INDEX

Action, center of, 112

Alternate interior angle, 25

American Meteorological Society, 329

Amplitude, (defined), 60

Angle, alternate interior, 25; arc, 9; between

     projected arcs, 26, 27; between two circles, 16;

dihedral, 6; phase, 61; polyhedral, 9; spherical, 7, 8

trihedral, 9

Angles of the hexagon, 48, 49

Angstrom units, 54

Angular number, 101, 116, 170; defined, 115

Antinodes, 64, 65

Antipodal point, 8

Apollonius, 83

Arc angle, 9

Arc of a circle, 5

Arc polygon, 10

Arcs, angle between projections of, 26, 27

Asymmetric symmetry, 80, 81

Averages, symmetry of, 76, 77

Benard, H., 47, 49, 97, 323

Bender, Daniel, xv, 331

Bilaterai symmetry, 68, 157, 159

Bjerknes, J., 1, 331

Bode's Law, 52

Bohr, Niels, 54, 55, 56

Bravais, August, 327

Bravais lattices, 327

Buffon, (Histoire Naturelle), 327

Bulletin of the American Meteorological Society, 328,330

Burt, 327

Cardan, 326

Catenoid, 84, 85

Center of Action, 112

Center of Gravity, 112

Center of Projection, 13

Central vortex, (nuclear vortex), 101, 102, 115

Charts, Circumferential, 115-168

Charts, Radial, 169-319

Chesterton, Gilbert, 80

Chladni, Ernst, 91-95

Chladni Plates, 99, 114, 125, 170

Chord, 9

Circle, arc of, 5; equatorial, 22; great, 4, 5, 117,

324; inclination of, 22; nodal, 92; polar distance

of, 22; primitive, 22; small, 5, 116, 324

Circle center, straight line traced by, 85

Circles, angle of projection between, 16; latitude, errors in projection of, 18-21; projection of center of, 21

Circumferential Charts, 115-188; #20, 155; #26A, 145; #26B, 146; `32, 147; #34, 138; 937, 132133; #39, 129; #40, 128; #42, 130, 131; `46A, 123; #45B, 124-127; #49, 156; #56A, 120, 121; #55B, 122; #58, 117-19; #60, 134, 135; #63, 148; #66, 139; #72A, 142, 143; #72B, 144; #76, 136, 137; #78A, 157; #78B, 158; #79, 159; #80, 160; #81, 161; #82, 162; #84, 183; #86, 141; #88, 140; #9OA, 164; #9OB, 165; $90C, 166; #9lA, 149; #9lB, 150; #9lC, 161; #9lD, 152; #93A, 153; #93B, 154; #99, 167; #103, 168

Circumferential Units, (CU), 116, 323, 324

Circumferential wavenumber,92

Classes of symmetry, {point, line, plane ), 67, 88

Close packing of spheres, 41-46

Col, defined, 28; 111, 124, 125, 324

Co-latitude, 18

Cone, right circular, 83

Conic section, straight line, 83

Conic sections, 82-84; Roulette, 84, 85

Conklin, 45

Constructive interference, 64

Crystal, 71, 73; with defects, 81; lattice, 73

CU (circumferential units), 116, 323, 324

Curved surface, 5

Cylinder, surfaces of revolution, 84-89

Cylindrical structures, 84, 86-88

D-day (June 6, 1944), 320

Degrees of feedom, 33

Delaunay, 84

Demi-reguls patterns, 38-39

Demi-regular tessellations, 36

Destructive interference, 64

Diad, two fold symmetry, 69

Diameter, nodal, 92

Dictyocha stapedia, 45

Diffraction grating, 99, 100, 103, 324

Dihedral angle, 6; magnitude of, 6

Dilation symmetry, 71, 73

Dispersion, 63

Distigma proteus, 89

Dodecahedral, 34

Dodecahedron, 30, 31, 327; regular, 29

333


Dynamic, equilibrium, 80

Edge of two planes, 6

Einstein, Albert, 79

Electron wavelength, 55, 56

Ellipse, straight line, 85; straight line through an, 113

Elliptical shapes of lows and highs, 112, 113, 118, 164

Enantiomorphism, 66

Equatorial circle, 22

Equatorial plane, 14

Equilateral triangle, 11, 28, 172, 184

Equilibrium, 79-81; dynamic, 80; position of, 59, 80 simulated, 80; static, 80; triangle, 301

Equivalent symmetry points, 76

Errors in projection of latitude circles, 18-21

Euler, Leonhard, 44, 48

Face of plane, 6

"Fan shape" formation, 319

Figurate numbers, 42-44; hexagonal, 44

Fischbeck, Dr. George, xv

"Flying kite" formation, 226

Forced oscillation, 59

Formation, "Fan shaped", 319; "Flying kite",

     226; hexagonal, 100, 102; "K", 216, 224, 229;

