Index

acceleration formulas, 55, 57

adsorbed, 3

Alexandrov's theorem, 27, 119

analytic, 44

analytic continuation, 100

angstrom, 4

arctan, 209

area-minimizing surface, 67, 71, 199

associated family, 210

astroid, 223

basis, 33

bat, 218

bending energy, 147

Bernstein's theorem, 95

Bjorling's problem, 96, 221

brachistochrone, 124, 137, 236

bubbles, 8, 153

capillarity, 166, 172

capillary tube, 26

Catalan's surface, 67, 82, 103, 197, 214,

222

Catalan's theorem, 66

catenary, 36, 55, 71, 125, 149, 178,

182, 183, 233

catenoid, 11, 36, 55, 60, 72, 82, 86,

105, 142, 179, 181, 185, 193, 222

Cauchy's theorem, 47

Cauchy-Riemann equations, 45

complex conjugate, 40, 45

complex numbers, 43

conformal, 87, 88, 92

constant mean curvature, 118, 256

constrained problem, 146, 147, 230

contact angle, 23, 166, 172

cycloid, 103, 139, 140

cylinder, 203

Delaunay surfaces (see surface of De-

launay), 153

Dirichlet integral, 144

disk-like minimal surface, 68

divergence theorem, 107

dotprod, 161, 175

double bubble theorem, 30, 115

dsolve, 225

energy minimization, 13

Enneper's surface, 36, 66, 83, 113, 199

Euler-Lagrange equations, 130-132, 225

extremals, 130

extremize, 124

Fermat's principle, 139

first fundamental form, 39

first integral, 134, 227

first principle of soap films, 14

fixed endpoint problem, 124

fsolve, 182

Fundamental Theorem of Calculus, 48

funnel, 8

fused bubbles, 21, 159, 163

Gauss curvature, 50, 52, 85, 176

Gauss map, 86, 89, 204

geographical coordinates, 35

gravitational constant, 24

Green's theorem, 47, 69, 73, 126, 132,

151

harmonic conjugate, 47

265

acceleration formulas, 55, 57

adsorbed, 3

Alexandrov's theorem, 27, 119

analytic, 44

analytic continuation, 100

angstrom, 4

arctan, 209

area-minimizing surface, 67, 71, 199

associated family, 210

astroid, 223

basis, 33

bat, 218

bending energy, 147

Bernstein's theorem, 95

Bjorling's problem, 96, 221

brachistochrone, 124, 137, 236

bubbles, 8, 153

capillarity, 166, 172

capillary tube, 26

Catalan's surface, 67, 82, 103, 197, 214,

222

Catalan's theorem, 66

catenary, 36, 55, 71, 125, 149, 178,

182, 183, 233

catenoid, 11, 36, 55, 60, 72, 82, 86,

105, 142, 179, 181, 185, 193, 222

Cauchy's theorem, 47

Cauchy-Riemann equations, 45

complex conjugate, 40, 45

complex numbers, 43

conformal, 87, 88, 92

constant mean curvature, 118, 256

constrained problem, 146, 147, 230

contact angle, 23, 166, 172

cycloid, 103, 139, 140

cylinder, 203

Delaunay surfaces (see surface of De-

launay), 153

Dirichlet integral, 144

disk-like minimal surface, 68

divergence theorem, 107

dotprod, 161, 175

double bubble theorem, 30, 115

dsolve, 225

energy minimization, 13

Enneper's surface, 36, 66, 83, 113, 199

Euler-Lagrange equations, 130-132, 225

extremals, 130

extremize, 124

Fermat's principle, 139

first fundamental form, 39

first integral, 134, 227

first principle of soap films, 14

fixed endpoint problem, 124

fsolve, 182

Fundamental Theorem of Calculus, 48

funnel, 8

fused bubbles, 21, 159, 163

Gauss curvature, 50, 52, 85, 176

Gauss map, 86, 89, 204

geographical coordinates, 35

gravitational constant, 24

Green's theorem, 47, 69, 73, 126, 132,

151

harmonic conjugate, 47

265