lunes, 8 de abril de 2013

Matemáticas para dibujar caras

Sí señores. Las matemáticas, esa ciencia tan árida que apenas si tiene aplicaciones prácticas (modo ironic off), pueden tener una utilidad artística como hacedora (¿existe este palabro?) de caricaturas. Los chicos de Wolfram Alpha disponen de una galería de 138 personajes (y 142 imágenes) a los que han realizado caricaturas a través de las matemáticas, más concretamente, mediante ecuaciones paramétricas, en las que las variables dependientes son [;(x,y);] (las coordenadas planas tradicionales) que dependen de una tercera variable [;t;] que se va moviendo.

Pero lo mejor es mirar algunos de los ejemplos más... espectaculares. En concreto, os presento a los dos únicos representantes españoles en tan elitista lista (muy a nuestro pesar): Mariano Rajoy y José Luis Rodríguez Zapatero:


Pero bueno, esto es un blog de Matemáticas, así que vamos a poner a la pareja de matemáticos que más ha dado que hablar en la historia: Newton y Leibniz:






Pero si vamos a hablar de personajes que han dado mucho que hablar en las matemáticas en general y en este blog en concreto, ese es Chuck Norris:

x(t)=((-35/17 sin(35/23-7 t)-111/11 sin(61/39-6 t)-3974/33 sin(47/30-2 t)+397/24 sin(t+41/26)+274/51 sin(3 t+80/17)+94/25 sin(4 t+75/16)+158/53 sin(5 t+41/26)+32503/89) theta(107 pi-t) theta(t-103 pi)+(-29/38 sin(59/38-7 t)-119/52 sin(53/34-5 t)-39/4 sin(39/25-3 t)-7/13 sin(71/46-2 t)-7129/62 sin(47/30-t)+172/35 sin(4 t+19/12)+71/32 sin(6 t+49/31)-7797/34) theta(103 pi-t) theta(t-99 pi)+(1957/10 sin(t+85/54)+5/13 sin(2 t+77/18)+3823/43) theta(99 pi-t) theta(t-95 pi)+(-1131/212 sin(36/23-2 t)+7267/95 sin(t+11/7)+130/31 sin(3 t+63/40)+67/32 sin(4 t+146/31)+149/41 sin(5 t+11/7)+30/23 sin(6 t+146/31)+49/33 sin(7 t+69/44)+9593/28) theta(95 pi-t) theta(t-91 pi)+(-1/7 sin(5/4-119 t)-14/25 sin(55/42-118 t)-2/13 sin(25/24-115 t)-38/45 sin(56/43-114 t)-7/15 sin(47/36-102 t)-19/23 sin(262/175-97 t)-26/25 sin(45/29-95 t)-6/37 sin(22/21-93 t)-23/16 sin(23/15-89 t)-13/18 sin(56/37-85 t)-87/56 sin(57/37-77 t)-399/92 sin(36/23-73 t)-212/85 sin(20/13-69 t)-78/41 sin(25/16-65 t)-40/17 sin(91/58-53 t)-51/20 sin(55/36-47 t)-204/29 sin(45/31-31 t)-1013/217 sin(209/139-28 t)-554/35 sin(45/29-27 t)-44/19 sin(80/53-22 t)-846/37 sin(45/29-19 t)-79/28 sin(43/33-16 t)-581/47 sin(53/36-15 t)-9505/297 sin(20/13-12 t)-5429/40 sin(58/37-8 t)+9958/19 sin(t+11/7)+6019/43 sin(2 t+146/31)+3217/28 sin(3 t+36/23)+857/7 sin(4 t+25/16)+437/5 sin(5 t+11/7)+2456/29 sin(6 t+47/30)+257/17 sin(7 t+41/26)+4506/53 sin(9 t+80/17)+1091/42 sin(10 t+34/21)+450/37 sin(11 t+174/37)+6550/111 sin(13 t+41/26)+143/3 sin(14 t+85/54)+1157/31 sin(17 t+43/27)+2011/134 sin(18 t+146/31)+280/37 sin(20 t+49/31)+421/37 sin(21 t+21/13)+121/32 sin(23 t+27/19)+181/29 sin(24 t+39/25)+19/96 sin(25 t+70/33)+54/29 sin(26 t+25/14)+61/15 sin(29 t+27/17)+547/58 sin(30 t+109/68)+77/20 sin(32 t+197/42)+4/9 sin(33 t+19/5)+307/43 sin(34 t+46/29)+49/18 sin(35 t+199/43)+110/41 sin(36 t+17/11)+35/24 sin(37 t+83/51)+131/23 sin(38 t+117/25)+128/19 sin(39 t+56/37)+185/42 sin(40 t+30/19)+244/43 sin(41 t+118/71)+25/21 sin(42 t+7/5)+136/19 sin(43 t+345/74)+51/26 sin(44 t+107/24)+85/64 sin(45 t+31/7)+74/27 sin(46 t+106/23)+50/31 