Phi

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[[Image:Phi.png|thumb|150px|Phi]]
[[Image:Phi.png|thumb|150px|Phi]]
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'''Phi''' (uppercase Φ, lowercase φ or math symbol ϕ), pronounced ˈfaɪ or sometimes /ˈfiː/ in English,<sup>[]</sup> and ˈfi in [[Modern Greek language|modern Greek]], is the 21st letter of the [[Greek alphabet]]. In modern Greek, it represents [f], a [[voiceless labiodental fricative]]. In Ancient Greek it represented [pʰ], an [[Aspiration (phonetics)|aspirated]] [[voiceless bilabial plosive]] (from which English ultimately inherits the spelling "[[ph (digraph)|ph]]" in words derived from Greek).  In the system of [[Greek numerals]] it has a value of 500 (φʹ) or 500,000 (͵φ). The Cyrillic letter [[Ef (Cyrillic)|Ef]] (Ф, ф) arose from Φ.
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'''Phi''' (uppercase Φ, lowercase φ or math symbol ϕ), pronounced ˈfaɪ or sometimes /ˈfiː/ in English,<sup>[1]</sup> and ˈfi in [[Modern Greek language|modern Greek]], is the 21st letter of the [[Greek alphabet]]. In modern Greek, it represents [f], a [[voiceless labiodental fricative]]. In Ancient Greek it represented [pʰ], an [[Aspiration (phonetics)|aspirated]] [[voiceless bilabial plosive]] (from which English ultimately inherits the spelling "[[ph (digraph)|ph]]" in words derived from Greek).  In the system of [[Greek numerals]] it has a value of 500 (φʹ) or 500,000 (͵φ). The Cyrillic letter [[Ef (Cyrillic)|Ef]] (Ф, ф) arose from Φ.
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== Use as a symbol ==
 
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The lower-case letter <math>\varphi \,</math> (or often its variant, <math>\phi \,</math>) is often used to represent the following:
 
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*The [[golden ratio]] <math>\tfrac{1 + \sqrt{5}}{2} \approx 1.61803\ldots</math> in mathematics, art, and architecture.
 
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*[[Euler's totient function]] ''φ''(''n'') in number theory; also called ''Euler's phi function''.
 
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*In algebra, [[Group (mathematics)|group]] or [[Ring (mathematics)|ring]] [[homomorphism]]s
 
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* In [[probability theory]], {{nowrap|1=''ϕ''(''x'') = (2π)<sup>−½</sup>''e''<sup>−''x''<sup>2</sup>/2</sup>}} is the [[probability density function]] of the [[normal distribution]].
 
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* In [[probability theory]], {{nowrap|1=''φ''<sub>''X''</sub>(''t'') = E[&thinsp;''e''<sup>''itX''</sup>&thinsp;]}} is the [[characteristic function (probability theory)|characteristic function]] of a random variable ''X''.
 
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*An [[angle]], typically the second angle mentioned, after ''θ'' ([[theta]]).  Especially:
 
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**The argument of a [[complex number]].
 
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**The [[phase (waves)|phase of a wave]] in signal processing.
 
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**In [[spherical coordinates]], mathematicians usually refer to phi as the polar angle (from the ''z''-[[Coordinate axis|axis]]).  The convention in physics is to use phi as the azimuthal angle (from the ''x''-axis).
 
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**One of the [[dihedral angle]]s in the backbones of [[protein]]s.
 
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**Internal or effective [[angle of friction]].
 
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*[[Electric potential]] in physics.
 
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*The [[work function]] in electronics.
 
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*A [[shorthand]] representation for an [[aromatic]] [[functional group]] in [[organic chemistry]].
 
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*The [[fugacity]] coefficient in [[thermodynamics]].
 
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*The ratio of [[Thermodynamic free energy|free energy]] destabilizations of protein [[mutant]]s in [[phi value analysis]].
 
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*In [[cartography]] and [[navigation]], [[latitude]].
 
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*In combustion engineering, equivalence ratio. The ratio between the actual fuel air ratio to the stoichiometric fuel air ratio.
 
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*A sentence in [[first-order logic]].
 
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*[[Porosity]] in geology and [[hydrology]].
 
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*Strength (or resistance) reduction factor in [[structural engineering]], used to account for statistical variabilities in materials and construction methods.
 
