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


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))))