sin(48 t+130/29)+237/32 sin(49 t+136/29)+18/55 sin(50 t+83/18)+65/19 sin(51 t+189/41)+36/35 sin(52 t+77/18)+167/45 sin(54 t+144/31)+79/27 sin(55 t+147/32)+29/37 sin(56 t+114/29)+7/5 sin(57 t+75/17)+101/45 sin(58 t+89/19)+172/115 sin(59 t+228/53)+41/32 sin(60 t+69/17)+37/14 sin(61 t+164/35)+55/16 sin(62 t+116/25)+55/83 sin(63 t+51/20)+37/21 sin(64 t+39/22)+45/67 sin(66 t+77/18)+84/31 sin(67 t+73/16)+61/29 sin(68 t+95/21)+25/43 sin(70 t+211/105)+53/37 sin(71 t+193/43)+32/29 sin(72 t+255/58)+74/53 sin(74 t+193/42)+12/25 sin(75 t+38/11)+11/8 sin(76 t+64/35)+76/43 sin(78 t+127/28)+23/45 sin(79 t+312/125)+36/29 sin(80 t+49/29)+1/41 sin(81 t+17/10)+55/31 sin(82 t+14/9)+17/18 sin(83 t+68/39)+13/66 sin(84 t+131/38)+1/23 sin(86 t+4)+15/46 sin(87 t+175/41)+5/41 sin(88 t+118/35)+30/37 sin(90 t+127/27)+23/20 sin(91 t+243/52)+16/21 sin(92 t+73/45)+12/37 sin(94 t+17/14)+7/24 sin(96 t+127/34)+11/40 sin(98 t+44/53)+19/21 sin(99 t+46/29)+109/49 sin(100 t+13/8)+7/15 sin(101 t+76/61)+43/72 sin(103 t+59/35)+25/23 sin(104 t+68/45)+8/29 sin(105 t+59/37)+2/13 sin(106 t+1/11)+7/33 sin(107 t+54/37)+19/24 sin(108 t+192/41)+29/23 sin(109 t+37/24)+29/44 sin(110 t+19/15)+8/63 sin(111 t+22/21)+27/82 sin(112 t+20/19)+30/91 sin(113 t+61/34)+4/31 sin(116 t+94/73)+15/16 sin(117 t+41/25)+1/9 sin(120 t+13/21)-1797/28) theta(91 pi-t) theta(t-87 pi)+(-4/19 sin(73/55-29 t)-140/43 sin(14/9-28 t)-19/9 sin(3/2-25 t)-52/21 sin(45/31-24 t)-62/37 sin(22/15-18 t)-31/28 sin(7/5-15 t)-119/43 sin(35/23-13 t)-206/65 sin(73/49-12 t)-257/47 sin(53/34-10 t)-355/41 sin(69/44-5 t)+3134/21 sin(t+47/30)+377/35 sin(2 t+55/36)+689/72 sin(3 t+369/79)+1875/67 sin(4 t+155/33)+1894/101 sin(6 t+36/23)+693/29 sin(7 t+179/38)+29/27 sin(8 t+50/13)+1039/51 sin(9 t+197/42)+577/43 sin(11 t+96/61)+198/31 sin(14 t+52/33)+42/25 sin(16 t+48/31)+9/34 sin(17 t+37/28)+47/17 sin(19 t+66/41)+11/50 sin(20 t+62/17)+128/15 sin(21 t+108/23)+32/33 sin(22 t+173/39)+119/23 sin(23 t+99/62)+61/22 sin(26 t+58/35)+27/38 sin(27 t+143/32)+59/16 sin(30 t+64/41)+3125/62) theta(87 pi-t) theta(t-83 pi)+(-17/5 sin(48/31-23 t)-58/27 sin(36/23-22 t)-75/26 sin(26/17-21 t)-58/31 sin(102/65-19 t)-31/92 sin(51/35-18 t)-67/39 sin(47/30-17 t)-77/37 sin(59/38-16 t)-43/30 sin(58/37-15 t)-465/61 sin(45/29-12 t)-107/37 sin(57/37-11 t)-231/16 sin(47/30-8 t)-149/67 sin(25/16-7 t)-1001/100 sin(77/50-5 t)-9801/19 sin(69/44-2 t)+1275/14 sin(t+41/26)+6892/179 sin(3 t+193/41)+253/17 sin(4 t+11/7)+107/22 sin(6 t+95/61)+228/53 sin(9 t+212/45)+86/39 sin(10 t+36/23)+31/11 sin(13 t+146/31)+17/44 sin(14 t+145/32)+9/34 sin(20 t+26/17)+38/35 sin(24 t+359/77)+43/20 sin(25 t+113/24)-670/9) theta(83 pi-t) theta(t-79 pi)+(-28/27 sin(41/28-14 t)-119/26 sin(48/31-12 t)-26/37 sin(190/127-11 t)-187/20 sin(73/47-9 t)-133/24 sin(59/38-6 t)-338/35 sin(58/37-2 t)+347/34 sin(t+80/17)+1448/15 sin(3 t+52/33)+1405/54 sin(4 t+63/40)+1016/107 sin(5 t+19/12)+493/31 sin(7 t+30/19)+433/54 sin(8 t+19/12)+568/21 sin(10 t+19/12)+347/39 sin(13 t+35/22)+21/13 sin(15 t+127/27)+300/43 sin(16 t+35/22)+23/13 sin(17 t+53/34)-30262/41) theta(79 pi-t) theta(t-75 pi)+(-23/57 sin(14/17-14 t)-789/158 sin(113/75-13 t)-367/59 sin(48/31-11 t)-43/23 sin(14/9-10 t)-397/32 sin(102/65-8 t)-289/27 sin(25/16-5 t)+443/42 sin(t+47/30)+719/74 sin(2 