Ka hōʻoia ʻana i ka ʻoiaʻiʻo o ka hana

Genesis 1: 1 - "I kinohi ʻo ke Akua hana i ka lani a me ka honua"

Pūʻulu 1 - Kuhi Kuhi - Matematika

Māhele 1 - kahi hoʻokele Mandelbrot - He ʻike i ka manaʻo o ke Akua

Introduction

ʻO ke kumuhana o Matematika e hoʻohiki e lawe i kekahi o nā pane ʻelua.

1. 1. ʻAʻohe pilikia, hoʻolako ʻole ia ʻaʻole paʻakikī a
   2. ʻAʻole wau makemake i ka pākuhi no kēia kumu xxxxxx.

Eia nō naʻe, ʻo kēlā me kēia mea i pane ʻia i ka ʻike o ka ʻōlelo 'Matematika' a i loaʻa iā ʻoe, e hoʻomau he mea ʻole ʻoe e pono ke nānā i kekahi mau kuʻuna e hiki ai iā ʻoe ke hoʻomaopopo i kēia mau hōʻike maikaʻi no ke ʻano o ke Akua.

E hoʻāʻo nō kēia ʻatikala e haʻi i nā kumu no ka hilinaʻi ʻoiaʻiʻo he Akua, ʻo ka mea i hana i nā mea a pau, ke kūʻē kūʻē iā mākou e like me ka manaʻo o ka Evolution.

No laila, e hoʻomau i kēia hoʻokolokolo me aʻu, no ka mea he mea kupaianaha loa ia.

makemakika

Ke ʻike mākou i kahi kiʻi nani a kiʻi kiʻi ʻole paha e like me ka Mona Lisa, ʻike mākou iā ia, a mahalo i ka mea nāna i hana, inā ʻaʻole hiki iā mākou ke manaʻo e pena i kēlā ʻano. Pela nō hoʻi me Matematika, hiki ʻole iā mākou ke hoʻomaopopo iki iā kākou, akā hiki nō iā kākou ke mahalo i kona nani, no ka mea he nani maoli kēia.

Heaha ka Matematika?

• • ʻO ka Matematika ke aʻo ʻana i nā pilina ma waena o nā helu.

Ehia nā helu?

• • Ua wehewehe maikaʻi ʻia lākou e like me a manaʻo o ka nui.

Heaha hoi na numera?

• • ʻAʻole helu ʻia nā helu i kākau ʻia, ʻo ia ke ʻano o kā mākou e hōʻike ai i ke ʻano o nā helu i kākau ʻia a i ʻike maka.
  • Hoʻolālā lākou i nā helu helu.

ʻO kahi mea nui, ʻo kahi kī nui e hoʻomanaʻo ai e pili ana i nā kānāwai āpau o ka makemakika mea manaʻo.

• • He manaʻo kuhi kahi mea i noʻonoʻo ʻia.

ʻO Basis

Ua ike pu kakou i na manaʻo o kahi "hoʻonohonoho". Loaʻa iā ʻoe paha kahi papa o nā kāleka pāʻani, a i ʻole kahi hoʻonohonoho o nā ʻeke chess a i ʻole kahi o nā aniani waina.

No laila, hiki iā mākou ke hoʻomaopopo i ka ho'ākāka:

SET: = ka hui pū ʻana o nā mea me nā waiwai i wehewehe ʻia.

I mea hoʻohālike, kēlā me kēia kāleka pāʻani pākahi i kahi o ke ʻano holoʻokoʻa o nā kāleka, a pēlā nō kēlā me kēia ʻāpana chess hapa pilikino kahi hapa o ka chess set. Hoʻohui ʻia kahi kīʻaha waina hoʻi kekahi o nā aniani o kahi ʻano kikoʻī me nā waiwai i hoʻolālā ʻia e lawe ai i ka maikaʻi mai ka waina, e like me ke ʻano o ke ʻano, a me ka ʻano.

Pēlā nō, i ka helu matematika, ʻo kahi hoʻonohonoho o nā helu kahi o nā helu me kahi waiwai a i ʻole kahi waiwai e wehewehe pono ai akā ʻaʻole paha i loko o kahi kolamu.

Ke kuo nei, e lawe i na helu mahope: 0, -2, 1, 2, -1, 3, -3, -½, ½.

