Sokoro waito
JF-Expert Member
- Nov 21, 2014
- 2,201
- 2,599
Heko kwenu wadau,
Wakati fulani nilipokuwa nasoma kitabu cha THINK LIKE A CHAMPION kilichoandikwa na Raisi Donald J. Trump nilisoma mahali fulani ambapo aliitaja hii namba 1.6180339887 kama GOLDEN RATIO ambayo imewahi kutumiwa na watu mbalimbali kwenye kazi zao, kwa mfano amemtaja DA VINCI.
Lakini pia ameielezea namba hii kwa ufupi sana huku akisisitiza kuwa ni namba ya maajabu. Trump akaandika pia kuwa yeye hashauri watu kuamini katika maajabu ya namba ili kufanikiwa katika uvumbuzi na kazi zao bali wafanye kazi kwa bidii na akili ili wafanikiwe.
sasa wadau, kama unajua chochote kuhusu namba hiyo karibu ututoe tongotongo kwa ujuzi wako.
Nitarudi kuielezea inafanyaje kazi...Siti ya mbele kabisa hapa
mkuu ukikaa mbele ujue kujibu maswali yoteSiti ya mbele kabisa hapa
mkuu wahi utupe maujuzi hapaNitarudi kuielezea inafanyaje kazi...
- List of numbers
- Irrational numbers
Binary1.1001111000110111011...Decimal1.6180339887498948482...
Hexadecimal1.9E3779B97F4A7C15F39...Continued fraction{\displaystyle 1+{\cfrac {1}{1+{\cfrac {1}{1+{\cfrac {1}{1+{\cfrac {1}{1+\ddots }}}}}}}}}Algebraic form{\displaystyle {\frac {1+{\sqrt {5}}}{2}}} Infinite series{\displaystyle {\frac {13}{8}}+\sum _{n=0}^{\infty }{\frac {(-1)^{(n+1)}(2n+1)!}{(n+2)!n!4^{(2n+3)}}}}
Two quantities a and b are said to be in the golden ratio φ if
{\displaystyle {\frac {a+b}{a}}={\frac {a}{b}}=\varphi .}
One method for finding the value of φ is to start with the left fraction. Through simplifying the fraction and substituting in b/a = 1/φ,
{\displaystyle {\frac {a+b}{a}}=1+{\frac {b}{a}}=1+{\frac {1}{\varphi }}.}
Therefore,
{\displaystyle 1+{\frac {1}{\varphi }}=\varphi .}
Multiplying by φ gives
{\displaystyle \varphi +1=\varphi ^{2}}
which can be rearranged to
{\displaystyle {\varphi }^{2}-\varphi -1=0.}
Using the quadratic formula, two solutions are obtained:
{\displaystyle \varphi ={\frac {1+{\sqrt {5}}}{2}}=1.61803\,39887\dots }
and
{\displaystyle \varphi ={\frac {1-{\sqrt {5}}}{2}}=-0.6180\,339887\dots }
Because φ is the ratio between positive quantities φ is necessarily positive:
{\displaystyle \varphi ={\frac {1+{\sqrt {5}}}{2}}=1.61803\,39887\dots }
Usijali..mkuu wahi utupe maujuzi hapa
Sisi vilaza(ambao tunapenda kujifunza) huwa tunakaa siti za mbele tuelewe vizuri, nyuma huwa kuna fujomkuu ukikaa mbele ujue kujibu maswali yote
sawa mkuu karibuSisi vilaza(ambao tunapenda kujifunza) huwa tunakaa siti za mbele tuelewe vizuri, nyuma huwa kuna fujo
teh teh mkuu pole sana, JF ina mchanganyiko wa watu tena wengine wamepita mikono salama kabisa na wana uelewa mkubwa tu wa mambo, ngoja tusubiri majibu.kuna maswali mengine, ukituuliza wanawa ccm. ni sawa na kutuchezea mapumbu tu
Nimetoka emptyNitarudi kuielezea inafanyaje kazi...
Line segments in the golden ratio
A golden rectangle with longer side a and shorter side b, when placed adjacent to a square with sides of length a, will produce a similar golden rectangle with longer side a + b and shorter side a. This illustrates the relationship {\displaystyle {\frac {a+b}{a}}={\frac {a}{b}}\equiv \varphi }.
- List of numbers
- Irrational numbers
Binary1.1001111000110111011...Decimal1.6180339887498948482...