t+14/9)+747/23 sin(3 t+11/7)+147/17 sin(4 t+25/16)+154/43 sin(6 t+50/31)+164/39 sin(7 t+103/22)+129/26 sin(9 t+57/35)+1046/37 sin(12 t+49/31)+157/8 sin(15 t+47/30)+299/30 sin(16 t+59/38)+122/15 sin(17 t+31/20)+10547/18) theta(75 pi-t) theta(t-71 pi)+(-253/95 sin(106/71-22 t)-83/17 sin(35/24-18 t)-98/37 sin(32/25-17 t)-335/21 sin(350/233-13 t)-55/39 sin(19/14-11 t)-837/65 sin(35/23-10 t)+2133/29 sin(t+41/26)+113/32 sin(2 t+107/23)+427/71 sin(3 t+93/58)+19/7 sin(4 t+145/31)+503/30 sin(5 t+53/33)+535/51 sin(6 t+5/3)+11/6 sin(7 t+57/31)+224/41 sin(8 t+61/37)+215/23 sin(9 t+59/37)+53/10 sin(12 t+34/23)+132/13 sin(14 t+27/16)+187/16 sin(15 t+33/19)+37/21 sin(16 t+56/29)+187/25 sin(19 t+29/17)+71/23 sin(20 t+39/19)+197/37 sin(21 t+50/29)+5005/16) theta(71 pi-t) theta(t-67 pi)+(-45/23 sin(55/36-22 t)-62/25 sin(38/25-21 t)-195/38 sin(59/38-20 t)-107/16 sin(45/29-19 t)-21/16 sin(71/46-13 t)-649/28 sin(80/51-12 t)-623/78 sin(61/39-6 t)-146/7 sin(53/34-5 t)-778/39 sin(25/16-4 t)-419/9 sin(113/72-2 t)+3124/25 sin(t+11/7)+1081/24 sin(3 t+245/52)+55/18 sin(7 t+103/22)+73/15 sin(8 t+29/18)+134/9 sin(9 t+49/31)+346/67 sin(10 t+64/41)+73/39 sin(11 t+63/41)+29/12 sin(14 t+44/29)+6 sin(15 t+11/7)+52/25 sin(16 t+107/23)+283/37 sin(17 t+212/45)+71/63 sin(18 t+67/46)+237/31 sin(23 t+179/38)-7935/22) theta(67 pi-t) theta(t-63 pi)+(-51/20 sin(61/39-15 t)+2985/32 sin(t+113/24)+1790/31 sin(2 t+80/17)+862/29 sin(3 t+47/10)+487/38 sin(4 t+174/37)+1/6 sin(5 t+213/61)+234/23 sin(6 t+47/10)+121/20 sin(7 t+127/27)+132/53 sin(8 t+47/30)+162/23 sin(9 t+14/9)+195/22 sin(10 t+169/36)+231/31 sin(11 t+155/33)+755/64 sin(12 t+39/25)+436/49 sin(13 t+221/47)+118/47 sin(14 t+19/12)+21/41 sin(16 t+12/7)+9389/25) theta(63 pi-t) theta(t-59 pi)+(-6/29 sin(41/27-11 t)-3/4 sin(81/52-9 t)+75/2 sin(t+63/40)+1462/41 sin(2 t+52/33)+118/23 sin(3 t+212/45)+430/41 sin(4 t+41/26)+27/14 sin(5 t+108/23)+20/37 sin(6 t+43/29)+242/145 sin(7 t+55/34)+62/29 sin(8 t+46/29)+21/52 sin(10 t+69/43)+24/19 sin(12 t+53/33)-977/34) theta(59 pi-t) theta(t-55 pi)+(-38/33 sin(37/24-12 t)-68/11 sin(17/11-6 t)-179/22 sin(31/20-4 t)-109/12 sin(31/20-3 t)+1744/19 sin(t+41/26)+193/21 sin(2 t+27/17)+12/49 sin(5 t+60/49)+33/38 sin(7 t+57/37)+15/32 sin(8 t+172/37)+36/35 sin(9 t+45/29)+194/195 sin(10 t+80/17)+57/40 sin(11 t+67/42)-97/13) theta(55 pi-t) theta(t-51 pi)+(-29/31 sin(65/42-17 t)+1164/13 sin(t+58/37)+1359/13 sin(2 t+47/30)+313/8 sin(3 t+36/23)+108/13 sin(4 t+96/61)+118/11 sin(5 t+65/41)+243/29 sin(6 t+80/17)+611/18 sin(7 t+118/75)+585/28 sin(8 t+174/37)+13/23 sin(9 t+189/44)+709/59 sin(10 t+113/72)+133/24 sin(11 t+39/25)+147/40 sin(12 t+207/44)+111/50 sin(13 t+46/29)+43/21 sin(14 t+14/9)+23/20 sin(15 t+71/46)+53/29 sin(16 t+67/43)-6539/17) theta(51 pi-t) theta(t-47 pi)+(-2/19 sin(53/36-12 t)-1/4 sin(7/8-11 t)-52/19 sin(7/31-8 t)-217/29 sin(45/37-2 t)+997/40 sin(t+45/13)+457/32 sin(3 t+19/30)+144/17 sin(4 t+57/17)+139/17 sin(5 t+14/47)+124/51 sin(6 t+543/136)+38/17 sin(7 t+29/20)+41/20 sin(9 t+56/17)+46/27 sin(10 t+4/31)+16835/29) theta(47 pi-t) theta(t-43 pi)+(-79/25 sin(16/13-13 t)-61/28 sin(182/121-8 t)+2034/29 sin(t+35/29)+1719/23 sin(2 t+14/9)+570/23 sin(3 t+101/24)+1505/61 sin(4 t+71/41)+293/33 sin(5 t+80/43)+35/23 sin(6 t+106/49)+83/26 sin(7 t+51/40)+83/22 