이 분수는 정말 특이합니다
Vložit
- čas přidán 22. 10. 2023
- 미지수의 계수가 수열의 각 항으로 되어 있는 멱급수 형태의 함수 즉, 그 수열을 계수로 하는 멱급수를 생성함수(生成函數, generating function)라고 합니다. 아브라암 드무아브르가 1730년에 일반 선형 점화식 문제를 풀기 위해 도입하였으며, 어떤 수열에 대한 점화식을 이용해 일반항을 알아낼 때 쓰입니다.
모든 세자리 수를 만드는 분수. 그런데 998을 제외한
• blog : rayc20.tistory.com/335
• 교육 목적으로 영상 및 블로그 자료를 자유롭게 사용하셔도 좋습니다.
• 외주 및 광고 관련 문의는 받지 않습니다.
#수학 #수열 #생성
1:13 피보나치 수열을 만드는 분수
1:50 생성함수
3:20 테일러 전개와 생성함수
(정정) 1:40에 세자리마다 반복하며 988까지의 피보나치 수열을 만들게 됩니다. ->
피보나치 수열의 16번째항은 987입니다. 988에서 처음으로 피보나치 수열이 깨지게 됩니다.
자막에도 수정해두었습니다.
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유익한 내용 감사합니다 ^^
이런 재밌는 수학에대한 설명을 해주는 책 중 추천해주실만한 것 있을까요?
제가 아는 분수와는 조금 다른 느낌을 주지만, 정말 신기한 분수이네요.. 분수에 대한 많은 지식을 쌓을 수 있게 도와주셔서 감사드립니다. =) 앞으로도 좋은 영상에 대한 응원 아끼지 않고 드리겠습니다. 감기 조심 하세요!
1/998001 = 0.0000010020030040050060070080090100110120130140150160170180190200210220230240250260270280290300310320330340350360370380390400410420430440450460470480490500510520530540550560570580590600610620630640650660670680690700710720730740750760770780790800810820830840850860870880890900910920930940950960970980991001011021031041051061071081091101111121131141151161171181191201211221231241251261271281291301311321331341351361371381391401411421431441451461471481491501511521531541551561571581591601611621631641651661671681691701711721731741751761771781791801811821831841851861871881891901911921931941951961971981992002012022032042052062072082092102112122132142152162172182192202212222232242252262272282292302312322332342352362372382392402412422432442452462472482492502512522532542552562572582592602612622632642652662672682692702712722732742752762772782792802812822832842852862872882892902912922932942952962972982993003013023033043053063073083093103113123133143153163173183193203213223233243253263273283293303313323333343353363373383393403413423433443453463473483493503513523533543553563573583593603613623633643653663673683693703713723733743753763773783793803813823833843853863873883893903913923933943953963973983994004014024034044054064074084094104114124134144154164174184194204214224234244254264274284294304314324334344354364374384394404414424434444454464474484494504514524534544554564574584594604614624634644654664674684694704714724734744754764774784794804814824834844854864874884894904914924934944954964974984995005015025035045055065075085095105115125135145155165175185195205215225235245255265275285295305315325335345355365375385395405415425435445455465475485495505515525535545555565575585595605615625635645655665675685695705715725735745755765775785795805815825835845855865875885895905915925935945955965975985996006016026036046056066076086096106116126136146156166176186196206216226236246256266276286296306316326336346356366376386396406416426436446456466476486496506516526536546556566576586596606616626636646656666676686696706716726736746756766776786796806816826836846856866876886896906916926936946956966976986997007017027037047057067077087097107117127137147157167177187197207217227237247257267277287297307317327337347357367377387397407417427437447457467477487497507517527537547557567577587597607617627637647657667677687697707717727737747757767777787797807817827837847857867877887897907917927937947957967977987998008018028038048058068078088098108118128138148158168178188198208218228238248258268278288298308318328338348358368378388398408418428438448458468478488498508518528538548558568578588598608618628638648658668678688698708718728738748758768778788798808818828838848858868878888898908918928938948958968978988999009019029039049059069079089099109119129139149159169179189199209219229239249259269279289299309319329339349359369379389399409419429439449459469479489499509519529539549559569579589599609619629639649659669679689699709719729739749759769779789799809819829839849859869879889899909919929939949959969979990000010020030040050060070080090100110120130140150160170180190200210220230240250260270280290300310320330340350360370380390400410420430440450460470480490500510520530540550560570580590600610620630640650660670680690700710720730740750760770780790800810820830840850860870880890900910920930940950960970980991001011021031041051061071081091101111121131141151161171181191201211221231241251261271281291301311321331341351361371381391401411421431441451