{"id":13907,"date":"2020-12-17T17:19:34","date_gmt":"2020-12-17T22:19:34","guid":{"rendered":"https:\/\/mathemalchemy.org\/2020\/12\/17\/primos-en-el-jardin\/"},"modified":"2025-10-02T20:58:59","modified_gmt":"2025-10-03T00:58:59","slug":"primos-en-el-jardin","status":"publish","type":"post","link":"https:\/\/mathemalchemy.org\/es\/2020\/12\/17\/primos-en-el-jardin\/","title":{"rendered":"Primos en el jard\u00edn"},"content":{"rendered":"\n

Cuando la gente me pregunta qu\u00e9 es la teor\u00eda de n\u00fameros (mi \u00e1rea de investigaci\u00f3n), invariablemente acabamos hablando de los n\u00fameros primos. Cuando me preguntan qu\u00e9 me gusta de mi campo, les cuento que me encanta ver patrones y establecer conexiones -algo que me gusta de todas las matem\u00e1ticas- y que la teor\u00eda de n\u00fameros en particular tiene problemas sencillos de entender, pero que conducen a teor\u00edas profundas y complejas. Estos temas son visibles en las tres representaciones de n\u00fameros primos del jard\u00edn. <\/p>\n\n

Las dos primeras escenas<\/h2>\n\n

Las ardillas descubren los n\u00fameros primos<\/h3>\n\n
\n
\n

Junto a la colina, un par de ardillas est\u00e1n clasificando los n\u00fameros enteros en una pila de primos y otra de compuestos. Est\u00e1n comprendiendo lo que significa ser primo, quiz\u00e1 explorando los primos por primera vez. (\u00a1Permanezca atento para saber m\u00e1s sobre esta escena en una futura entrada del blog!) <\/p>\n<\/div>\n\n\n\n

\n
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Primer dise\u00f1o de la escena de los n\u00fameros primos propuesta en la Reuni\u00f3n Conjunta JMM de 2020.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n\n

Las ardillas inteligentes y la Criba de Erat\u00f3stanes<\/a> <\/h3>\n\n
\n
\n
\"Criba<\/figure>\n<\/div>\n\n\n\n
\n

En medio del jard\u00edn, algunas ardillas est\u00e1n adoptando un enfoque un poco m\u00e1s avanzado. En lugar de pensar en cada n\u00famero uno por uno, est\u00e1n usando la Criba de Erat\u00f3stenes<\/g> para encontrar todos los n\u00fameros primos de una sola vez. Ya han eliminado los m\u00faltiplos de dos, tres y cinco, y una caracter\u00edstica adicional de sus cribas transl\u00facidas especiales es que pueden ver las factorizaciones de los n\u00fameros compuestos solo con base en el color: como la criba correspondiente a los m\u00faltiplos de 2 es roja y la criba correspondiente a los m\u00faltiplos de 3 es amarilla, \u00a1los m\u00faltiplos de 6 son naranjas! <\/p>\n<\/div>\n<\/div>\n\n

\"\"
Ardillas que utilizan la Criba de Erat\u00f3stenes para encontrar todos los primos a la vez.<\/figcaption><\/figure>\n\n

Se desarrolla un camino<\/h2>\n\n

Estas dos vi\u00f1etas estaban en los primeros planes de nuestra instalaci\u00f3n; de hecho, una versi\u00f3n de la escena de la ardilla estaba en el primer dise\u00f1o propuesto por Ingrid<\/a> y Dominique<\/a> en el JMM 2020. Me entusiasm\u00f3 la idea de unirme al grupo del Jard\u00edn, en parte porque era all\u00ed donde estaban los primos. <\/p>\n\n

Cuando empezamos a dar forma a la visi\u00f3n para el jard\u00edn en marzo, pregunt\u00e9 si pod\u00edamos a\u00f1adir otra capa a las exploraciones de los n\u00fameros primos: un sendero en el jard\u00edn que mostrara la Criba de Erat\u00f3stenes para los enteros gaussianos<\/a>, tambi\u00e9n conocidos como Z[i] \u00a1Me emocion\u00f3 que todos estuvieran de acuerdo! <\/p>\n\n

\"mosaico<\/figure>\n\n

Los n\u00fameros enteros gaussianos<\/h2>\n\n

Los enteros de Gauss son un an\u00e1logo en n\u00fameros complejos de los enteros normales, y es el conjunto de n\u00fameros complejos que pueden escribirse como,a+bi<\/em>donde a y b son n\u00fameros enteros. Al igual que los n\u00fameros enteros m\u00e1s familiares, algunos n\u00fameros enteros de Gauss se pueden factorizar: por ejemplo, 3+i<\/g>= (1+2i<\/g>)(1-i<\/g>), o 5 = (1+2i<\/g>)(1-2i<\/g>). Otros, como 1+2i,<\/g> 1-i<\/g> y 1-2i,<\/g> no pueden. En el camino del jard\u00edn, cada ficha elimina m\u00faltiplos de otro entero de Gauss primo, por lo que los enteros de Gauss compuestos acaban elimin\u00e1ndose. <\/p>\n\n

Clasificar los n\u00fameros primos de Z<\/strong>[i] nos lleva a preguntarnos qu\u00e9 n\u00fameros enteros pueden escribirse como la suma de dos cuadrados, \u00a1y mucho m\u00e1s! \u00bfQu\u00e9 patrones ve en los primos de Z<\/strong>[i]? <\/p>\n

\n
\"\"<\/figure>\n<\/div>","protected":false},"excerpt":{"rendered":"

Cuando la gente me pregunta qu\u00e9 es la teor\u00eda de n\u00fameros (mi \u00e1rea de investigaci\u00f3n), invariablemente acabamos hablando de los n\u00fameros primos. Cuando me preguntan qu\u00e9 me gusta de mi campo, les cuento que me encanta ver patrones y establecer conexiones -algo que me gusta de todas las matem\u00e1ticas- y que la teor\u00eda de n\u00famerosSigue leyendo \u00abPrimos en el jard\u00edn\u00bb<\/span><\/a><\/p>\n","protected":false},"author":44503779,"featured_media":13908,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[7466],"tags":[7399,7397,7396,7398],"class_list":["post-13907","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-teoria-en-matemalquimia","tag-criba-de-eratostanes","tag-enteros-gaussianos","tag-jardin-es","tag-primos","entry"],"yoast_head":"\nPrimos en el jard\u00edn - Mathemalchemy<\/title>\n<meta name=\"description\" content=\"Cuando la gente me pregunta qu\u00e9 es la teor\u00eda de n\u00fameros (mi \u00e1rea de investigaci\u00f3n), invariablemente acabamos hablando de los n\u00fameros primos. 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Les cuento c\u00f3mo me encanta ver patrones y establecer conexiones, c\u00f3mo la teor\u00eda de n\u00fameros en particular tiene problemas que son sencillos de entender, pero que conducen a teor\u00edas profundas y complejas. 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Les cuento c\u00f3mo me encanta ver patrones y establecer conexiones, c\u00f3mo la teor\u00eda de n\u00fameros en particular tiene problemas que son sencillos de entender, pero que conducen a teor\u00edas profundas y complejas. 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She earned her BS from MIT and her PhD from Brown University, both in mathematics. Her research is in the field of analytic number theory and automorphic forms. 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