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*The symbol for a [[voiceless bilabial fricative]] in the [[International Phonetic Alphabet]] (using the straight line variant character)
 
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*In economics, this is usually an additive term.{{Clarify|date=October 2009}}
 
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*In [[flight dynamics]], the roll angle.
 
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The upper-case letter Φ is used as a symbol for:
 
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*The [[Golden_ratio#Golden_ratio_conjugate|golden ratio conjugate]] −0.618... in mathematics.
 
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*The [[magnetic flux]] and [[electric flux]] in physics, with subscripts distinguishing the two.
 
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*The [[cumulative distribution function]] of the [[normal distribution]] in [[mathematics]] and [[statistics]].
 
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*[[Philosophy]].
 
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*The number of phases in a power system in [[electrical engineering]], for example 1Φ for [[single phase]], 3Φ for [[three phase]].
 
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*A common symbol for the parametrization of a surface in vector [[calculus]].
 
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*In [[Lacanian algebra]], Φ stands for the imaginary phallus and also represents phallic signification. -Φ stands in for castration.<sup>[]</sup>
 
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The [[diameter]] symbol in [[engineering]], [[⌀]], is often incorrectly referred to as "phi". This symbol is used to indicate the diameter of a circular section, for example "⌀14", means the diameter of the [[circle]] is 14 [[Units of measurement|units]].
 
== See also ==
== See also ==
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{{DEFAULTSORT:Phi (Letter)}}
{{DEFAULTSORT:Phi (Letter)}}
[[Category:Greek letters]]
[[Category:Greek letters]]
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{{Donate}}

Current revision

Phi
Phi

Phi (uppercase Φ, lowercase φ or math symbol ϕ), pronounced ˈfaɪ or sometimes /ˈfiː/ in English,[1] and ˈfi in modern Greek, is the 21st letter of the Greek alphabet. In modern Greek, it represents [f], a voiceless labiodental fricative. In Ancient Greek it represented [pʰ], an aspirated voiceless bilabial plosive (from which English ultimately inherits the spelling "ph" in words derived from Greek). In the system of Greek numerals it has a value of 500 (φʹ) or 500,000 (͵φ). The Cyrillic letter Ef (Ф, ф) arose from Φ.


See also

References

The King James Version 2023 Edition New Testament is now complete and in print format here.
The King James Version 2023 Edition New Testament is now complete and in print format here.

List of New Testament Papyri

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List of New Testament minuscules