No kēlā mau helu e pili ana

• • Ka hoʻonohonoho wahi: {-2, -1, -3, -½}
  • Nā kūlana kūpono: {1, 2, 3, ½}
  • Nā Hoho Hou: {-½, ½}
  • Ka Helu Helu Pau: {1, 2, 3}

A pēlā aku.

ʻO kekahi o ia hoʻonohonoho, ʻo ia ka Mandelbrot set:

ʻO kēia ka hoʻonohonoho o nā helu āpau (c) no ka lāʻau Z_n² + c = Z_n+1 a me Z_n ua noho liʻiliʻi.

E hoʻokau ana i nā helu ʻāpana o ka hoʻonohonoho Mandelbrot

I kekahi laʻana, e nānā inā loaʻa ka helu 1 i ka ʻāpana o Mandelbrot:

Inā c = 1 a hoʻomaka me Z_n = 0.

Ke hoʻololi nei i kēia mau helu i kēia ʻike mākou:

(Z) 0² + (c) 1 = 1. No laila ʻo Z_n = 0 a 1.

Ke lawe nei i ka hopena o 1, hoʻonohonoho iā Z = 1 ka loaʻa iā mākou:

(Z) 1²+ (c) 1 = 2.

Ke lawe nei i ka hopena o 2, hoʻonohonoho iā Z = 2 ka loaʻa iā mākou:

2²+1 = 5

Ke lawe nei i ka hopena o 5, hoʻonohonoho iā Z = 5 ka loaʻa iā mākou:

5²+1 = 26

Ke lawe nei i ka hopena o 26, hoʻonohonoho iā Z = 26 ka loaʻa iā mākou:

26²+1 = 677

No laila Z_n= 0, 1, 2, 5, 26, 677,…

A laila hiki iā mākou ke ʻike i ka waiwai o c = 1 i aole hapa ʻāpana o ka Mandelbrot i ka waiho ʻole ʻana o ka helu i ka liʻiliʻi, ʻoiaiʻo ka wikiwiki ua lilo i 677.

No laila, ʻo ia c = -1 hapa ʻāpana o ka Mandelbrot?

ʻO ka pane pōkole ʻo ia, e like me ka hahai ʻana i nā papahele e like me ka mea i kau aʻe ma luna ua loaʻa iā mākou ka helu e helu ai.

Hoʻomaka hou me Z_n = 0. Ke hoʻololi nei i kēia mau helu i kēia hana ua loaʻa iā mākou:

(Z) 0² (c) -1 = -1. No laila Z_n = -1.

Ke lawe nei i ka hopena o -1, e kau ana iā Z = -1 loaʻa iā mākou:

-1² -1 = 0.

Ke lawe nei i ka hopena o 0, hoʻonohonoho iā Z = 0 ka loaʻa iā mākou:

 0²-1 = -1

Ke lawe nei i ka hopena o -1, e kau ana iā Z = -1 loaʻa iā mākou:

-1² -1 = 0.

Ke lawe nei i ka hopena o 0, hoʻonohonoho iā Z = 0 ka loaʻa iā mākou:

 0²-1 = -1

ʻO ka hopena, ʻo Z_n= 0, -1, 0, -1, 0, -1, 0, -1,….

No laila hiki iā mākou ke ʻike i kēlā c = -1 is hapa ʻāpana o ka Mandelbrot e noho mau ana i ka liʻiliʻi.

Aia kekahi manaʻo Pono mākou e kūkākūkā e like me ka wā ma mua o ka hiki ʻana ke ʻike i ka nani.

ʻO ka ʻōkuhi Mandelbrot kekahi mau helu 'kuhihewa' helu.

• • ʻO ka helu o kahi 'helu noʻonoʻo' he helu maikaʻi ʻole.
  • E like me i ka²= -1 ma hea wau kahi helu noʻonoʻo.

E nānā iā lākou e noʻonoʻo i ka axis x ākea o kahi pakuhi e loaʻa nā helu Negative ma o ka ʻole i nā helu maikaʻi. A laila e hele ana ke axis Y mai ka piko, - ½i ma o ka zero (ke kiko keʻa o nā axis ʻelua) a piʻi i luna i ½i a i.