"K", defined, 214; nested, 46; octagonal, 102;

pentagonal, 102; square, 28, 45, 100-102, triangular, 100, 101;

"V", 229-232, 254, 268, 270,

277, 281, 284, 285, 311, 315, 316; "X", 213, 214, 229, 252, 253;

"X", defined, 213; "Y",defined, 203

Four-fold symmetry, 76

Fourier analysis, 61-63

Fourier, J.B., 61, 169

Frank, Richard A., Administrator of NOAA, xiii

Frankenheim, 327

Free oscillation, 59

Friedrlch and Knipping, 100

Fujiwhara, xiii

Fundamenatal harmonic, 62, 63

Galileo, Galilei, 1

Glide reflection symmetry, 71, 72

Goldberger, 327

Gravity, center of, 112

Great circle, 4, 5, 117, 324; straight line, 117

Haeckel, Ernst, 34

Hales, Stephen, 45, 326, 327

Harmonic, analysis, 106, 169; fundamental, 1st.

2nd, 3rd, 4th, 5th, resultant, 62, 63; law, 52;

motion, simple, 59; movement, 60, 61; vibration, 91-93

Hexed, six fold symmetry, 69

Hexagon, angles of, 48, 49; regular, 28, 31

Hexagonal, compression and elongation, 41;

figurate numbers, 44; formations, 100, 102; shapes, 46-49

Hexahedral, 34

Hexahedron, 30; regular, 29

High, elliptical shape of, 112, 113

Histoire Naturelle (Buffon ), 327

Hofmeiater, Wilhelm F., 88

Icosahedral, 34; pattern, 11

Icosahedron, 30, 31; regular, 29

Identification map, 108-110

Image, mirror, 66, 69

Inclination of a circle, 22

Interference, 2, 63-66; constructive, 64; destructive, 64

Irregular polygon, 28

Isobars, 111

June 6, 1944 (D-day}, 320-322

Kepler, Johannes, 51

Kepler's Law, 51, 52

"K" formation, 214, 216, 224, 229

Knipping and Friedrich, 100

Lagrange, Joseph Louis, 89

La Rue, Jerry, 328

Latitude circles, errors in projection of, 18-21

Latitude, standard, 14

Lattice, Bravais, 327; crystal, 73

Laue, Max, 99

Law, Bode's, 52; Harmonic, 52; Kepler's, 51, 52;

Quantum, 54, 55; Roche's, 53, 54; Wolf's, 52, 53

LCD (Lowest Common Denominator), 170

Leduc, Stephane, 46

Line, classes of symmetry, 67-68; of longitude,

15; of measures, 23; mirror, 69; straight, see

straight line; symmetry, 67, 68, 92; tangent, 6

Liverwort, 57

Lock, definition of, x

Lockhart, Thomas J., 330

Longitude, line of, 15

Longitudinal glide reflection, 124, 155

Low, elliptical shape of, 112, 113, 118, 164

Lowest Common Denominator, (LCD), 170

Lufkin, Daniel, xiii, xiv

Lune, 8

Magnitude of dihedral angle, 6

Map, polar stereographic, 3, 12-27, 71; scale of, 14

Maximum symmetry, 118

McGrady, Pat (The Story of DMSO), 329

Measures, line of, 23

Menaechmus, 83

Mirror, image, 69; image equality symmetry, 66; line, 69; plane, 70

Modes of operation, 60

National Weather Service, xv

Natural oscillation, 59

Nested formation, 45

Net, parallelogram, 75

Network of points, symmetry, 71-78

Newton, Chester, (Editor, Monthly Weather Review), xii

Nodal, circle, 92; diameter, 92

Node, 64, 65, 91

Nodoid, 84, 85

Nuclear vortex, 101, 102, 115

Number, angular, 101, 115, 116, 170; significance of, xii

Numbers, figurate, 42-44; square, 42, 43; triangular, 42, 43

Octagonal formation, 102

Octahedral, 34

Octahedron, 30, 31; regular, 29

334


Olsen, Harry F. 93

Operation, modea of, 60; aymmetry, 68-71

Oscillation, defined, 59; forced, 59; free, 59; natural, 59

Pappus, 46

Parabolic rate of increase, 136, 261, 264

Parallelogons, 40

Parallelogram net, 76

Patterns, demi-regular, 38, 39; icosahedrai, 11; radial, 114, 115; step, 136, 261, 264

Pentagon, regular, 31

Pentagonal formation, 102

Periodic time function, 61

Phase angle, 61

Plane, 4; equatorial, 14; face of, 6; mirror, 70; primitive, 14; projection of, 15; surfaces of revolution, 84-89