461471481491501511521531541551561571581591601611621631641651661671681691701711721731741751761771781791801811821831841851861871881891901911921931941951961971981992002012022032042052062072082092102112122132142152162172182192202212222232242252262272282292302312322332342352362372382392402412422432442452462472482492502512522532542552562572582592602612622632642652662672682692702712722732742752762772782792802812822832842852862872882892902912922932942952962972982993003013023033043053063073083093103113123133143153163173183193203213223233243253263273283293303313323333343353363373383393403413423433443453463473483493503513523533543553563573583593603613623633643653663673683693703713723733743753763773783793803813823833843853863873883893903913923933943953963973983994004014024034044054064074084094104114124134144154164174184194204214224234244254264274284294304314324334344354364374384394404414424434444454464474484494504514524534544554564574584594604614624634644654664674684694704714724734744754764774784794804814824834844854864874884894904914924934944954964974984995005015025035045055065075085095105115125135145155165175185195205215225235245255265275285295305315325335345355365375385395405415425435445455465475485495505515525535545555565575585595605615625635645655665675685695705715725735745755765775785795805815825835845855865875885895905915925935945955965975985996006016026036046056066076086096106116126136146156166176186196206216226236246256266276286296306316326336346356366376386396406416426436446456466476486496506516526536546556566576586596606616626636646656666676686696706716726736746756766776786796806816826836846856866876886896906916926936946956966976986997007017027037047057067077087097107117127137147157
8이 없다는 것에만 집중하면 보이지 않지만, 이를 무시하고 1부터 모든 수가 차례대로 있다고 가정하고 합을 구해보면 자연스럽게 8이 올림되어 사라지는 것이 보이네요
5:17 자막
그 수만큼 앞에 이 붙게 됩니다.
->
그 수만큼 앞에 0이 붙게 됩니당
내가 뭘본거지;; 너무 멋있는 수학이네요 매력적이야
@@user-siballyeonmigaegukmin 핥
감사합니다 불면증이 치료되었습니다....
이 영상을 보고 제 ‘분수’를 알아야한단걸 깨달았습니다. 감사합니다.
8이 없는게 딱 예상했던 이유지만 분석 방법이 있다는게 신기하네요
대박 이런 유리수가 있다니
어릴적 이런걸 전혀 몰랐을 때 1을 81로 나눴더니 순환마디가 012345679인걸 보고 신기해했더랩죠
생각해보니 광기네 ㄷㄷ
구라치지마세요 특별해보이고싶죠?
@@user-qb4bi5pu3m왜그살
@@user-hx8jj7ei4q 지역차별 빼고는 동감
@@user-qb4bi5pu3m걍 그런갑다 하고 넘어가;
소수나열은 그렇게 신기하진 않은데 뭔가 아이디어를 주는 점에선 흥미로움
내가 계산기로 12345679×(9의 배수) 곱하면서 노는 동안 수학자들은 이러고 있었구나...
저도 이 생각했는데 ㅋㅋ
4:18 1/(1-z)^2 을 n번 미분했을 때 식이 잘못된 거 아닌가요? n이 1이면 미분된 함수의 계수가 - 인데, 저 식에서는 + 인데요?
안볼수가 없따 이건
근데 그러면 벤포드의 법칙이 여기서도 성립하나요 ??
칼큘 급수 파트 보면 연습문제로 있는 문제였는데, 새록새록 하네요
8만 빠진 거 보고 어렸을 때 봤던 게 떠올랐네요
12345679 × 9의배수 하면 똑같은 숫자가 나열합니다
12345679 × 9 = 111,111,111
12345679 × 18 = 222,222,222
12345679 × 27 = 333,333,333
1/998001 = 0.0000010020030040050060070080090100110120130140150160170180190200210220230240250260270280290300310320330340350360370380390400410420430440450460470480490500510520530540550560570580590600610620630640650660670680690700710720730740750760770780790800810820830840850860870880890900910920930940950960970980991001011021031041051061071081091101111121131141151161171181191201211221231241251261271281291301311321331341351361371381391401411421431441451461471481491501511521531541551561571581591601611621631641651661671681691701711721731741751761771781791801811821831841851861871881891901911921931941951961971981992002012022032042052062072082092102112122132142152162172182192202212222232242252262272282292302312322332342352362372382392402412422432442452462472482492502512522532542552562572582592602612622632642652662672682692702712722732742752762772782792802812822832842852862872882892902912922932942952962972982993003013023033043053063073083093103113123133143153163173183193203213223233243253263273283293303313323333343353363373383393403413423433443453463473483493503513523533543553563573583593603613623633643653663673683693703713723733743753763773783793803813823833843853863873883893903913923933943953963973983994004014024034044054064074084094104114124134144154164174184194204214224234244254264274284294304314324334344354364374384394404414424434444454464474484494504514524534544554564574584594604614624634644654664674684694704714724734744754764774784794804814824834844854864874884894904914924934944954964974984995005015025035045055065075085095105115125135145155165175185195205215225235245255265275285295305315