sin(9 t+333/83)+49/31 sin(10 t+73/30)+47/13 sin(11 t+112/29)+18/5 sin(12 t+4/3)+43/37 sin(14 t+4)+83/34 sin(15 t+142/33)-9683/13) theta(43 pi-t) theta(t-39 pi)+(-7/33 sin(1/19-9 t)-8/21 sin(9/31-7 t)+190/31 sin(t+95/23)+161/32 sin(2 t+38/35)+107/24 sin(3 t+83/71)+18/25 sin(4 t+192/47)+16/21 sin(5 t+35/31)+33/41 sin(6 t+7/2)+7/30 sin(8 t+155/49)+4/25 sin(10 t+61/20)+4/33 sin(11 t+15/26)+9/43 sin(12 t+46/13)-16672/55) theta(39 pi-t) theta(t-35 pi)+(133/26 sin(t+148/35)+299/83 sin(2 t+37/18)+110/21 sin(3 t+53/33)+67/28 sin(4 t+131/35)+29/57 sin(5 t+113/85)+10/13 sin(6 t+159/49)+4/13 sin(7 t+7/23)+4/35 sin(8 t+77/25)+5/37 sin(9 t+16/45)+5/19 sin(10 t+637/159)+12/49 sin(11 t+19/26)+5/22 sin(12 t+26/7)+3193/14) theta(35 pi-t) theta(t-31 pi)+(522/13 sin(t+49/34)+56/43 sin(2 t+101/25)+47/24 sin(3 t+59/41)+11614/51) theta(31 pi-t) theta(t-27 pi)+(-44/37 sin(11/32-3 t)+789/20 sin(t+46/39)+11/12 sin(2 t+116/39)+28/23 sin(4 t+59/25)-2693/9) theta(27 pi-t) theta(t-23 pi)+(-10/17 sin(37/43-12 t)-18/23 sin(21/19-10 t)-25/22 sin(24/17-8 t)+4549/51 sin(t+62/35)+102/35 sin(2 t+35/13)+83/12 sin(3 t+67/35)+52/23 sin(4 t+183/50)+51/25 sin(5 t+55/29)+71/44 sin(6 t+48/11)+12/13 sin(7 t+107/54)+13/36 sin(9 t+20/9)+3/26 sin(11 t+13/8)+5220/23) theta(23 pi-t) theta(t-19 pi)+(3349/31 sin(t+95/21)+206/53 sin(2 t+255/98)+621/62 sin(3 t+193/46)+416/119 sin(4 t+41/22)+126/37 sin(5 t+109/29)+89/50 sin(6 t+73/53)+22/21 sin(7 t+88/27)+44/37 sin(8 t+21/19)+18/73 sin(9 t+171/43)+31/29 sin(10 t+17/19)+25/49 sin(11 t+41/10)+17/22 sin(12 t+4/23)-12496/47) theta(19 pi-t) theta(t-15 pi)+(-9/37 sin(46/61-6 t)-21/25 sin(36/23-2 t)+1661/8 sin(t+31/19)+945/41 sin(3 t+29/17)+18/43 sin(4 t+109/49)+315/37 sin(5 t+62/35)+86/21 sin(7 t+65/33)+4/21 sin(8 t+79/34)+87/32 sin(9 t+55/28)+10/29 sin(10 t+77/37)+31/18 sin(11 t+73/36)+1/5 sin(12 t+67/16)+534/7) theta(15 pi-t) theta(t-11 pi)+(-451/32 sin(39/40-6 t)+129267/209 sin(t+46/43)+351/7 sin(2 t+599/133)+897/29 sin(3 t+97/42)+409/26 sin(4 t+122/41)+25/2 sin(5 t+49/27)+67/30 sin(7 t+33/29)+109/23 sin(8 t+105/29)+139/21 sin(9 t+49/26)+19/9 sin(10 t+12/31)+103/22 sin(11 t+47/37)+182/61 sin(12 t+105/38)+42/13 sin(13 t+51/26)+161/44 sin(14 t+53/29)+59/22 sin(15 t+76/37)+177/71 sin(16 t+73/30)+122/39 sin(17 t+86/29)-1190/39) theta(11 pi-t) theta(t-7 pi)+(-81/35 sin(31/21-29 t)-99/41 sin(7/45-28 t)-38/33 sin(67/100-22 t)-206/23 sin(26/17-19 t)-167/18 sin(39/29-18 t)-317/41 sin(28/23-16 t)-133/25 sin(17/16-12 t)-3123/31 sin(47/43-6 t)-4090/31 sin(6/13-3 t)+9971/19 sin(t+52/27)+3769/31 sin(2 t+107/28)+2635/28 sin(4 t+131/31)+845/24 sin(5 t+16/27)+247/5 sin(7 t+101/26)+1637/63 sin(8 t+103/25)+217/18 sin(9 t+61/14)+308/47 sin(10 t+47/14)+742/61 sin(11 t+8/43)+117/32 sin(13 t+77/26)+289/25 sin(14 t+99/37)+275/21 sin(15 t+11/6)+103/14 sin(17 t+526/117)+107/80 sin(20 t+173/74)+66/13 sin(21 t+17/30)+61/22 sin(23 t+104/35)+61/14 sin(24 t+209/61)+89/26 sin(25 t+93/35)+43/24 sin(26 t+83/22)+6/17 sin(27 t+61/38)+17/15 sin(30 t+73/27)+32/31 sin(31 t+7/33)+43/25 sin(32 t+477/110)-4075/41) theta(7 pi-t) theta(t-3 pi)+(-28/29 sin(1/21-14 t)-147/17 sin(52/37-11 t)-469/74 sin(16/13-10 t)-794/49 sin(9/20-9 t)-713/57 sin(19/47-6 t)-1559/29 sin(62/43-5 t)-2507/42 sin(12/11-3 t)+32912/27 sin(t+24/25)+3611/31 sin(2 t+25/14)+3725/39 sin(4 t+21/23)+494/23 sin(7 t+67/15)+469/29 sin(8 t+97/49)+297/43 sin(12 t+57/17)+11/4 sin(13 t+23/20)+99/35 sin(15 t+169/36)+29/25 sin(16 t+33/13)-3223/20) theta(3 pi-t) theta(t+pi)) theta(sqrt(sgn(sin(t/2))))