Planes, edge of two, 6

Plateau, Joseph, 84-89; Problem of, 89, 112, 113, 153; Surfaces of revolution, 94

Point, antipodal, 8; polar diatance of, 22; rotation around, symmetry, 69

Points, crossed by straight lines, 77; polar, 8; network of, aymmetry, 71-78

Polar distance of a circle, 22

Polar distance of a point, 22

Polar furrow, 46

Polar points, 8

Polar stereographic map, 3, 12-27, 71; distortions of, 17-21; straight line on, 17

Polar stereographic projection, xii-xiv

polygon, 43; arc, 10; irregular, 28; regular, 28; spherical, 9

Polyhedral, angle, 9

Polyhedron, 28, 29, 32; regular, 29

Position of equillibrium, 59, 80

Positions, quantum, 54

Pournelle, J E, xii

Primitive, circle, 22; plane, 14

Principle of, similitude, 50, 51; superposition, 63, 124

Problem of Plateau, 89

Projection, center of, 13; of center of circles, 21; on a plane, 15

Pyramid, spherical, 7

Pythagoreans, 28, 29, 42

Quanta, 48

Quantum,, Law, 54, 55; positions, 54; sized vortex,97-99; units, 34; units in packages, 96

Radial Charts, 169-319 #20A, 170, 171; #20B, 172; #20C, 173; #20D, 174; #20E, 175; #20F, 176

#26A, 177; #26B, 178; #26C 178 #26D 180; #26E, 181; #26F, 182

#32A, 183; #32B, 184, 185

#34A, 186; #34B, 187; #34C, 188; #34D 189; #34E, 190

#37A, 191; #37B, 192; #37C, 193

#39A, 194; #39B, 195; #39C, 196; #39D, 197; #39E, 198

#40A, 199; #40B, 200; #40C, 201; #40D, 202; #40E, 203; #40F, 204; #40G, 205

#42A, 206; #42B, 207; #42C, 208; #42D, 209; #42E, 210

#45A, 211; #45B, 212; #45C, 213; #45D, 214; #45E, 21; #45F, 216

#49A, 217; #49B, 218; #49C, 219; #49D, 220; #49E, 221; #49F, 222; #49G, 223; #49H, 224

#55A, 225; #55B, 226; #55C, 227

#58A, 228; #58B, 229, #58C, 230; #58D, 231 #58E, 232; #58F, 233; #58G, 234

#60A, 235; #60B, 236; #60C, 237; #60D,238; #60E, 239

#63A, 240; #63B, 241; #63C, 242; #63D, 243

#66A, 244; #66B,245; #66C, 246; #66D, 247

#72A, 248; #72B, 249; #72C, 250, 251; #72D, 252; #72E, 253

#76A, 254; 076B, 255; #76C, 256; #76D, 257; #76E, 258; #76F, 259; #76G, 260

#78A, 261; #78B, 262; #78C, 263; #78D, 264; #78E, 265

#79A, 266; #79B, 267; #79C, 268; #79D, 269

#80A, 270; #80B, 271; #80C, 272; #80D, 273; #80E, 274; #80F, 276

#81A, 276; #81B, 277; #81C, 278; #81D, 279; #81E, 280; #81F, 281; #81G, 282

#82A, 283; #82B, 284; #82C, 286; #82D, 286; #82E, 287

#84A, 288; #84B, 289; #84C, 290; #84D, 291

#86A, 292; #86B, 293; #86C, 294; #86D, 295

#88A, 296; #88B, 297; #88C, 298

#90A, 299; #90B, 300; #90C, 301; #90D, 302

#91A, 303; #91B, 304; #91C, 305; #91D, 306

#93A, 307; #93B, 308; #93C, 309; #93D, 310

#99A, 311; #99B, 312; #99C, 313; #99D, 314

#103A, 315; #103B, 316; #103C, 317; #103D, 318; #103E, 319

Radial patterns, 114, 115

Radial Units, (RU ), 117, 323, 324

Radial wavenumber, 92

Radiolaria, 44

Radius, 5

Rake, 198, 231, 250, 290, 311; defined, 198 Random time functions, 65

Rayleigh, Lord, 89

Referee "B", anonymous editor, xiii

Referee "C",anonymoua editor, xiii

Reflection line symmetry, 69

Reflection symmetry, 69, 75

Regular, dodecahedron, 29; hexagon, 31; hexahedron, 29; icosahedron, 29; octahedron, 29; pentagon, 31; polygon, 28; polyhedron, 29; solid, 29; tessellations, 36; tetrahedron, 29