325335345355365375385395405415425435445455465475485495505515525535545555565575585595605615625635645655665675685695705715725735745755765775785795805815825835845855865875885895905915925935945955965975985996006016026036046056066076086096106116126136146156166176186196206216226236246256266276286296306316326336346356366376386396406416426436446456466476486496506516526536546556566576586596606616626636646656666676686696706716726736746756766776786796806816826836846856866876886896906916926936946956966976986997007017027037047057067077087097107117127137147157167177187197207217227237247257267277287297307317327337347357367377387397407417427437447457467477487497507517527537547557567577587597607617627637647657667677687697707717727737747757767777787797807817827837847857867877887897907917927937947957967977987998008018028038048058068078088098108118128138148158168178188198208218228238248258268278288298308318328338348358368378388398408418428438448458468478488498508518528538548558568578588598608618628638648658668678688698708718728738748758768778788798808818828838848858868878888898908918928938948958968978988999009019029039049059069079089099109119129139149159169179189199209219229239249259269279289299309319329339349359369379389399409419429439449459469479489499509519529539549559569579589599609619629639649659669679689699709719729739749759769779789799809819829839849859869879889899909919929939949959969979990000010020030040050060070080090100110120130140150160170180190200210220230240250260270280290300310320330340350360370380390400410420430440450460470480490500510520530540550560570580590600610620630640650660670680690700710720730740750760770780790800810820830840850860870880890900910920930940950960970980991001011021031041051061071081091101111121131141151161171181191201211221231241251261271281291301311321331341351361371381391401411421431441451461471481491501511521531541551561571581591601611621631641651661671681691701711721731741751761771781791801811821831841851861871881891901911921931941951961971981992002012022032042052062072082092102112122132142152162172182192202212222232242252262272282292302312322332342352362372382392402412422432442452462472482492502512522532542552562572582592602612622632642652662672682692702712722732742752762772782792802812822832842852862872882892902912922932942952962972982993003013023033043053063073083093103113123133143153163173183193203213223233243253263273283293303313323333343353363373383393403413423433443453463473483493503513523533543553563573583593603613623633643653663673683693703713723733743753763773783793803813823833843853863873883893903913923933943953963973983994004014024034044054064074084094104114124134144154164174184194204214224234244254264274284294304314324334344354364374384394404414424434444454464474484494504514524534544554564574584594604614624634644654664674684694704714724734744754764774784794804814824834844854864874884894904914924934944954964974984995005015025035045055065075085095105115125135145155165175185195205215225235245255265275285295305315325335345355365375385395405415425435445455465475485495505515525535545555565575585595605615625635645655665675685695705715725735745755765775785795805815825835845855865875885895905915925935945955965975985996006016026036046056066076086096106116126136146156166176186196206216226236246256266276286296306316326336346356366376386396406416426436446456466476486496506516526536546556566576586596606616626636646656666676686696706716726736746756766776786796806816826836846856866876886896906916926936946956966976986997007017027037047057067077087097107117127137147157
123456789에 두자리수 곱할시 1234567890이 순서가 불규칙하게 하나씩 나오는데 그건 왜일까요.두자리수의 합이 9를 초과해선 안되고
3의 배수면 안됨..
안녕하세요 지나가다 알고리즘에 떠서 영상을 보게 된 문돌이 입니다. 음... 다시 지나가보겠습니다.
혹시 글씨체 뭐 쓰세요?
약간 소름이 돋았습니다
와아 신기하다
혹시 142857 에 대한것도 다루어주실수있나요?
1/7의 마술 👍👍
아 베르나르 책에서 봤던 거네요 ㅋㅋ 그거 은근 신기하더라고요
1 / 142857 = 0.000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007000007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@@seubman 베르나르의 어느 책인가요?
어느 순간부터 멍때리기 시작함
수학은 정말... 아름답네요...
2인자는 필요가 없죠
진핑이가 좋아하는 수 일 것으로 생각이 듭니다.
재밌네
에이급 수학에 있습니다~
3:47 1에서 10의 거듭제곱을 뺀수의 제곱 아닌가요 어차피 같은말이긴 한데 쓰여있는개 그렇게 쓰여있어서
말할 때 익숙한거랑 식을 쓸 때 익숙한게 조금 달라서 둘 다 저한테 익숙한 걸로 하다보니 이렇게 되었습니다. >_
@@Ray수학>_< 왤캐 귀엽지..
내 이럴 줄 알았다!!!
