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Coca-Cola shape-like curve  (popular curve) | plot


Equations:

Parametric equations:

x(t) = ((-3\/41 sin(32\/33 - 12 t) - 6\/59 sin(41\/33 - 8 t) - 2\/23 sin(36\/29 - 4 t) + 8301\/43 sin(t + 159\/55) + 31\/29 sin(2 t + 1\/26) + 290\/13 sin(3 t + 14\/29) + 155\/21 sin(5 t + 153\/49) + 9\/26 sin(6 t + 14\/83) + 472\/111 sin(7 t + 33\/46) + 83\/38 sin(9 t + 101\/30) + 5\/22 sin(10 t + 8\/31) + 34\/19 sin(11 t + 27\/29) + 1337\/41) theta(51 pi - t) theta(t - 47 pi) + (-2\/19 sin(33\/37 - 11 t) - 3\/7 sin(32\/37 - 9 t) - 7\/13 sin(23\/17 - 8 t) - 13\/31 sin(14\/15 - 7 t) - 191\/60 sin(26\/19 - 4 t) + 4283\/25 sin(t + 121\/36) + 779\/67 sin(2 t + 37\/28) + 330\/31 sin(3 t + 18\/7) + 68\/39 sin(5 t + 65\/22) + 609\/305 sin(6 t + 73\/16) + 2\/11 sin(10 t + 5\/29) + 17\/44 sin(12 t + 12\/29) - 31430\/11) theta(47 pi - t) theta(t - 43 pi) + (-9\/34 sin(4\/11 - 12 t) - 11\/31 sin(26\/17 - 11 t) - 2\/15 sin(53\/62 - 10 t) - 9\/16 sin(40\/31 - 8 t) - 105\/46 sin(29\/23 - 4 t) + 8023\/47 sin(t + 137\/41) + 71\/5 sin(2 t + 19\/17) + 335\/36 sin(3 t + 102\/41) + 85\/29 sin(5 t + 132\/49) + 18\/23 sin(6 t + 139\/31) + sin(7 t + 92\/27) + 16\/23 sin(9 t + 125\/32) + 18572\/9) theta(43 pi - t) theta(t - 39 pi) + (-125\/46 sin(11\/10 - 8 t) - 134\/31 sin(10\/19 - 5 t) + 4355\/17 sin(t + 142\/41) + 4379\/199 sin(2 t + 140\/33) + 325\/14 sin(3 t + 83\/51) + 151\/13 sin(4 t + 103\/40) + 199\/32 sin(6 t + 4\/5) + 1437\/718 sin(7 t + 81\/28) + 26\/19 sin(9 t + 10\/37) + 37\/38 sin(10 t + 103\/40) + 69\/43 sin(11 t + 22\/5) + 35\/32 sin(12 t + 7\/24) + 32708\/19) theta(39 pi - t) theta(t - 35 pi) + (-28\/25 sin(1\/22 - 9 t) - 73\/21 sin(49\/44 - 8 t) - 506\/75 sin(9\/26 - 5 t) + 16124\/61 sin(t + 113\/33) + 618\/29 sin(2 t + 56\/13) + 8587\/318 sin(3 t + 65\/41) + 522\/43 sin(4 t + 117\/46) + 141\/22 sin(6 t + 22\/31) + 101\/63 sin(7 t + 109\/33) + 94\/63 sin(10 t + 63\/22) + 58\/37 sin(11 t + 55\/13) + 61\/60 sin(12 t + 25\/38) - 89345\/28) theta(35 pi - t) theta(t - 31 pi) + (9801\/31 sin(t + 180\/43) + 363\/28 sin(2 t + 108\/31) + 734\/25 sin(3 t + 227\/57) + 167\/37 sin(4 t + 67\/25) + 239\/25 sin(5 t + 109\/29) + 53\/32 sin(6 t + 49\/27) + 289\/62 sin(7 t + 111\/29) + 28\/25 sin(8 t + 62\/35) + 82\/37 sin(9 t + 