y(t)=((-127/19 sin(39/25-5 t)-263/39 sin(39/25-4 t)-1095/38 sin(58/37-t)+419/58 sin(2 t+52/33)+323/36 sin(3 t+49/31)+175/19 sin(6 t+49/31)+197/49 sin(7 t+46/29)-8513/27) theta(107 pi-t) theta(t-103 pi)+(-125/36 sin(37/24-7 t)-122/87 sin(299/199-6 t)-255/38 sin(45/29-5 t)-142/39 sin(37/24-4 t)-340/21 sin(53/34-3 t)-5450/41 sin(47/30-t)+38/25 sin(2 t+58/37)-13493/33) theta(103 pi-t) theta(t-99 pi)+(191/8 sin(t+85/54)+241/60 sin(2 t+49/31)-40287/47) theta(99 pi-t) theta(t-95 pi)+(-13/16 sin(31/20-6 t)-67/17 sin(102/65-5 t)-48/47 sin(81/52-4 t)-575/38 sin(69/44-3 t)-1473/13 sin(113/72-t)+83/26 sin(2 t+155/33)+70/31 sin(7 t+113/24)-24723/37) theta(95 pi-t) theta(t-91 pi)+(-137/44 sin(57/37-120 t)-35/53 sin(13/33-116 t)-46/37 sin(33/28-115 t)-31/32 sin(48/31-111 t)-8/49 sin(16/37-106 t)-65/38 sin(11/9-98 t)-47/17 sin(4/3-89 t)-86/39 sin(23/15-88 t)-57/31 sin(149/112-85 t)-187/112 sin(262/175-81 t)-78/29 sin(13/9-75 t)-24/19 sin(6/5-74 t)-57/29 sin(122/87-71 t)-37/43 sin(41/37-70 t)-6/7 sin(174/173-66 t)-44/43 sin(19/22-65 t)-57/29 sin(29/21-62 t)-255/32 sin(3/2-61 t)-9/2 sin(53/39-57 t)-42/31 sin(39/29-52 t)-119/64 sin(47/34-50 t)-12/7 sin(9/7-46 t)-81/52 sin(47/37-41 t)-292/15 sin(59/38-35 t)-13/14 sin(22/37-34 t)-259/22 sin(59/38-29 t)-235/39 sin(11/7-25 t)-389/28 sin(57/37-19 t)-899/34 sin(45/29-18 t)-424/31 sin(57/37-15 t)-2529/26 sin(58/37-3 t)+28/19 sin(t+86/49)+47989/129 sin(2 t+11/7)+2869/29 sin(4 t+107/68)+1023/28 sin(5 t+39/25)+3295/33 sin(6 t+85/54)+977/17 sin(7 t+45/29)+403/9 sin(8 t+36/23)+922/19 sin(9 t+69/44)+862/35 sin(10 t+45/29)+721/37 sin(11 t+37/24)+393/14 sin(12 t+69/44)+293/11 sin(13 t+59/38)+134/31 sin(14 t+29/20)+124/13 sin(16 t+55/34)+1003/43 sin(17 t+202/43)+628/29 sin(20 t+19/12)+541/24 sin(21 t+36/23)+58/37 sin(22 t+29/25)+137/20 sin(23 t+88/59)+38/29 sin(24 t+144/31)+121/34 sin(26 t+41/30)+34/33 sin(27 t+919/230)+295/42 sin(28 t+108/23)+2149/104 sin(30 t+179/38)+123/23 sin(31 t+73/50)+424/35 sin(32 t+8/5)+17/6 sin(33 t+41/26)+777/67 sin(36 t+59/37)+439/48 sin(37 t+41/27)+268/25 sin(38 t+14/9)+59/14 sin(39 t+36/25)+122/23 sin(40 t+48/31)+38/11 sin(42 t+61/37)+103/23 sin(43 t+14/9)+155/49 sin(44 t+331/71)+149/14 sin(45 t+268/57)+163/45 sin(47 t+183/40)+17/22 sin(48 t+31/27)+503/43 sin(49 t+55/36)+251/40 sin(51 t+47/32)+11/14 sin(53 t+28/29)+62/7 sin(54 t+41/27)+14/19 sin(55 t+115/26)+179/26 sin(56 t+95/63)+183/35 sin(58 t+36/23)+165/17 sin(59 t+14/9)+16/27 sin(60 t+31/17)+193/39 sin(63 t+49/29)+5/16 sin(64 t+38/39)+179/43 sin(67 t+14/9)+149/28 sin(68 t+25/17)+123/32 sin(69 t+124/83)+11/34 sin(72 t+78/23)+1/35 sin(73 t+31/13)+127/28 sin(76 t+18/11)+111/38 sin(77 t+41/29)+105/158 sin(78 t+125/27)+165/32 sin(79 t+313/67)+64/23 sin(80 t+43/30)+49/15 sin(82 t+71/44)+150/31 sin(83 t+73/51)+326/89 sin(84 t+174/37)+175/23 sin(86 t+23/15)+53/36 sin(87 t+76/37)+29/25 sin(90 t+103/26)+156/155 sin(91 t+114/25)+82/23 sin(92 t+54/37)+212/47 sin(93 t+83/18)+42/37 sin(94 t+41/29)+41/29 sin(95 t+18/17)+17/18 sin(96 t+111/34)+39/23 sin(97 