Peanut Surfaces: Trace as "circle of best fit" to <Ax,x>x
thanks to Desmos demo "parameterized surface of revolution" for teaching how to make surfaces
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Expression 19: "S" left parenthesis, "u" , "v" , right parenthesisSu,v
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Expression 20: "e" Subscript, 1 , Baseline left parenthesis, "u" , "v" , right parenthesis equals "d" Subscript, 1 , Baseline "s" Subscript, 1 , Baseline left parenthesis, "u" , "v" , right parenthesis plus "a" "s" Subscript, 2 , Baseline left parenthesis, "u" , "v" , right parenthesis plus "b" "s" Subscript, 3 , Baseline left parenthesis, "u" , "v" , right parenthesise1u,v=d1s1u,v+as2u,v+bs3u,v
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Expression 21: "e" Subscript, 2 , Baseline left parenthesis, "u" , "v" , right parenthesis equals "a" Subscript, 2 , Baseline "s" Subscript, 1 , Baseline left parenthesis, "u" , "v" , right parenthesis plus "d" Subscript, 2 , Baseline "s" Subscript, 2 , Baseline left parenthesis, "u" , "v" , right parenthesis plus "c" "s" Subscript, 3 , Baseline left parenthesis, "u" , "v" , right parenthesise2u,v=a2s1u,v+d2s2u,v+cs3u,v
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Expression 22: "e" Subscript, 3 , Baseline left parenthesis, "u" , "v" , right parenthesis equals "b" Subscript, 2 , Baseline "s" Subscript, 1 , Baseline left parenthesis, "u" , "v" , right parenthesis plus "c" Subscript, 2 , Baseline "s" Subscript, 2 , Baseline left parenthesis, "u" , "v" , right parenthesis plus "d" Subscript, 3 , Baseline "s" Subscript, 3 , Baseline left parenthesis, "u" , "v" , right parenthesise3u,v=b2s1u,v+c2s2u,v+d3s3u,v
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Expression 23: "E" left parenthesis, "u" , "v" , right parenthesis equals left parenthesis, "e" Subscript, 1 , Baseline left parenthesis, "u" , "v" , right parenthesis , "e" Subscript, 2 , Baseline left parenthesis, "u" , "v" , right parenthesis , "e" Subscript, 3 , Baseline left parenthesis, "u" , "v" , right parenthesis , right parenthesisEu,v=e1u,v,e2u,v,e3u,v
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Expression 24: "E" left parenthesis, "u" , "v" , right parenthesisEu,v
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Expression 25: "S" left parenthesis, alpha , beta , right parenthesisSα,β
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Expression 26: "E" left parenthesis, alpha , beta , right parenthesisEα,β
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Expression 27: alpha equals 1.8α=1.8
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Expression 28: beta equals 0.0 7β=0.07
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Expression 29: "P" left parenthesis, "u" , "v" , right parenthesis equals left parenthesis, "s" Subscript, 1 , Baseline left parenthesis, "u" , "v" , right parenthesis "g" left parenthesis, "u" , "v" , right parenthesis , "s" Subscript, 2 , Baseline left parenthesis, "u" , "v" , right parenthesis "g" left parenthesis, "u" , "v" , right parenthesis , "s" Subscript, 3 , Baseline left parenthesis, "u" , "v" , right parenthesis "g" left parenthesis, "u" , "v" , right parenthesis , right parenthesisPu,v=s1u,vgu,v,s2u,vgu,v,s3u,vgu,v
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Expression 30: "g" left parenthesis, "u" , "v" , right parenthesis equals "f" left parenthesis, "s" Subscript, 1 , Baseline left parenthesis, "u" , "v" , right parenthesis , "s" Subscript, 2 , Baseline left parenthesis, "u" , "v" , right parenthesis , "s" Subscript, 3 , Baseline left parenthesis, "u" , "v" , right parenthesis , right parenthesisgu,v=fs1u,v,s2u,v,s3u,v
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Expression 31: "P" left parenthesis, "u" , "v" , right parenthesisPu,v
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Expression 32: "P" left parenthesis, alpha , beta , right parenthesisPα,β
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Expression 33: segment left parenthesis, left parenthesis, 0 , 0 , 0 , right parenthesis , 2 "P" left parenthesis, alpha , beta , right parenthesis , right parenthesissegment0,0,0,2Pα,β
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Expression 34: segment left parenthesis, "P" left parenthesis, alpha , beta , right parenthesis , "E" left parenthesis, alpha , beta , right parenthesis , right parenthesissegmentPα,β,Eα,β
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Expression 35: "x" squared plus "y" squared plus "z" squared equals left parenthesis, 1 third left parenthesis, "d" Subscript, 1 , Baseline plus "d" Subscript, 2 , Baseline plus "d" Subscript, 3 , Baseline , right parenthesis , right parenthesis squaredx2+y2+z2=13d1+d2+d32