83\/22) + 11\/13 sin(10 t + 23\/14) + 17\/13 sin(11 t + 81\/23) + 35\/43 sin(12 t + 17\/12) + 115816\/67) theta(31 pi - t) theta(t - 27 pi) + (-11\/20 sin(26\/53 - 12 t) - 71\/72 sin(9\/31 - 10 t) - 19\/14 sin(3\/17 - 8 t) + 8779\/26 sin(t + 47\/11) + 239\/23 sin(2 t + 39\/20) + 2773\/64 sin(3 t + 133\/34) + 84\/25 sin(4 t + 47\/35) + 578\/35 sin(5 t + 91\/25) + 53\/31 sin(6 t + 35\/39) + 266\/33 sin(7 t + 92\/27) + 152\/31 sin(9 t + 29\/9) + 170\/57 sin(11 t + 167\/56) + 32191\/9) theta(27 pi - t) theta(t - 23 pi) + (-31\/43 sin(20\/23 - 12 t) - 23\/27 sin(31\/42 - 10 t) + 4441\/13 sin(t + 149\/35) + 129\/14 sin(2 t + 59\/27) + 2773\/64 sin(3 t + 134\/35) + 106\/35 sin(4 t + 12\/13) + 484\/29 sin(5 t + 67\/19) + 19\/10 sin(6 t + 20\/37) + 127\/15 sin(7 t + 62\/19) + 23\/24 sin(8 t + 1\/17) + 221\/47 sin(9 t + 47\/16) + 133\/44 sin(11 t + 97\/37) - 30593\/28) theta(23 pi - t) theta(t - 19 pi) + (-215\/214 sin(8\/15 - 12 t) - 40\/29 sin(33\/28 - 10 t) - 79\/21 sin(51\/103 - 4 t) - 965\/18 sin(28\/19 - 3 t) - 973\/26 sin(61\/62 - 2 t) - 7660\/13 sin(31\/21 - t) + 535\/33 sin(5 t + 107\/23) + 29\/42 sin(6 t + 319\/72) + 137\/14 sin(7 t + 137\/30) + 48\/31 sin(8 t + 144\/31) + 152\/23 sin(9 t + 244\/53) + 139\/31 sin(11 t + 103\/22) + 104533\/24) theta(19 pi - t) theta(t - 15 pi) + (-1234\/33 sin(44\/41 - 12 t) - 1321\/22 sin(29\/21 - 9 t) - 26813\/246 sin(37\/34 - 7 t) - 3091\/20 sin(47\/37 - 5 t) - 805\/6 sin(68\/53 - 4 t) + 59867\/49 sin(t + 79\/41) + 16271\/32 sin(2 t + 23\/37) + 13093\/43 sin(3 t + 29\/11) + 1258\/35 sin(6 t + 60\/29) + 1347\/17 sin(8 t + 86\/19) + 1691\/36 sin(10 t + 11\/19) + 1259\/74 sin(11 t + 47\/11) - 3939\/2) theta(15 pi - t) theta(t - 11 pi) + (-71\/25 sin(52\/73 - 24 t) - 589\/64 sin(32\/25 - 21 t) - 171\/23 sin(32\/53 - 19 t) - 817\/50 sin(84\/67 - 16 t) - 29 sin(23\/26 - 14 t) - 868\/37 sin(29\/27 - 9 t) + 21649\/24 sin(t + 57\/35) + 38226\/29 sin(2 t + 27\/25) + 1282\/17 sin(3 t + 125\/47) + 1284\/25 sin(4 t + 81\/65) + 1687\/31 sin(5 t + 16\/21) + 2557\/27 sin(6 t + 14\/31) + 194\/7 sin(7 t + 1\/11) + 1051\/26 sin(8 t + 26\/19) + 1963\/46 sin(10 t + 5\/24) + 655\/43 sin(11 t + 89\/20) + 1091\/35 sin(12 t + 3\/23) + 439\/40 sin(13 t + 67\/23) + 210\/31 sin(15 t + 55\/27) + 1231\/123 sin(17 t + 13\/22) + 63\/5 sin(18 t + 