t+101/76)+128/27 sin(99 t+151/33)+145/37 sin(100 t+16/11)+19/44 sin(101 t+83/37)+109/26 sin(102 t+173/37)+92/43 sin(103 t+25/17)+92/39 sin(104 t+88/19)+5/16 sin(105 t+47/16)+15/22 sin(107 t+35/19)+94/63 sin(108 t+75/16)+13/25 sin(109 t+157/34)+112/33 sin(110 t+59/38)+7/20 sin(112 t+33/28)+77/50 sin(113 t+46/35)+11/20 sin(114 t+74/21)+15/17 sin(117 t+28/9)+20/39 sin(118 t+11/29)+28/41 sin(119 t+17/16)-28588/37) theta(91 pi-t) theta(t-87 pi)+(-11/18 sin(16/11-22 t)-29/14 sin(65/42-13 t)-106/13 sin(161/107-5 t)-73/18 sin(29/20-3 t)+133/9 sin(t+59/38)+2037/26 sin(2 t+36/23)+2040/37 sin(4 t+36/23)+894/23 sin(6 t+64/41)+82/35 sin(7 t+15/11)+369/44 sin(8 t+59/38)+62/33 sin(9 t+42/25)+58/13 sin(10 t+108/23)+68/35 sin(11 t+31/20)+397/61 sin(12 t+45/29)+15/29 sin(14 t+55/29)+115/58 sin(15 t+131/28)+137/28 sin(16 t+38/25)+117/23 sin(17 t+103/69)+229/47 sin(18 t+50/33)+107/39 sin(19 t+193/41)+33/65 sin(20 t+136/33)+11/18 sin(21 t+35/8)+37/36 sin(23 t+25/17)+135/52 sin(24 t+67/43)+43/60 sin(25 t+211/45)+7/19 sin(26 t+695/149)+11/18 sin(27 t+146/31)+107/53 sin(28 t+49/32)+48/55 sin(29 t+58/43)+23/17 sin(30 t+43/30)-16160/29) theta(87 pi-t) theta(t-83 pi)+(-81/19 sin(39/25-25 t)-9/16 sin(35/24-24 t)-23/27 sin(42/29-22 t)-395/76 sin(17/11-21 t)-81/65 sin(67/45-17 t)-267/31 sin(14/9-11 t)-633/17 sin(36/23-7 t)-21148/133 sin(36/23-3 t)+3711/23 sin(t+107/68)+7619/60 sin(2 t+63/40)+6225/32 sin(4 t+52/33)+1461/26 sin(5 t+74/47)+340/27 sin(6 t+52/33)+397/30 sin(8 t+46/29)+107/15 sin(9 t+59/37)+267/16 sin(10 t+19/12)+65/41 sin(12 t+17/11)+33/34 sin(13 t+41/25)+328/25 sin(14 t+27/17)+18/7 sin(15 t+131/82)+77/37 sin(16 t+54/35)+160/17 sin(18 t+27/17)+607/135 sin(19 t+101/63)+79/29 sin(20 t+80/51)+177/68 sin(23 t+108/23)-25989/19) theta(83 pi-t) theta(t-79 pi)+(-101/21 sin(49/32-16 t)-123/38 sin(53/34-15 t)-334/29 sin(53/34-13 t)-1233/22 sin(25/16-7 t)-243/19 sin(64/41-6 t)-1253/40 sin(39/25-5 t)-1204/15 sin(47/30-3 t)-394/15 sin(80/51-2 t)-284/13 sin(69/44-t)+1213/36 sin(4 t+63/40)+533/64 sin(8 t+30/19)+565/22 sin(9 t+27/17)+73/8 sin(10 t+41/26)+40/9 sin(11 t+21/13)+121/29 sin(12 t+74/47)+31/9 sin(14 t+41/26)+81/26 sin(17 t+13/8)-27970/33) theta(79 pi-t) theta(t-75 pi)+(-464/37 sin(45/29-12 t)-199/16 sin(14/9-9 t)-201/28 sin(14/9-6 t)-1789/24 sin(69/44-t)+743/15 sin(2 t+118/75)+21/4 sin(3 t+43/28)+689/36 sin(4 t+36/23)+367/56 sin(5 t+36/23)+16/9 sin(7 t+103/22)+56/67 sin(8 t+46/27)+91/25 sin(10 t+41/26)+409/62 sin(11 t+74/47)+25/4 sin(13 t+21/13)+119/39 sin(14 t+125/27)+971/40 sin(15 t+113/24)+398/29 sin(16 t+174/37)+229/47 sin(17 t+136/29)-1465/26) theta(75 pi-t) theta(t-71 pi)+(-97/39 sin(87/61-22 t)-93/26 sin(232/155-20 t)-73/19 sin(45/31-18 t)-71/95 sin(53/54-17 t)-51/26 sin(52/35-16 t)-129/28 sin(57/37-13 t)-51/10 sin(98/65-10 t)-29/24 sin(32/25-9 t)-99/16 sin(40/27-8 t)-1715/156 sin(46/31-7 t)-177/13 sin(139/93-6 t)-533/35 sin(95/63-5 t)-227/24 sin(32/21-4 t)-353/30 sin(47/30-t)+103/23 sin(2 t+19/12)+1/26 sin(3 t+37/18)+13/29 sin(11 t+53/31)+56/15 sin(12 t+31/19)+25/7 sin(14 t+38/23)+4/5 sin(15 t+74/43)+87/41 sin(19 t+53/35)+24/37 sin(21 t+21/19)-181/30) theta(71 pi-t) theta(t-67 pi)+(-32/33 sin(20/13-23 t)-49/36 sin(14/9-20 t)-9/7 sin(35/23-19 t)-82/25 sin(80/51-16 t)-78/37 sin(57/37-8 t)-486/35 