Hexadecimal1.9E3779B97F4A7C15F39...Continued fraction{\displaystyle 1+{\cfrac {1}{1+{\cfrac {1}{1+{\cfrac {1}{1+{\cfrac {1}{1+\ddots }}}}}}}}}Algebraic form{\displaystyle {\frac {1+{\sqrt {5}}}{2}}} Infinite series{\displaystyle {\frac {13}{8}}+\sum _{n=0}^{\infty }{\frac {(-1)^{(n+1)}(2n+1)!}{(n+2)!n!4^{(2n+3)}}}}
Two quantities a and b are said to be in the golden ratio φ if
{\displaystyle {\frac {a+b}{a}}={\frac {a}{b}}=\varphi .}
One method for finding the value of φ is to start with the left fraction. Through simplifying the fraction and substituting in b/a = 1/φ,
{\displaystyle {\frac {a+b}{a}}=1+{\frac {b}{a}}=1+{\frac {1}{\varphi }}.}
Therefore,
{\displaystyle 1+{\frac {1}{\varphi }}=\varphi .}
Multiplying by φ gives
{\displaystyle \varphi +1=\varphi ^{2}}
which can be rearranged to
{\displaystyle {\varphi }^{2}-\varphi -1=0.}
Using the quadratic formula, two solutions are obtained:
{\displaystyle \varphi ={\frac {1+{\sqrt {5}}}{2}}=1.61803\,39887\dots }
and
{\displaystyle \varphi ={\frac {1-{\sqrt {5}}}{2}}=-0.6180\,339887\dots }
Because φ is the ratio between positive quantities φ is necessarily positive:
{\displaystyle \varphi ={\frac {1+{\sqrt {5}}}{2}}=1.61803\,39887\dots }
Huwez elewa mzee baba this is for gifted ones...Nimetoka empty
Nieleweshe japo kwa ufupi tuuHuwez elewa mzee baba this is for gifted ones...
like me hahahaaa tupo wachache sana.Huwez elewa mzee baba this is for gifted ones...
Mkuu si umepewa maelezo kabisa hapo juu labda tuwe ana kwa ana ndio utaelewa. Hizo ni namba bossNieleweshe japo kwa ufupi tuu
Ndio mkuu waliokimbia mase wanalo humu..like me hahahaaa tupo wachache sana.
Ngwini hapati hata punje hapo.Nitarudi kuielezea inafanyaje kazi...
Huyu mshenzi ndio alitengeza hiki kitu alikua mwanafunzi wa Johannes Kepler
Line segments in the golden ratio
A golden rectangle with longer side a and shorter side b, when placed adjacent to a square with sides of length a, will produce a similar golden rectangle with longer side a + b and shorter side a. This illustrates the relationship {\displaystyle {\frac {a+b}{a}}={\frac {a}{b}}\equiv \varphi }.
- List of numbers
- Irrational numbers
Binary1.1001111000110111011...Decimal1.6180339887498948482...
Hexadecimal1.9E3779B97F4A7C15F39...Continued fraction{\displaystyle 1+{\cfrac {1}{1+{\cfrac {1}{1+{\cfrac {1}{1+{\cfrac {1}{1+\ddots }}}}}}}}}Algebraic form{\displaystyle {\frac {1+{\sqrt {5}}}{2}}} Infinite series{\displaystyle {\frac {13}{8}}+\sum _{n=0}^{\infty }{\frac {(-1)^{(n+1)}(2n+1)!}{(n+2)!n!4^{(2n+3)}}}}
Two quantities a and b are said to be in the golden ratio φ if
{\displaystyle {\frac {a+b}{a}}={\frac {a}{b}}=\varphi .}
One method for finding the value of φ is to start with the left fraction. Through simplifying the fraction and substituting in b/a = 1/φ,
{\displaystyle {\frac {a+b}{a}}=1+{\frac {b}{a}}=1+{\frac {1}{\varphi }}.}
Therefore,
{\displaystyle 1+{\frac {1}{\varphi }}=\varphi .}
Multiplying by φ gives
{\displaystyle \varphi +1=\varphi ^{2}}
which can be rearranged to
{\displaystyle {\varphi }^{2}-\varphi -1=0.}
Using the quadratic formula, two solutions are obtained:
{\displaystyle \varphi ={\frac {1+{\sqrt {5}}}{2}}=1.61803\,39887\dots }
and
{\displaystyle \varphi ={\frac {1-{\sqrt {5}}}{2}}=-0.6180\,339887\dots }
Because φ is the ratio between positive quantities φ is necessarily positive:
{\displaystyle \varphi ={\frac {1+{\sqrt {5}}}{2}}=1.61803\,39887\dots }
Kama ulishindwa i hata general formula hapa lazima ukune eggsNgwini hapati hata punje hapo.
Hahahah nimekuelewaSimpo,1.6180339887~2