Kiʻi 1: Ke hōʻike nei i nā helu kuhihewa ʻO nā helu ʻē aʻe i ka hoʻonohonoho Mandelbrot he 0, -1, -2, ¼, akā ʻo 1, -3, ½ ʻaʻole. ʻO nā helu hou aʻe i kēia pūʻulu e komo pū me i, -i, ½i, - ½I, akā ʻaʻole 2i, -2i.

ʻO ia ka hopena o ka makemakika paʻakikī.

Eia kēia ma laila e loaʻa ai ka hoihoi loa!

Nā hopena o kēia ʻano

E like me kāu e noʻonoʻo ai i ka helu ʻana a laila e hoʻomohala i nā waiwai āpau a me ka maikaʻi ʻole ma ka lima e lōʻihi loa ia.

Akā hiki i nā kamepiula ke kau i ka hoʻohana maikaʻi loa e helu ai i ka 100 o nā tausani, ʻo ia hoʻi o nā miliona o ka waiwai a laila e noʻonoʻo i nā hopena o kēia ʻano kikoʻī ma ke pakuhi.

Ke ʻike maʻalahi ma ka maka ʻana i nā māka kūpono i hōʻailona ʻia i nā ʻeleʻele, a he hōʻailona i nā ʻōmole nā ​​kumu kuhikuhi maikaʻi ʻole, a ʻo nā kumu i kokoke loa, akā ʻaʻole i kūpono nā māka i hōʻailona ʻia.

Inā holo mākou i kahi polokalamu kamepiula e hana i kēlā, loaʻa iā mākou ka hopena i hōʻike ʻia ma lalo nei.

(Hiki iā ʻoe ke hoʻāʻo iā ʻoe iho me nā papahana pūnaewele like ʻole e like me kēia:

1. 1. http://math.hws.edu/eck/js/mandelbrot/MB.html
   2. https://sciencedemos.org.uk/mandelbrot.php
   3. http://www.jakebakermaths.org.uk/maths/mandelbrot/canvasmandelbrotv12.html
   4. http://davidbau.com/mandelbrot/
   5. https://fractalfoundation.org/resources/fractal-software/
   6. https://www.youtube.com/watch?v=PD2XgQOyCCk

)

Kuhi 2: Ka hopena o ke kaʻi ʻana i ka hoʻohālikelike ʻo Mandelbrot

Kakau 1

Hoʻomaka mākou e helu i nā lālā melemele ma nā pōkā uliuli nunui ma nā ʻeleʻele nui e like me ka helehelena.

Ma luna o ka pōkole liʻiliʻi ʻeleʻele luna ma luna o nā ʻāpana nunui ʻōpiopio nui kā mākou iā 3 mau lālā. Inā mākou e neʻe i ka pōpoki liʻiliʻi ma ka hema, loaʻa mākou i 5 mau lālā.

ʻO ka mea nui loa ma ka ʻaoʻao hema he 7, a pēlā aku, 9, 11, 13, etc., nā helu ʻano ʻē loa a pau loa.

Kuhi 3: Nā lālā

Kakau 2

ʻĀnō, e hele ana i ka ʻaoʻao ʻākau o ka hāmaʻa ʻeleʻele mai ka luna ka mea e ʻike ai i ka helu ʻana. Loaʻa iā mākou he 4, 5, 6, 7, 8, 9, 10 a ma hope aku e lilo i ka helu o nā lālā ma ka pono o nā pōpō pupu loa.

Kakau 3

Akā ʻaʻole mākou i pau. Ke hele nei i hema a mai luna, ʻo ka pōkā ʻoloka nui loa mai luna mai ma waena o ka palena o nā lālā a me 3 a he 5 mau lālā, ʻo ka huina o nā lālā mai nā kahe i ka ʻaoʻao ʻelua paha! A ma waena o 8 a 5 paha o ka pōʻai liʻiliʻi ʻuʻuku he 7, a pēlā aku.

Loaʻa ʻia nā huina like me ka holo ʻākau. No laila, ʻo ka pōpō nui loa ma waena o 3 a he 4 he mau lālā 7, a ma waena o 4 a me 5 he mau lālā 9 a pēlā aku.

Kuhi 4: Hiki i nā lālā ke hana i ka makemakika pū kekahi!

Kakau 4

Eia kekahi, hiki ke hoʻomau ʻia kēia mau ʻano like ʻole, a e hana hou nā ʻano like.