317\/79) + 116\/35 sin(20 t + 32\/9) + 64\/39 sin(22 t + 56\/31) + 137\/17 sin(23 t + 47\/12) + 245\/39 sin(25 t + 206\/59) + 69\/22 sin(26 t + 108\/23) + 155\/37 sin(27 t + 71\/30) + 127\/33 sin(28 t + 165\/43) + 99\/61 sin(29 t + 71\/34) + 89\/26 sin(30 t + 97\/29) + 41\/35 sin(31 t + 4\/5) + 61\/26 sin(32 t + 65\/24) + 57\/44 sin(33 t + 67\/21) + 47\/27 sin(34 t + 47\/20) + 39\/31 sin(35 t + 107\/39) + 14\/15 sin(36 t + 45\/22) + 61\/30 sin(37 t + 57\/29) - 126637\/39) theta(11 pi - t) theta(t - 7 pi) + (-173\/27 sin(38\/35 - 28 t) - 429\/37 sin(1\/36 - 24 t) - 169\/22 sin(49\/41 - 23 t) - 36\/17 sin(3\/22 - 16 t) - 299\/22 sin(69\/70 - 13 t) - 124\/7 sin(11\/14 - 12 t) - 2228\/31 sin(18\/71 - 9 t) - 1129\/15 sin(35\/24 - 8 t) - 197\/5 sin(81\/80 - 7 t) - 9403\/82 sin(1\/3 - 6 t) + 31022\/33 sin(t + 79\/21) + 24719\/33 sin(2 t + 2\/25) + 7576\/21 sin(3 t + 47\/12) + 7481\/34 sin(4 t + 13\/34) + 7221\/23 sin(5 t + 16\/17) + 2670\/43 sin(10 t + 67\/35) + 1157\/53 sin(11 t + 66\/23) + 761\/55 sin(14 t + 50\/37) + 170\/13 sin(15 t + 25\/11) + 483\/53 sin(17 t + 95\/33) + 271\/25 sin(18 t + 127\/32) + 241\/39 sin(19 t + 32\/25) + 454\/29 sin(20 t + 44\/19) + 593\/57 sin(21 t + 5\/3) + 209\/24 sin(22 t + 29\/16) + 247\/62 sin(25 t + 127\/85) + 219\/82 sin(26 t + 130\/33) + 1072\/165 sin(27 t + 111\/26) + 46\/27 sin(29 t + 49\/17) + 451\/150 sin(30 t + 136\/35) + 172\/55 sin(31 t + 37\/18) + 68\/19 sin(32 t + 63\/20) + 48878\/43) theta(7 pi - t) theta(t - 3 pi) + (-354\/35 sin(21\/29 - 24 t) - 400\/57 sin(29\/23 - 22 t) - 407\/39 sin(25\/24 - 13 t) - 1129\/25 sin(14\/17 - 12 t) - 939\/16 sin(35\/29 - 11 t) - 2603\/34 sin(2\/15 - 10 t) - 643\/27 sin(86\/57 - 9 t) - 2676\/25 sin(11\/14 - 7 t) - 11063\/56 sin(8\/29 - 6 t) + 15888\/23 sin(t + 55\/19) + 56918\/65 sin(2 t + 63\/47) + 7453\/40 sin(3 t + 1\/25) + 6765\/31 sin(4 t + 73\/35) + 5584\/21 sin(5 t + 61\/16) + 5407\/81 sin(8 t + 171\/43) + 271\/17 sin(14 t + 33\/19) + 311\/24 sin(15 t + 19\/33) + 310\/19 sin(16 t + 290\/63) + 419\/25 sin(17 t + 92\/21) + 203\/23 sin(18 t + 28\/31) + 627\/29 sin(19 t + 113\/30) + 446\/37 sin(20 t + 61\/25) + 347\/34 sin(21 t + 17\/44) + 311\/17 sin(23 t + 212\/47) + 429\/29 sin(25 t + 85\/24) + 112\/11 sin(26 t + 46\/39) + 53\/19 sin(27 t + 37\/8) + 71443\/23) theta(3 pi - t) theta(t + pi)) theta(sqrt(sgn(sin(t\/2))))\ny(t) = ((-6\/49 sin(14\/11 - 12 t) - 47\/95 sin(7\/13 - 11 t) - 4\/35 sin(40\/33 - 8 t) - 36\/19 sin(11\/18 - 7 t) - 1\/7 sin(4\/3 - 4 t) - 399\/29 sin(12\/17 - 3 t) + 4987\/33 sin(t + 87\/22) + 45\/29 sin(2 t + 2\/31) + 125\/18 sin(5 t + 65\/16) + 10\/19 sin(6 t + 11\/50) + 47\/20 sin(9 t + 121\/29) + 7\/24 sin(10 t + 9\/22) + 14377\/30) theta(51 pi - t) theta(t - 47 pi) + (-4432\/21 sin(65\/44 - t) + 290\/31 sin(2 t + 4\/21) + 115\/16 sin(3 t + 108\/23) + 221\/30 sin(4 t + 21\/53) + 8\/19 sin(5 t + 11\/31) + 111\/40 sin(6 t + 4\/11) + 37\/23 sin(7 t + 45\/26) + 17\/25 sin(8 t + 37\/39) + 38\/35 sin(9 t + 37\/18) + 11\/23 sin(10 t + 97\/30) + 17\/45 sin(11 t + 98\/41) + 13\/29 sin(12 t + 135\/38) + 4649\/16) theta(47 pi - t) theta(t - 43 pi) + (-97\/37 sin(5\/31 - 6 t) - 103\/52 sin(16\/15 - 5 t) - 174\/25 sin(4\/15 - 4 t) - 274\/39 sin(6\/11 - 2 t) - 8758\/39 sin(55\/36 - t) + 377\/36 sin(3 t + 155\/34) + 22\/27 sin(7 t + 17\/60) + 23\/16 sin(8 t + 1\/7) + 17\/32 sin(9 t + 10\/23) + 107\/160 sin(10 t + 35\/41) + 37\/75 sin(11 t + 46\/51) + 11\/36 sin(12 t + 31\/25) - 1881\/4) theta(43 pi - t) theta(t - 39 pi) + (-26\/17 sin(17\/13 - 9 t) + 7121\/22 sin(t + 173\/38) + 457\/19 sin(2 t + 70\/23) + 148\/7 sin(3 t + 46\/11) + 3389\/226 sin(4 t + 79\/35) + 275\/41 sin(5 t + 212\/49) + 157\/20 sin(6 t + 48\/31) + 81\/31 sin(7 t + 21\/5) + 87\/32 sin(8 t + 61\/48) + 27\/14 sin(10 t + 17\/12) + 171\/86 sin(11 t + 108\/23) + 23\/18 sin(12 t + 17\/16) - 34203\/35) theta(39 pi - t) theta(t - 35 pi) + (-94\/41 sin(28\/19 - 11 t) - 90\/47 sin(40\/41 - 9 t) + 12001\/37 sin(t + 140\/31) + 1376\/55 sin(2 t + 179\/56) + 587\/28 sin(3 t + 78\/19) + 277\/15 sin(4 t + 62\/27) + 232\/39 sin(5 t + 31\/7) + 429\/47 sin(6 t + 49\/32) + 47\/22 sin(7 t + 159\/38) + 255\/73 sin(8 t + 30\/31) + 39\/22 sin(10 t + 49\/37) + 34\/31 sin(12 t + 32\/33) - 3589\/17) theta(35 pi - t) theta(t - 31 pi) + (-1073\/27 sin(53\/35 - 3 t) - 1183\/3 sin(63\/47 - t) + 134\/19 sin(2 t + 1\/20) + 65\/33 sin(4 t + 19\/18) + 328\/27 sin(5 t + 172\/37) + 53\/21 sin(6 t + 11\/12) + 361\/56 sin(7 t + 233\/51) + 19\/14 sin(8 t + 77\/64) + 129\/38 sin(9 t + 157\/35) + 34\/33 sin(10 t + 36\/23) + 49\/29 sin(11 t + 183\/43) + 59\/53 sin(12 t + 80\/57) + 