수리논술에 나올거같은 주제다 옛날 입시였으면..ㅋㅋ
'CALCULATED'
1:40 에서 610까지 피보나치 아닌가요?
16번째 항인 987이 깨진다고 말했어야하는데 잘못 작성했습니다. 댓글과 자막에 수정해두겠습니다. 알려주셔서 정말 감사합니다.^^
@@Ray수학 감사합니당 ㅎㅎ
제목만보고 분수인줄알았지만 분수였다.
오 유익한데요?
와 ㅈㄴ신기하다
이야
사실 신이 997까지 만들다 졸아서 998은 건너 뛰었다는게 학계의 정설
혹시 1557이나 88848은 무슨일이 일어나나요?
ㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋ
초비랑 피넛이 우승할줄 알았는데, 올해 페이커 우승하고 내년에 꼭 초비랑 피넛이 우승하면 좋겠네요. ㅠㅠ
미친 ㅋㅋㅋㅋㅋㅋㅋㅋ
중간에 못알아듣다가 우와 3:56
이왜진 ㅋㅋㅋㅋ 개신기하네 ㅋㅋ
수능 보기 전 최고의 선택
문과생:항상 1등은 2등을 싫어하기때문이죠
중딩때
12,345,679×63=777,777,777
12,345,679×36=444,444,444
이게 너무 신기했는데
이 영상보니 갑자기 기억나네요.
문송합니다
지금 이걸 볼 때 9.98만 인게 아이러니
12345679 × 9 같네요 재밌습니다
12345679에 18 27 36 등을 곱해봤는데 111111111 222222222 등 같은 숫자가 나오는게 신기햇어요
12345679가 사실은
123456789(10)이 겹친 거였다니 왜 이 간단한 생각을 못 했지..!
어메이징하다
과거 주판 배우신분은 알거예요...123456789 를 9번 더하면 1111111101 나온다는 사실을...
12,345,679 * 9 = 111,111,111 ,, 12,345,679 * (9 ^ 9) = 999,999,999
???: 그건 모르겠고~ 자네는 왜 유효숫자 처리안해서 제출했나?
피보나치 987인데 988이라고 나와있네요
고정댓글과 자막에 수정되어있습니다 >_
중국에서 길하다고 여기는 8을 왕따시키는 분수라니 이 얼마나 아름다운가
8이 빠진 12345679 X 9 = 111111111 이 되는 것과 같은 원리입니다.
구신... 우리협지좀챙겨줘
오
분명히 우리나라 말인데,, 왜 이해가 안 되지? 거 참 희한하네~?
이해한 사람? 나만 이해안됨?
천부경
세상에 단 1도 못알아듣겠어..
111111111/9=12345679
여기 8 없는것과 같은 느낌
아홉수는 미완의 수 인간의 한계
추측하기로는, 99 0 1 2 .. 97 까지 반복되는거 아닐지
오 맛있다
이게 머선 소리고...
이게머꼬......
음.. 무슨 소린지 전혀 모르겠군
숫자. 수학. 수의 체계도 절대자의 기막힌 설계없으면 불가능하다.
자꾸 어디서 절대자를 찾는거임
@@대시 님의 존재도 절대자의 뜻에 의하여 탄생한 것임..
수천조 분의 1 의 확률로 태어난 모든 생명체..
@@user-kf3ws4pc7n 그게 샤먼교와 애니미즘의 기원임
지능적으로 쌓인 것 없는 원시인들이 보통 절대자, 신 이런거 믿으면서 이해할 수 없는 현상등을 제멋대로 해석하는것
물론 그당시엔 모두가 믿었고 결속력이 강해지는 순기능이 있었음
그런데 지금의 천주교, 무속신앙등 우상숭배 집단은 지탄받아 마땅한 대상임, 결속이란 순기능은 사라지고 분란과 조장을 고사하고 인류 진보를 저해하기만 하는 저능하기 그지없는 행동이라서.
물론 그 절대자라는게 진짜 있을수도 있음. 설사 그렇다해도 절대자한테 의도라는 건 없으며 절대자가 우리의 존재를 인식할 수 있는 방법도, 우리가 절대자의 존재를 인식할 수 있는 방법도 없음. 인류와 우주와는 단 하나도 관계없는 다른 세상 소리라는 얘기,
절대자를 광신하는 건 유전적 지능의 문제이므로 그만 믿으라는 말은 못하지만, 인류 진보에 저해되는 행동
숫자의 정의는 사람이 정한겁니다
@@KR_Crew 사람이 정할 수 있는 기준을 발견할 수 있도록 절대자가 설계해 놓으셨는데요.. 그 거대한 흐름을 인간이 임의로 설정하면 어떻게 되는지 생각해 보시길..
신기하네
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