1 · 2 · 3 · 4 · 5 · 6 · 7 · 8 · 9 · 10 · 11 · 12 · 13 · 14 · 15 · 16 · 17 · 18 · 19 · 20 · 21 · 22 · 23 · 24 · 25 · 26 · 27 · 28 · 29 · 30 · 31 · 32 · 33 · 34 · 35 · 36 · 37 · 38 · 39 · 40 · 41 · 42 · 43 · 44 · 45 · 46 · 47 · 48 · 49 · 50 · 51 · 52 · 53 · 54 · 55 · 56 · 57 · 58 · 59 · 60 · 61 · 62 · 63 · 64 · 65 · 66 · 67 · 68 · 69 · 70 · 71 · 72 · 73 · 74 · 75 · 76 · 77 · 78 · 79 · 80 · 81 · 82 · 83 · 84 · 85 · 86 · 87 · 88 · 89 · 90 · 91 · 92 · 93 · 94 · 95 · 96 · 97 · 98 · 99 · 100 · 101 · 102 · 103 · 104 · 105 · 106 · 107 · 108 · 109 · 110 · 111 · 112 · 113 · 114 · 115 · 116 · 117 · 118 · 119 · 120 · 121 · 122 · 123 · 124 · 125 · 126 · 127 · 128 · 129 · 130 · 131 · 132 · 133 · 134 · 135 · 136 · 137 · 138 · 139 · 140 · 141 · 142 · 143 · 144 · 145 · 146 · 147 · 148 · 149 · 150 · 151 · 152 · 153 · 154 · 155 · 156 · 157 · 158 · 159 · 160 · 161 · 162 · 163 · 164 · 165 · 166 · 167 · 168 · 169 · 170 · 171 · 172 · 173 · 174 · 175 · 176 · 177 · 178 · 179 · 180 · 181 · 182 · 183 · 184 · 185 · 186 · 187 · 188 · 189 · 190 · 191 · 192 · 193 · 194 · 195 · 196 · 197 · 198 · 199 · 200 · 201 · 202 · 203 · 204 · 205 · 206 · 207 · 208 · 209 · 210 · 211 · 212 · 213 · 214 · 215 · 216 · 217 · 218 · 219 · 220 · 221 · 222 · 223 · 224 · 225 · 226 · 227 · 228 · 229 · 230 · 231 · 232 · 233 · 234 · 235 · 236 · 237 · 238 · 239 · 240 · 241 · 242 · 243 · 244 · 245 · 246 · 247 · 248 · 249 · 250 · 251 · 252 · 253 · 254 · 255 · 256 · 257 · 258 · 259 · 260 · 261 · 262 · 263 · 264 · 265 · 266 · 267 · 268 · 269 · 270 · 271 · 272 · 273 · 274 · 275 · 276 · 277 · 278 · 279 · 280 · 281 · 282 · 283 · 284 · 285 · 286 · 287 · 288 · 289 · 290 · 291 · 292 · 293 · 294 · 295 · 296 · 297 · 298 · 299 · 300 · 301 · 302 · 303 · 304 · 305 · 306 · 307 · 308 · 309 · 310 · 311 · 312 · 313 · 314 · 315 · 316 · 317 · 318 · 319 · 320 · 321 · 322 · 323 · 324 · 325 · 326 · 327 · 328 · 329 · 330 · 331 · 332 · 333 · 334 · 335 · 336 · 337 · 338 · 339 · 340 · 341 · 342 · 343 · 344 · 345 · 346 · 347 · 348 · 349 · 350 · 351 · 352 · 353 · 354 · 355 · 356 · 357 · 358 · 359 · 360 · 361 · 362 · 363 · 364 · 365 · 366 · 367 · 368 · 369 · 370 · 371 · 372 · 373 · 374 · 375 · 376 · 377 · 378 · 379 · 380 · 381 · 382 · 383 · 384 · 385 · 386 · 387 · 388 · 389 · 390 · 391 · 392 · 393 · 394 · 395 · 396 · 397 · 398 · 399 · 400 · 401 · 402 · 403 · 404 · 405 · 406 · 407 · 408 · 409 · 410 · 411 · 412 · 413 · 414 · 415 · 416 · 417 · 418 · 419 · 420 · 421 · 422 · 423 · 424 · 425 · 426 · 427 · 428 · 429 · 430 · 431 · 432 · 433 · 434 · 435 · 436 · 437 · 438 · 439 · 440 · 441 · 442 · 443 · 444 · 445 · 446 · 447 · 448 · 449 · 450 · 451 · 452 · 453 · 454 · 455 · 456 · 457 · 458 · 459 · 460 · 461 · 462 · 463 · 464 · 465 · 466 · 467 · 468 · 469 · 470 · 471 · 472 · 473 · 474 · 475 · 476 · 477 · 478 · 479 · 480 · 481 · 482 · 483 · 484 · 485 · 486 · 487 · 488 · 489 · 490 · 491 · 492 · 493 · 494 · 495 · 496 · 497 · 498 · 499 · 500 · 501 · 502 · 503 · 504 · 505 · 506 · 507 · 543 · 544 · 565 · 566 · 579 · 585 · 614 · 639 · 653 · 654 · 655 · 656 · 657 · 658 · 659 · 660 · 661 · 669 · 676 · 685 · 700 · 798 · 823 · 824 · 825 · 826 · 827 · 828 · 829 · 830 · 831 · 876 · 891 · 892 · 893 · 1071 · 1143 · 1152 · 1241 · 1253 · 1423 · 1424 · 1432 · 1582 · 1739 · 1780 · 1813 · 1834 · 2050 · 2053 · 2059 · 2060 · 2061 · 2062 · 2174 · 2268 · 2344 · 2423 · 2427 · 2437 · 2444 · 2445 · 2446 · 2460 · 2464 · 2491 · 2495 · 2612 · 2613 · 2614 · 2615 · 2616 · 2641 · 2754 · 2755 · 2756 · 2757 · 2766 · 2767 · 2768 · 2793 · 2802 · 2803 · 2804 · 2805 · 2806 · 2807 · 2808 · 2809 · 2810 · 2811 · 2812 · 2813 · 2814 · 2815 · 2816 · 2817 · 2818 · 2819 · 2820 · 2821 · 2855 · 2856 · 2857 · 2858 · 2859 · 2860 · 2861 · 2862 · 2863 · 2881 · 2882 · 2907 · 2965 ·