Resonance, 60, 105

Resultant, 62, 63

Revolution, surfaces of, 84-89

Ridge, 111

Right circular cone, 83

Roche, E, 54

Roche limit, 54

Roche's Law, 53, 54

Rossby, Carl, 323, 331

Rossby waves, xi

335


Rotational symmetry, 69, 75, 250

Rotation symmetry around a point, 69

Roulette, conic sections, 84, 85; straight line, 85

RU (Radial Units), 117, 323, 324

Sanders, Professor Frederick (Editor, Focus on forecasting, Bulletin of the American Meteorological Society), 328

Saturn, rings and spokes, 53

Scale of a map, 14

Sem-regular tessellations, 36

Septagon, 30

Shapes, hexagonal, 46-49

Similitude, principle of, 50, 51

Simple harmonic motion, 59

Simulated Equilibrium, 80

Sine wave, 61, 62

Singer's Lock, x, xii, xiv, 1, 8, 76, 124, 130, 169, 170, 324; defined, x

Six fold symmetry, 69

Size (of objects), 96

Small circle, 5, 116, 324

Solid, regular, 29

Spengler, Kenneth C., 327

Spheres, close packing of, 41-46

Spherical, angle, 7, 8; excess of a triangle, 10; geometry, 4-11; polygon, 9; pyramid, 7; surface, 4; triangle, 7, 9

Splash of a drop, 89

Spray, defined, 187

Square, compression, 41; elongation, 41; formations, 28, 45, 100-102; numbers, 42, 43

Staggered wavenumber, 57

Standard latitude, 14

Standing waves, 64

Static equilibrium, 80

Statistics, xi, 2, 49, 50, 68, 105; wavenumber averages, 323, 324

"Stepladder" pattern, 319 "Step" pattern, 261, 264

Stereographic map, see Polar stereographic map

Straight line, conic section, 83; ellipse, 85, 113; first use in meteorology, 324; great circle, 117; points crossed by, 77; on a polar stereographic map, 17, 21, 33; roulette, 85; symmetry along, 71, 72; through an ellipse, 113; traced by circle center, 85; of vortexes, 95

Structures, cylindrical, 84, 86-88

Suitable equality symmetry, 66

Superpostion, principle of, 63, 124

Surface, curved, 5; spherical, 4

Surfaces of Revolution, 84-89, 94

Symmetry, along a straight line, 71, 72; asymmetric, 80, 81; of averages, 76, 77; bilateral, 68, 157, 159; classes of, 67, 68; definition of, 66; 67; diad, 69; dilation, 71, 73; elements, 68; four fold, 76; geometrically regular, 66, 67; glide reflection, 71, 72; lines, 67, 68, 92; maximum, 118; mirror image equality, 66; network of points, 71-78; operations, 68-71; patterns, xii; points, equivalent, 76; reflection, 69, 75; reflection line, 69; rotational, 69, 75, 250; rotation around a point, 69; suitable equality, 66; three fold, 69, 76; translational, 70-72; triad, 69, 76; two fold, 69; wall paper pattern, 74

Tangent line, 6

Tartaglia, 326

Tessellations, demi-regular, 36; regular, 36; sem-regular, 36

Tetrad, four fold symmetry, 69

Tetrahedral, 34

Tetrahedron, 30, 31, 34; regular, 29

Three fold symmetry, 69

Titius, 52

Translational symmetry, 70-72

Triad, three fold symmetry, 69, 76

Trianea, 88

Triangle, equilateral, 28; equilibrium, 301; spherical, 7, 9; spherical excess of, 10 Triangular formations, 100, 101

Triangular, numbers, 42, 43

Trihedral angle, 9

Trough, 111

Two axis, (x,y), 229, 230-232, 246, 250, 256, 257, 260, 284, 285, 288, 291; defined, 229

Two fold symmetry, 69

Unduloid, surfaces of revolution, 84-89

Units, angstrom, 54; circumferential, 116, 323, 324; quantum, 34; radial, 117, 323, 324

Vegetable Statics, (by Stephen Hales), 326, 327

Vertex, 8, 9

"V" formation, 229-232, 254, 268, 270, 277, 281, 284, 285, 311, 315, 316

Vibration, 59; harmonic, 91-93

Vortex, central, 101, 102, 115; nuclear, 101, 102, 115; quantum sized, 97-99

Vortexes, straight line of, 96

"Wallpaper" pattern symmetry, 74

Wave, pulses, 63; sine, 61, 62; standing, 64

Wavelength, electron, 55, 56; also see wave. number

Wavenumber, 56, 57, 94, 99, 100, 323-325; circumferential, 92; radial, 92; staggered, 57

Waves, 58-65

Weather tool, 102-105

Weber, E., 48

Wolf's Law, 52, 53

Worthington, A. M., 89

"X" formation, 213, 214, 229, 252, 253; defined, 213

"Y" formation, defined, 203

336


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