sin(36/23-5 t)+1272/41 sin(t+11/7)+304/23 sin(2 t+74/47)+295/23 sin(3 t+113/24)+553/43 sin(4 t+69/44)+37/18 sin(6 t+30/19)+1093/156 sin(7 t+113/24)+271/21 sin(9 t+80/51)+544/39 sin(10 t+146/31)+74/47 sin(11 t+49/31)+40/29 sin(12 t+23/15)+21/22 sin(13 t+174/37)+31/44 sin(14 t+202/43)+107/45 sin(15 t+11/7)+85/39 sin(17 t+80/17)+71/44 sin(18 t+37/24)+12/5 sin(21 t+146/31)+7/23 sin(22 t+38/25)-563/9) theta(67 pi-t) theta(t-63 pi)+(-24/11 sin(58/37-3 t)+1021/31 sin(t+47/30)+5923/103 sin(2 t+47/30)+527/28 sin(4 t+174/37)+85/6 sin(5 t+174/37)+77/39 sin(6 t+61/38)+7/17 sin(7 t+53/35)+23/19 sin(8 t+145/31)+146/43 sin(9 t+169/36)+10/47 sin(10 t+53/30)+67/41 sin(11 t+136/29)+119/52 sin(12 t+75/16)+11/10 sin(13 t+14/3)+17/20 sin(14 t+131/28)+49/54 sin(15 t+177/38)+8/13 sin(16 t+131/28)-7502/43) theta(63 pi-t) theta(t-59 pi)+(-47/34 sin(57/37-10 t)-7/4 sin(37/24-9 t)-7/25 sin(31/20-7 t)-76/41 sin(45/29-6 t)-151/88 sin(67/43-5 t)-201/37 sin(67/43-4 t)-1477/36 sin(47/30-t)+53/4 sin(2 t+41/26)+45/7 sin(3 t+49/31)+19/23 sin(8 t+8/5)+1/78 sin(11 t+128/29)+2/23 sin(12 t+53/33)-7571/44) theta(59 pi-t) theta(t-55 pi)+(-17/20 sin(77/51-12 t)-25/32 sin(35/24-11 t)-13/9 sin(65/42-8 t)-8/17 sin(67/47-7 t)-57/22 sin(20/13-6 t)-436/97 sin(32/21-5 t)-417/34 sin(48/31-4 t)-65/36 sin(46/31-3 t)-2465/53 sin(39/25-2 t)+727/18 sin(t+63/40)+16/23 sin(9 t+31/20)+1/29 sin(10 t+65/23)+764/31) theta(55 pi-t) theta(t-51 pi)+(-6/5 sin(49/32-13 t)-14/31 sin(68/47-11 t)-157/34 sin(31/20-8 t)+5295/47 sin(t+69/44)+237/11 sin(2 t+39/25)+103/14 sin(3 t+113/24)+601/24 sin(4 t+127/27)+1150/63 sin(5 t+47/10)+1003/70 sin(6 t+245/52)+151/11 sin(7 t+39/25)+131/40 sin(9 t+179/38)+29/10 sin(10 t+47/30)+13/24 sin(12 t+74/49)+122/37 sin(14 t+80/51)+53/29 sin(15 t+89/19)+32/31 sin(16 t+201/43)+103/69 sin(17 t+74/47)-9148/33) theta(51 pi-t) theta(t-47 pi)+(-65/81 sin(10/11-12 t)+18672/107 sin(t+75/17)+2477/86 sin(2 t+84/19)+437/44 sin(3 t+57/22)+781/46 sin(4 t+103/25)+175/26 sin(5 t+77/54)+158/19 sin(6 t+83/23)+97/30 sin(7 t+37/32)+63/20 sin(8 t+133/39)+137/46 sin(9 t+46/29)+93/92 sin(10 t+176/39)+91/34 sin(11 t+55/31)-11433/32) theta(47 pi-t) theta(t-43 pi)+(-59/33 sin(4/29-11 t)-349/52 sin(30/61-7 t)-769/57 sin(3/19-6 t)-4967/62 sin(49/73-2 t)-8336/41 sin(26/19-t)+503/25 sin(3 t+16/63)+794/21 sin(4 t+209/46)+841/28 sin(5 t+57/37)+16/11 sin(8 t+145/31)+110/29 sin(9 t+12/5)+206/39 sin(10 t+22/29)+37/24 sin(12 t+354/77)+59/26 sin(13 t+73/31)+31/33 sin(14 t+43/34)+15/19 sin(15 t+42/11)-13301/25) theta(43 pi-t) theta(t-39 pi)+(-1/6 sin(17/21-12 t)-5/51 sin(1/3-10 t)-21/34 sin(37/24-6 t)-9/16 sin(17/26-4 t)+101/39 sin(t+7/16)+39/8 sin(2 t+81/26)+35/9 sin(3 t+53/21)+15/17 sin(5 t+71/31)+5/26 sin(7 t+25/18)+1/25 sin(8 t+61/26)+3/23 sin(9 t+36/11)+7/41 sin(11 t+83/28)-2286/11) theta(39 pi-t) theta(t-35 pi)+(-15/2 sin(1/31-t)+82/13 sin(2 t+149/39)+297/85 sin(3 t+79/26)+72/35 sin(4 t+209/47)+25/42 sin(5 t+23/33)+14/23 sin(6 t+120/31)+17/39 sin(7 t+5/33)+17/43 sin(8 t+48/17)+13/51 sin(9 t+9/50)+3/28 sin(10 t+121/28)+5/29 sin(11 t+19/30)+5/31 sin(12 t+272/71)-3908/25) theta(35 pi-t) theta(t-31 pi)+(-698/21 sin(3/14-t)+39/10 sin(2 t+59/18)+91/22 sin(3 t+3/26)-5904/37) theta(31 pi-t) theta(t-27 pi)+(-83/50 sin(28/33-3 t)-1327/40 sin(6/19-t)+26/17 sin(2 