#1
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⨷ÂìÊÇÂæ
ʺÒÂæÂÒÁ»Ô´à·ÍÁ ÍÂèÒ«ÕàÃÕÂÊ
⨷ÂìÊÇÂæÊͧ¢éÍ ¢éÍáá $ \ \ 31 \ 41 \ 59 \ 26 \ 53 \ ..$ what is the next two digits ? ¢éÍ·ÕèÊͧ
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ÁÒËÒ¤ÇÒÁÃÙéäÇéµÔÇËÅÒ¹ áµèËÅÒ¹äÁèàÍÒàÅ¢áÅéÇ à¢éÒÁÒ·ÓàÅ¢àÍÒÁѹÍÂèÒ§à´ÕÂÇ ¤ÇÒÁÃÙéà»ç¹ÊÔè§à´ÕÂÇ·ÕèÂÔè§ãËé ÂÔè§ÁÕÁÒ¡ ÃÙéÍÐäÃäÁèÊÙé ÃÙé¨Ñ¡¾Í (¡àÇ鹤ÇÒÁÃÙé äÁèµéͧ¾Í¡çä´é ËÒäÇéÁÒ¡æáËÅдÕ) (áµè¡çÍÂèÒãËéÁÒ¡¨¹·èÇÁËÑÇ àÍÒµÑÇäÁèÃÍ´) |
#2
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¢éÍáá à»ç¹àŢⴴáµèÅÐËÅÑ¡¢Í§¤èÒ $\pi$
¢éÍÊͧ à´ÒÇèÒ $= \pi$ ¤ÃѺ |
#3
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¢éÍ1 ?58
¢éÍ2 ?0 ãªè¤èÒ$\pi $¨ÃÔ§´éÇ ã¤Ã¨ÐªèÇÂáÊ´§ÇÔ¸Õ¾ÔÊÙ¨¹ìãËé´Ù˹èÍÂä´éÁÑê¤ÃѺ¢é͹Õé âË´ÊØ´æ 26 àÁÉÒ¹ 2012 12:11 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 2 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ artty60 |
#4
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¢éÍ1.⪤´Õ·Õè¼Áà¤Â¨ÓàÅè¹ 3.141592653523846...
¢éÍ2·ÓäÁèà»ç¹ ÍéÒǼÁá»é¡ µéͧà»ç¹áºº¤Ø³artty 26 àÁÉÒ¹ 2012 22:44 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 2 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ polsk133 |
#5
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à·¾àÇÍÃì ⨷ÂìäÁè«ÕàÃÕÂÊàÅÂÍèÐ áÎèæ à˹áÅéǢͪÔè§
¢ÍÇÔ¸Õ·Ó¢éÍ 2 ˹èͤèÒ |
#6
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¤Ò´äÁè¶Ö§¨ÃÔ§æ -*- ÃÍÂËÂÑ¡¢Í§¼ÁÂѧ¹é͹ѡ
26 àÁÉÒ¹ 2012 19:23 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ HL~arc-en-ciel |
#7
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¤èÒ $\pi =3.14159 2653 \quad58\quad 9793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230...$
Íա˹Öè§ÊٵäèÒ $\pi =\frac{4}{1}-\frac{4}{3}+\frac{4}{5}-\frac{4}{7}+\frac{4}{9}-\frac{4}{11}+\frac{4}{13}-...$ 26 àÁÉÒ¹ 2012 22:56 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 2 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ artty60 |
#8
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à¡è§æ¡Ñ¹·Ø¡¤¹àŤÃѺ
¢éÍáá The first 100 decimal digits of $ \pi \ $are 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679... ¢éÍÊͧ ref : http://en.wikipedia.org/wiki/Pi
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ÁÒËÒ¤ÇÒÁÃÙéäÇéµÔÇËÅÒ¹ áµèËÅÒ¹äÁèàÍÒàÅ¢áÅéÇ à¢éÒÁÒ·ÓàÅ¢àÍÒÁѹÍÂèÒ§à´ÕÂÇ ¤ÇÒÁÃÙéà»ç¹ÊÔè§à´ÕÂÇ·ÕèÂÔè§ãËé ÂÔè§ÁÕÁÒ¡ ÃÙéÍÐäÃäÁèÊÙé ÃÙé¨Ñ¡¾Í (¡àÇ鹤ÇÒÁÃÙé äÁèµéͧ¾Í¡çä´é ËÒäÇéÁÒ¡æáËÅдÕ) (áµè¡çÍÂèÒãËéÁÒ¡¨¹·èÇÁËÑÇ àÍÒµÑÇäÁèÃÍ´) |
#9
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¢Í§á¶Á
¤ÇÒÁÊÑÁ¾Ñ¹¸ìÃÐËÇèÒ§ $ \ \sqrt{3} \ $ ¡Ñº $ \ \pi $ As a continued fraction, the square root of 3 can be written as : Here is pi series: For more on the next continued fraction below, see An Elegant Continued Fraction for Pi by L J Large in American Mathematical Monthly vol 106, May 1999, pages 456-8. We research the connection between the value of sqrt (3) and the value of pi... We use the equation : If we assume x=squart(3), we get: or: and: Pythagoras' Constant, the Square Root of 2, is related to the Archimedes` Constant pi, as shown below : or So, we get: ref : http://milan.milanovic.org/math/engl...t3/sqart3.html
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ÁÒËÒ¤ÇÒÁÃÙéäÇéµÔÇËÅÒ¹ áµèËÅÒ¹äÁèàÍÒàÅ¢áÅéÇ à¢éÒÁÒ·ÓàÅ¢àÍÒÁѹÍÂèÒ§à´ÕÂÇ ¤ÇÒÁÃÙéà»ç¹ÊÔè§à´ÕÂÇ·ÕèÂÔè§ãËé ÂÔè§ÁÕÁÒ¡ ÃÙéÍÐäÃäÁèÊÙé ÃÙé¨Ñ¡¾Í (¡àÇ鹤ÇÒÁÃÙé äÁèµéͧ¾Í¡çä´é ËÒäÇéÁÒ¡æáËÅдÕ) (áµè¡çÍÂèÒãËéÁÒ¡¨¹·èÇÁËÑÇ àÍÒµÑÇäÁèÃÍ´) |
#10
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⨷ÂìÊÇÂáµè·ÓäÁèä´é
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#11
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proof
$\sqrt{3}=1+\sqrt{3}-1$ $=1+ \frac{2}{\sqrt3+1}$ $=1+\frac{2}{2+\frac{2}{\sqrt3+1}}$ $=1+\frac{2}{2+\frac{2}{2+\frac{2}{\sqrt{3}+1}}}$ 28 àÁÉÒ¹ 2012 17:10 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 3 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ polsk133 |
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