Kuhi 5: Ka hoʻohālike ʻana i ka pena like ʻole

ʻO ka poko liʻiliʻi liʻiliʻi ma ka ʻaoʻao hema o ke laina ʻeleʻele e hele ana ma ka hema, inā i hoʻonui ʻia ʻo ia ke kiʻi like me kā mākou e ʻike ai ma aneʻi. He kūlohelohe maoli nō ia.

Kakau 5

Ma waena o ka nui o ka puʻuwai ākea a me ka pōkole ʻeleʻele e pili ana ma ka ʻaoʻao hema he wahi e like me ke awāwa ʻo Seahorse no nā ʻano nani o ʻike ʻia.

Kuhi 6: nā awāwa o nā Seahorses!

Ke hoʻololi nei i ka ʻulaʻula no ka uliuli a me ka melemele no ke keʻokeʻo no ka maʻalahi o ka hoʻohālikelike ʻana, ke ʻimi nei mākou i kahi kokoke, ʻike mākou i nā hiʻohiʻona maikaʻi loa a ʻoi hou ka hana maʻamau o ke ʻano kumu ʻākala o ka hana ʻia o ka pōpō me ka pōpoki hakakā i ka ʻaoʻao hema.

Kuhi 7: Seahorse i pili kokoke

Ke hele nei i loko o ke keʻokeʻo keʻokeʻo ʻike mākou:

Kuhi 8: Kuhi o ka whorl Whitish ma waenakonu o Seahorse

A hele hou aʻe i kahi ʻoi loa i ka luna waena i loaʻa iā mākou:

Kuhi 9: Hoʻomaka nui aʻe i loko!

Ke hele nui a ʻike mākou i kekahi o kā mākou mea like:

Kuhi 10: ʻO kona ʻano

Inā mākou e pīhoihoi i loko o kekahi o nā kohola, e loaʻa iā mākou ka mea like:

Kuhi 11: Ka lawenaʻa ʻana ma ka mana

A i ka waenakonu o ka uila e loaʻa iā mākou i kēia mau mea:

Kuhi 12: Ke hele nei anei kuʻu mau maka i loko o ka puahiohio?

Hoʻomaka hou ma luna o kekahi o nā puahi koa ʻelua i loaʻa iā mākou i kēia mau kiʻi ʻelua e pili ana i kekahi ʻano hoʻomaka me Mandelbrot kidney form a me ka pōpoki.

Kūkākūkā 13: Aia wale nō ʻoe i ʻike i ka hope o kēlā ʻano ʻeleʻele.

Kuhi 14: ʻAe, ua hoʻi hou, i hoʻopuni ʻia e ke ʻano nani ʻokoʻa

Kakau 6

Ke hoʻi nei i ko mākou kiʻi mua o ka hoʻonohonoho ʻo Mandelbrot a huli i ke 'awāwa' ma ka ʻaoʻao ʻākau o ka puʻuwai nui nui a hoʻoulu ʻia i loko o kā mākou ʻike ʻana i nā ʻano elepani, a e kapa ʻia mākou i ke awāwa ʻElephant.

Kuhi 15: Awāwa ʻElani

Ke hele nei mākou i loko, e loaʻa iā mākou kekahi ʻano o nā mea like ʻole like ʻole like ʻole:

Kuhi 16: E hāhai i ka pipi. Hup ʻelua, ʻekolu, ʻehā, huakaʻi ʻElani.

Hiki iā mākou ke hele a hele a.

Kakau 7

No laila, he aha ka mea e hoʻonani ai i ka nani i kēia mau Fractals mai ka hoʻohālikelike Mandelbrot?

ʻAe, ua hoʻohana paha ke kamepiula i kahi ʻōnaehana hana like a ke kanaka, akā ʻo nā hiʻohiʻona nā mea i kau nui ʻia, ʻo ia ka hopena o ka hopena matematika ma mua. ʻAʻole hiki ke loli, a loli.

Hōʻike ka nani i ka makana, ʻo ia hoʻi ka paʻakikī.

Kakau 8

ʻAʻole paha ʻoe i ʻike i kekahi huaʻōlelo i hoʻomau mau ʻia ai. O kēlā 'ōlelo "Manaʻo".

• He kumumanaʻo kahi manaʻo.
• He manaʻo wale nō i loko o ko mākou manaʻo.

Kakau 9

Hoʻonui kēia i nā nīnau i loko o ka manaʻo o nā poʻe noʻonoʻo.