List of New Testament uncials

01 · 02 · 03 · 04 · 05 · 06 · 07 · 08 · 09 · 010 · 011 · 012 · 013 · 014 · 015 · 016 · 017 · 018 · 019 · 020 · 021 · 022 · 023 · 024 · 025 · 026 · 027 · 028 · 029 · 030 · 031 · 032 · 033 · 034 · 035 · 036 · 037 · 038 · 039 · 040 · 041 · 042 · 043 · 044 · 045 · 046 · 047 · 048 · 049 · 050 · 051 · 052 · 053 · 054 · 055 · 056 · 057 · 058 · 059 · 060 · 061 · 062 · 063 · 064 · 065 · 066 · 067 · 068 · 069 · 070 · 071 · 072 · 073 · 074 · 075 · 076 · 077 · 078 · 079 · 080 · 081 · 082 · 083 · 084 · 085 · 086 · 087 · 088 · 089 · 090 · 091 · 092 · 093 · 094 · 095 · 096 · 097 · 098 · 099 · 0100 · 0101 · 0102 · 0103 · 0104 · 0105 · 0106 · 0107 · 0108 · 0109 · 0110 · 0111 · 0112 · 0113 · 0114 · 0115 · 0116 · 0117 · 0118 · 0119 · 0120 · 0121 · 0122 · 0123 · 0124 · 0125 · 0126 · 0127 · 0128 · 0129 · 0130 · 0131 · 0132 · 0134 · 0135 · 0136 · 0137 · 0138 · 0139 · 0140 · 0141 · 0142 · 0143 · 0144 · 0145 · 0146 · 0147 · 0148 · 0149 · 0150 · 0151 · 0152 · 0153 · 0154 · 0155 · 0156 · 0157 · 0158 · 0159 · 0160 · 0161 · 0162 · 0163 · 0164 · 0165 · 0166 · 0167 · 0168 · 0169 · 0170 · 0171 · 0172 · 0173 · 0174 · 0175 · 0176 · 0177 · 0178 · 0179 · 0180 · 0181 · 0182 · 0183 · 0184 · 0185 · 0186 · 0187 · 0188 · 0189 · 0190 · 0191 · 0192 · 0193 · 0194 · 0195 · 0196 · 0197 · 0198 · 0199 · 0200 · 0201 · 0202 · 0203 · 0204 · 0205 · 0206 · 0207 · 0208 · 0209 · 0210 · 0211 · 0212 · 0213 · 0214 · 0215 · 0216 · 0217 · 0218 · 0219 · 0220 · 0221 · 0222 · 0223 · 0224 · 0225 · 0226 · 0227 · 0228 · 0229 · 0230 · 0231 · 0232 · 0234 · 0235 · 0236 · 0237 · 0238 · 0239 · 0240 · 0241 · 0242 · 0243 · 0244 · 0245 · 0246 · 0247 · 0248 · 0249 · 0250 · 0251 · 0252 · 0253 · 0254 · 0255 · 0256 · 0257 · 0258 · 0259 · 0260 · 0261 · 0262 · 0263 · 0264 · 0265 · 0266 · 0267 · 0268 · 0269 · 0270 · 0271 · 0272 · 0273 · 0274 · 0275 · 0276 · 0277 · 0278 · 0279 · 0280 · 0281 · 0282 · 0283 · 0284 · 0285 · 0286 · 0287 · 0288 · 0289 · 0290 · 0291 · 0292 · 0293 · 0294 · 0295 · 0296 · 0297 · 0298 · 0299 · 0300 · 0301 · 0302 · 0303 · 0304 · 0305 · 0306 · 0307 · 0308 · 0309 · 0310 · 0311 · 0312 · 0313 · 0314 · 0315 · 0316 · 0317 · 0318 · 0319 · 0320 · 0321 · 0322 · 0323 ·