t+70/19)+21/29 sin(4 t+87/22)-2719/13) theta(27 pi-t) theta(t-23 pi)+(-41/18 sin(13/42-4 t)-169/22 sin(25/26-2 t)+537/14 sin(t+13/23)+253/48 sin(3 t+49/39)+60/31 sin(5 t+19/18)+3/35 sin(6 t+111/26)+5/9 sin(7 t+21/26)+9/26 sin(8 t+87/28)+13/20 sin(9 t+13/23)+23/93 sin(10 t+245/61)+13/37 sin(11 t+11/19)+14/51 sin(12 t+445/127)-4609/28) theta(23 pi-t) theta(t-19 pi)+(-10/23 sin(42/31-12 t)-1/19 sin(15/19-10 t)-3/11 sin(17/26-3 t)+757/21 sin(t+79/27)+255/16 sin(2 t+219/59)+63/23 sin(4 t+65/18)+63/23 sin(5 t+79/39)+11/17 sin(6 t+191/64)+86/53 sin(7 t+73/45)+23/33 sin(8 t+244/65)+15/13 sin(9 t+23/37)+17/30 sin(11 t+11/21)-9799/47) theta(19 pi-t) theta(t-15 pi)+(-8/13 sin(81/71-9 t)-37/35 sin(53/38-5 t)+1615/33 sin(t+18/23)+149/39 sin(2 t+124/41)+211/53 sin(3 t+13/24)+113/43 sin(4 t+196/45)+73/24 sin(6 t+87/28)+94/39 sin(7 t+7/11)+2/3 sin(8 t+106/33)+13/23 sin(10 t+47/10)+9/25 sin(11 t+21/25)+44/53 sin(12 t+23/15)-47955/56) theta(15 pi-t) theta(t-11 pi)+(-41/27 sin(1/10-15 t)-113/39 sin(109/219-12 t)-299/48 sin(38/39-11 t)-349/37 sin(13/31-8 t)-55/3 sin(44/31-7 t)-329/52 sin(19/31-6 t)-753/32 sin(10/37-5 t)-277/14 sin(21/23-4 t)-5968/13 sin(13/24-t)+1567/24 sin(2 t+149/41)+1010/9 sin(3 t+181/42)+119/13 sin(9 t+7/40)+52/9 sin(10 t+35/34)+99/28 sin(13 t+28/37)+87/22 sin(14 t+35/22)+28/23 sin(16 t+15/19)+18/17 sin(17 t+15/7)-5437/15) theta(11 pi-t) theta(t-7 pi)+(-57/28 sin(9/28-26 t)-229/61 sin(61/50-24 t)-247/64 sin(8/9-23 t)-126/17 sin(2/23-16 t)-40/13 sin(14/13-13 t)-53/19 sin(37/29-9 t)-225/19 sin(17/27-8 t)-257/22 sin(5/13-7 t)-391/21 sin(7/11-6 t)-6663/31 sin(24/43-2 t)+9547/30 sin(t+199/56)+7322/67 sin(3 t+52/43)+656/27 sin(4 t+121/32)+779/24 sin(5 t+19/10)+409/31 sin(10 t+11/25)+771/67 sin(11 t+37/16)+210/37 sin(12 t+178/47)+248/29 sin(14 t+78/19)+181/33 sin(15 t+160/39)+125/19 sin(17 t+8/23)+314/45 sin(18 t+5/23)+113/32 sin(19 t+7/17)+31/22 sin(20 t+55/26)+163/35 sin(21 t+64/31)+15/23 sin(22 t+2/13)+127/52 sin(25 t+193/45)+69/55 sin(27 t+37/28)+57/34 sin(28 t+9/7)+72/43 sin(29 t+10/19)+38/51 sin(30 t+17/37)+15/38 sin(31 t+89/25)+4/19 sin(32 t+526/117)+16757/37) theta(7 pi-t) theta(t-3 pi)+(-80/27 sin(4/7-15 t)-151/54 sin(47/70-14 t)-110/7 sin(16/29-10 t)-1280/39 sin(30/31-6 t)+6319/23 sin(t+130/71)+3300/29 sin(2 t+144/37)+10544/41 sin(3 t+43/37)+1557/29 sin(4 t+117/73)+1167/17 sin(5 t+7/29)+1247/48 sin(7 t+63/29)+243/20 sin(8 t+43/50)+815/48 sin(9 t+31/29)+26/5 sin(11 t+1269/317)+46/15 sin(12 t+59/18)+107/39 sin(13 t+38/33)+41/11 sin(16 t+119/26)+519/20) theta(3 pi-t) theta(t+pi)) theta(sqrt(sgn(sin(t/2))))

¿No te lo crees? Mira que te dividirá entre 0.





Si quieres, puedes entretenerte en buscar otros matemáticos en la lista. Yo he descubierto a Gauss y a Ramanujan, ¿y tú?


Tito Eliatron Dixit

PD: Si alguien conoce cómo, a partir de una imagen, obtener estas ecuaciones paramétricas, por favor que lo indique en los comentarios.

PD2: Vía FayerWayer a través de puntogeek.

2 comentarios:

  1. Si no me equivoco, aquí tienes todas las caras que se han currado los chiflados de Wolfram! http://imgur.com/iLpuRfu

    ResponderEliminar

Si no comentas, Gauss se comerá una integral.
Y, por favor, respeta a todos con tus opiniones.

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