No hea mai nei nā kānāwai o ka makemakika?

• • He kumumanaʻo, hiki wale nō lākou mai ka noʻonoʻo ʻē aʻe, pono e ʻike i ka ʻike kiʻekiʻe ma mua o kā mākou e hōʻoia i ka holo ʻana o ke ao holoʻokoʻa.

Ua uluʻe nā kānāwai o ka makemakika? Inā pēlā, pehea lā lākou?

• • ʻAʻole hiki i nā mea like ke loli me ka ke kino.

Ua hana a hana paha paha nā kānaka i kēia mau kānāwai o Matematika?

• • ʻAʻole, ua loaʻa nā kānāwai o ka makemakika ma mua o nā kānaka.

Hele mai lākou mai ka honua nei anei?

• • ʻAʻole, ʻaʻole hiki i kekahi mea o ka ʻōpiopio mai ka manawa maʻamau. ʻAʻohe manaʻo o ka honua.

ʻO kahi hopena wale nō i hiki ai iā kākou ke hele mai i ka noʻonoʻo o ka loa i ke kanaka. ʻO ke ʻano wale nō i hiki ai iā lākou ke hele mai i laila ʻo ia ka mea e hana ai i ke ao, mai ia mai ke Akua mai.

ʻO nā kānāwai o ka makemakika ka:

• • ke kumuhana
  • honua
  • invarian,
  • nā hui ʻē aʻe-liʻiliʻi.

Hiki iā lākou ke hele mai mai ke Akua mai:

• • He mau manaʻo ka manaʻo o ke Akua (Isaia 55: 9)
  • Ua hana ke Akua i ke ao āpau (Genesis 1: 1)
  • ʻAʻole hoʻololi ke Akua (Isaia 43: 10b)
  • ʻIke ke Akua i nā mea hana honua āpau, ʻaʻohe mea i nalowale (Isaia 40:26)

hopena a

1. 1. Ma kēia nīnau loiloi pōkole o nā Fractals a me ka hoʻohālikelike Mandelbrot ua ʻike mākou i ka nani a me ka ʻono i loko o ka Matematika a me ka hoʻolālā o ke aniani.
   2. Hāʻawi kēia iā mākou i ka noʻonoʻo o ke Akua, ka mea i ʻike i ke kahakaha, nā nani a me nā ʻano leʻa ʻole a he hōʻike ia no ka noʻonoʻo nui aku.
   3. E hōʻike pū ana nō hoʻi kona aloha i kāna hāʻawi ʻana iā mākou i ka ʻike e hiki ai ke ʻike a (a i kekahi kumumanaʻo!) Mahalo i kēia mau mea.

No laila, e hōʻike mākou i kēlā manaʻo o ka mahalo i nā mea āna i hana ai a nona hoʻi kahi mea nāna i hana.

Hihi Kahiki:

Me ka mahalo mahalo no ka Uila e hāʻawi ʻia ana e ka wikiō YouTube "The Secret Code of Creation" mai nā Hōʻike Kuhi ʻia e Cornerstone Television Network.

Hoʻohana kūpono: ʻO kekahi o nā kiʻi i hoʻohana ʻia, he mau kiʻi kope kope ʻole, ka hoʻohana ʻole ʻia ʻana o nā mea kope ʻole i hoʻohana ʻole ʻia. Ke hana nei mākou i kēlā me kēia mau mea i kā mākou mau hoʻoikaika ʻana e hoʻomohala i ka ʻike pili ʻana i nā pono ʻepekema a me nā hoʻomana. A laila ua manaʻo mākou he mea kūpono kēia o nā waihona kope kūlike i hāʻawi ʻia i loko o ka pauku 107 o ka US Copyright Law. E like me ke Kaona 17 USC Pauku 107, ua loaʻa ka ʻikepili ma kēia pūnaewele me ka loaʻa ʻole o ka uku kālā i ka poʻe e hōʻike ana i ke aloha no ka hoʻokipa ʻana a me ka nānā ʻana i nā mea no kā lākou noiʻi a me ka moʻoʻike hoʻonaʻauao. Inā makemake ʻoe e hoʻohana i nā mea i kope ʻia e hele i kahi kūpono ʻole, pono ʻoe e kiʻi mai ka mea ʻona kope.

Tadua

Nā ʻatikala e Tadua.