33002\/47) theta(31 pi - t) theta(t - 27 pi) + (-7\/19 sin(27\/43 - 10 t) - 23\/27 sin(29\/31 - 8 t) - 24\/49 sin(40\/31 - 6 t) - 41\/28 sin(30\/29 - 4 t) - 1519\/32 sin(32\/21 - 3 t) - 267\/25 sin(51\/46 - 2 t) - 2347\/5 sin(35\/24 - t) + 323\/21 sin(5 t + 47\/10) + 119\/18 sin(7 t + 79\/17) + 363\/91 sin(9 t + 115\/26) + 54\/23 sin(11 t + 147\/34) + 8\/45 sin(12 t + 2\/25) - 3942\/5) theta(27 pi - t) theta(t - 23 pi) + (-7\/30 sin(6\/19 - 12 t) - 11\/27 sin(61\/41 - 8 t) - 27\/25 sin(49\/43 - 6 t) - 145\/78 sin(45\/32 - 4 t) - 630\/71 sin(23\/26 - 2 t) - 11383\/24 sin(3\/2 - t) + 1804\/37 sin(3 t + 221\/47) + 682\/45 sin(5 t + 114\/25) + 220\/31 sin(7 t + 127\/29) + 142\/39 sin(9 t + 71\/17) + 13\/43 sin(10 t + 221\/49) + 44\/21 sin(11 t + 139\/36) - 952\/27) theta(23 pi - t) theta(t - 19 pi) + (-156\/19 sin(31\/22 - 7 t) + 8161\/26 sin(t + 79\/18) + 551\/8 sin(2 t + 107\/51) + 1301\/27 sin(3 t + 122\/29) + 157\/22 sin(4 t + 89\/37) + 437\/22 sin(5 t + 73\/16) + 99\/28 sin(6 t + 20\/39) + 172\/39 sin(8 t + 35\/37) + 47\/16 sin(9 t + 175\/38) + 115\/37 sin(10 t + 25\/17) + 65\/22 sin(11 t + 163\/40) + 35\/26 sin(12 t + 50\/27) + 30125\/33) theta(19 pi - t) theta(t - 15 pi) + (-1139\/44 sin(21\/29 - 12 t) - 3787\/36 sin(43\/28 - 9 t) - 20129\/76 sin(46\/39 - 5 t) + 11777\/25 sin(t + 57\/16) + 7005\/28 sin(2 t + 77\/45) + 8944\/33 sin(3 t + 133\/43) + 849\/10 sin(4 t + 127\/39) + 67\/5 sin(6 t + 70\/27) + 1002\/7 sin(7 t + 7\/26) + 2129\/23 sin(8 t + 61\/14) + 647\/11 sin(10 t + 37\/25) + 1221\/25 sin(11 t + 78\/17) - 2950\/23) theta(15 pi - t) theta(t - 11 pi) + (-100\/21 sin(32\/31 - 32 t) - 37\/7 sin(1\/3 - 30 t) - 67\/21 sin(55\/82 - 29 t) - 25\/43 sin(29\/24 - 21 t) - 43\/18 sin(99\/79 - 20 t) - 3578\/53 sin(18\/31 - 7 t) + 21154\/15 sin(t + 239\/54) + 10453\/21 sin(2 t + 31\/25) + 2369\/21 sin(3 t + 32\/35) + 8835\/41 sin(4 t + 110\/31) + 1153\/20 sin(5 t + 115\/31) + 1364\/21 sin(6 t + 29\/11) + 418\/9 sin(8 t + 32\/15) + 1201\/28 sin(9 t + 283\/66) + 62\/3 sin(10 t + 122\/65) + 4253\/107 sin(11 t + 218\/53) + 133\/36 sin(12 t + 62\/43) + 1127\/38 sin(13 t + 73\/25) + 279\/26 sin(14 t + 52\/31) + 1079\/59 sin(15 t + 83\/33) + 22\/5 sin(16 t + 51\/37) + 382\/33 sin(17 t + 71\/53) + 239\/31 sin(18 t + 7\/13) + 155\/42 sin(19 t + 17\/20) + 72\/43 