List of New Testament lectionaries

1 · 2 · 3 · 4 · 5 · 6 · 7 · 8 · 9 · 10 · 11 · 12 · 13 · 14 · 15 · 16 · 17 · 18 · 19 · 20 · 21 · 22 · 23 · 24 · 25 · 25b · 26 · 27 · 28 · 29 · 30 · 31 · 32 · 33 · 34 · 35 · 36 · 37 · 38 · 39 · 40 · 41 · 42 · 43 · 44 · 45 · 46 · 47 · 48 · 49 · 50 · 51 · 52 · 53 · 54 · 55 · 56 · 57 · 58 · 59 · 60 · 61 · 62 · 63 · 64 · 65 · 66 · 67 · 68 · 69 · 70 · 71 · 72 · 73 · 74 · 75 · 76 · 77 · 78 · 79 · 80 · 81 · 82 · 83 · 84 · 85 · 86 · 87 · 88 · 89 · 90 · 91 · 92 · 93 · 94 · 95 · 96 · 97 · 98 · 99 · 100 · 101 · 102 · 103 · 104 · 105 · 106 · 107 · 108 · 109 · 110 · 111 · 112 · 113 · 114 · 115 · 116 · 117 · 118 · 119 · 120 · 121 · 122 · 123 · 124 · 125 · 126 · 127 · 128 · 129 · 130 · 131 · 132 · 133 · 134 · 135 · 136 · 137 · 138 · 139 · 140 · 141 · 142 · 143 · 144 · 145 · 146 · 147 · 148 · 149 · 150 · 151 · 152 · 153 · 154 · 155 · 156 · 157 · 158 · 159 · 160 · 161 · 162 · 163 · 164 · 165 · 166 · 167 · 168 · 169 · 170 · 171 · 172 · 173 · 174 · 175 · 176 · 177 · 178 · 179 · 180 · 181 · 182 · 183 · 184 · 185 · 186 · 187 · 188 · 189 · 190 · 191 · 192 · 193 · 194 · 195 · 196 · 197 · 198 · 199 · 200 · 201 · 202 · 203 · 204 · 205 · 206a · 206b · 207 · 208 · 209 · 210 · 211 · 212 · 213 · 214 · 215 · 216 · 217 · 218 · 219 · 220 · 221 · 222 · 223 · 224 · 225 · 226 · 227 · 228 · 229 · 230 · 231 · 232 · 233 · 234 · 235 · 236 · 237 · 238 · 239 · 240 · 241 · 242 · 243 · 244 · 245 · 246 · 247 · 248 · 249 · 250 · 251 · 252 · 253 · 254 · 255 · 256 · 257 · 258 · 259 · 260 · 261 · 262 · 263 · 264 · 265 · 266 · 267 · 268 · 269 · 270 · 271 · 272 · 273 · 274 · 275 · 276 · 277 · 278 · 279 · 280 · 281 · 282 · 283 · 284 · 285 · 286 · 287 · 288 · 289 · 290 · 291 · 292 · 293 · 294 · 295 · 296 · 297 · 298 · 299 · 300 · 301 · 302 · 303 · 304 · 305 · 306 · 307 · 308 · 309 · 310 · 311 · 312 · 313 · 314 · 315 · 316 · 317 · 318 · 319 · 320 · 321 · 322 · 323 · 324 · 325 · 326 · 327 · 328 · 329 · 330 · 331 · 332 · 368 · 449 · 451 · 501 · 502 · 542 · 560 · 561 · 562 · 563 · 564 · 648 · 649 · 809 · 965 · 1033 · 1358 · 1386 · 1491 · 1423 · 1561 · 1575 · 1598 · 1599 · 1602 · 1604 · 1614 · 1619 · 1623 · 1637 · 1681 · 1682 · 1683 · 1684 · 1685 · 1686 · 1691 · 1813 · 1839 · 1965 · 1966 · 1967 · 2005 · 2137 · 2138 · 2139 · 2140 · 2141 · 2142 · 2143 · 2144 · 2145 · 2164 · 2208 · 2210 · 2211 · 2260 · 2261 · 2263 · 2264 · 2265 · 2266 · 2267 · 2276 · 2307 · 2321 · 2352 · 2404 · 2405 · 2406 · 2411 · 2412 ·



New book available with irrefutable evidence for the reading in the TR and KJV.
Revelation 16:5 book
Revelation 16:5 and the Triadic Declaration - A defense of the reading of “shalt be” in the Authorized Version

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