sin(22 t + 87\/19) + 56\/25 sin(23 t + 53\/23) + 115\/22 sin(24 t + 9\/4) + 37\/12 sin(25 t + 31\/24) + 113\/24 sin(26 t + 41\/30) + 140\/39 sin(27 t + 2\/19) + 944\/149 sin(28 t + 9\/13) + 127\/52 sin(31 t + 123\/29) + 36\/23 sin(33 t + 61\/20) + 62\/21 sin(34 t + 75\/17) + 37\/17 sin(35 t + 59\/32) + 123\/74 sin(36 t + 32\/9) + 29\/12 sin(37 t + 3\/17) - 18711\/40) theta(11 pi - t) theta(t - 7 pi) + (-426\/31 sin(12\/31 - 23 t) - 1001\/100 sin(4\/31 - 19 t) - 245\/23 sin(5\/37 - 13 t) - 437\/29 sin(41\/48 - 9 t) - 1698\/11 sin(28\/33 - 8 t) - 4699\/28 sin(10\/7 - 7 t) - 68398\/117 sin(50\/39 - 3 t) + 33209\/30 sin(t + 73\/19) + 3249\/16 sin(2 t + 90\/91) + 3906\/25 sin(4 t + 37\/8) + 7226\/39 sin(5 t + 35\/52) + 4533\/31 sin(6 t + 19\/25) + 2999\/41 sin(10 t + 59\/15) + 149\/19 sin(11 t + 157\/57) + 1075\/42 sin(12 t + 53\/22) + 245\/24 sin(14 t + 5\/3) + 131\/19 sin(15 t + 15\/14) + 168\/11 sin(16 t + 9\/10) + 80\/9 sin(17 t + 36\/35) + 71\/36 sin(18 t + 205\/68) + 151\/23 sin(20 t + 11\/9) + 425\/42 sin(21 t + 57\/40) + 111\/29 sin(22 t + 65\/29) + 50\/11 sin(24 t + 9\/19) + 152\/17 sin(25 t + 73\/16) + 13\/19 sin(26 t + 61\/14) + 68\/11 sin(27 t + 51\/16) + 422\/169 sin(28 t + 122\/37) + 37\/24 sin(29 t + 31\/15) + 104\/55 sin(30 t + 74\/29) + 48\/35 sin(31 t + 20\/23) + 14\/3 sin(32 t + 20\/11) + 1325\/23) theta(7 pi - t) theta(t - 3 pi) + (-73\/30 sin(55\/42 - 26 t) - 2657\/161 sin(14\/37 - 24 t) - 272\/13 sin(100\/67 - 23 t) - 591\/29 sin(54\/35 - 16 t) - 808\/13 sin(51\/47 - 13 t) - 855\/13 sin(83\/58 - 12 t) - 1793\/30 sin(27\/26 - 11 t) - 5991\/29 sin(1\/19 - 7 t) - 3268\/31 sin(29\/51 - 6 t) + 30189\/31 sin(t + 161\/38) + 5914\/15 sin(2 t + 119\/65) + 3830\/37 sin(3 t + 122\/31) + 4667\/19 sin(4 t + 68\/33) + 4693\/15 sin(5 t + 95\/24) + 2861\/24 sin(8 t + 169\/38) + 457\/14 sin(9 t + 61\/43) + 1475\/17 sin(10 t + 86\/115) + 1759\/43 sin(14 t + 79\/28) + 1452\/41 sin(15 t + 37\/62) + 3125\/71 sin(17 t + 152\/33) + 505\/51 sin(18 t + 57\/20) + 585\/23 sin(19 t + 48\/11) + 382\/17 sin(20 t + 93\/41) + 264\/37 sin(21 t + 257\/258) + 1299\/118 sin(22 t + 37\/15) + 407\/18 sin(25 t + 205\/48) + 367\/26 sin(27 t + 43\/11) - 5384\/13) theta(3 pi - t) theta(t + pi)) theta(sqrt(sgn(sin(t\/2))))

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