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  #31  
Old 10 àÁÉÒ¹ 2010, 20:22
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¾ÅÒâµàÅÁÕ¤¹·ÕèËÒÃÑÈÁբͧâÅ¡ä´éÍèФѺ ¹èҨФ¹à´ÕÂǡѹ

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ÍéÍ ! ¼Á¹Ö¡ÍÍ¡áÅéǤÃѺ Ptolemy à»ç¹¤¹ ¾ÔÊÙ¨¹ì¤èÒ $Sin ( A+ B ) Cos ( A + B )$
«Öè§Áѹ¨Ðà»ç¹ ¨Ø´àÃÔèÁµé¹¢Í§ µÃÕ⡳ÁÔµÔ áÅÐ ¤Ô´ Ptolemy's Theorem (à¡ÕèÂǡѺǧ¡ÅÁ)´éǤÃѺ
¤¹ä·ÂÁÑ¡àÃÕ¡ª×èÍÇèÒ »·ÍàÅÁÕ ÍФÃѺ
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10 àÁÉÒ¹ 2010 20:27 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 2 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ ¤usÑ¡¤³Ôm
µÍº¾ÃéÍÁÍéÒ§ÍÔ§¢éͤÇÒÁ¹Õé
  #32  
Old 10 àÁÉÒ¹ 2010, 20:31
¹Ñ¡Ê׺ÍѨ©ÃÔÂÐ's Avatar
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ãªèàŤÃѺ ààÅéÇãªéËÒ sin 1 ä´é»èÒǤÃѺ
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  #33  
Old 10 àÁÉÒ¹ 2010, 20:38
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ãªèàŤÃѺ ààÅéÇãªéËÒ sin 1 ä´é»èÒǤÃѺ
ãªéÇԸբͧ Ptolemy ËÒ¤ÍÃì´áÅéÇ ãªéÊٵà $sin (x/2) = (cord x)/120$¤ÃѺ
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  #34  
Old 11 àÁÉÒ¹ 2010, 15:45
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¤Ó¶ÒÁàà»Å¡æ¤ÃѺ

1.ãËé xààÅÐy à»ç¹¨Ó¹Ç¹àµçÁºÇ¡ààÅéÇ x=(13^2)-(12^2)ààÅÐy^2=(x^2)-((20+35-16-19)^2)

¨§ËÒ¤èҢͧ [(y-99)(y-97)(y-95).............(y-3)(y-1)]/[(y-99)(y-97)(y-95).............(y-3)(y-1)]

2.Çѹ˹Ö觢³Ð·Õè´.ª.¡ ä¡è à´Ô¹ä»ÃéÒ¹¢¹Á»Ñ§à¢ÒÊǹ·Ò§¡Ñºà´ç¡ 4¤¹ààµèÅФ¹¾Ò¹éͧÁÒÍÕ¡ 4¤¹ ¹éͧ¢Í§à´ç¡ààµèÅФ¹ÍØéÁààÁǤ¹ÅÐ 4µÑÇ

¶ÒÁÇèÒÁÕ¤¹ààÅÐààÁǨӹǹà·èÒä÷Õèä»ÃéÒ¹¢¹Á»Ñ§

ààµè§àͧ¤ÃѺ
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11 àÁÉÒ¹ 2010 15:47 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ ¹Ñ¡Ê׺ÍѨ©ÃÔÂÐ
µÍº¾ÃéÍÁÍéÒ§ÍÔ§¢éͤÇÒÁ¹Õé
  #35  
Old 12 àÁÉÒ¹ 2010, 10:06
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1.ãËé xààÅÐy à»ç¹¨Ó¹Ç¹àµçÁºÇ¡ààÅéÇ x=(13^2)-(12^2)ààÅÐy^2=(x^2)-((20+35-16-19)^2)
¨§ËÒ¤èҢͧ [(y-99)(y-97)(y-95).............(y-3)(y-1)]/[(y-99)(y-97)(y-95).............(y-3)(y-1)]


$x=(13^2)-(12^2) = 5^2 = 25$ ààÅÐ $y^2=(x^2)-((20+35-16-19)^2)=25^2-20^2=15^2$

¨Ðä´é¤èÒ y = +15 ËÃ×Í (y-15) = 0,

´Ñ§¹Ñ鹤èҢͧ $\dfrac{(y-99)(y-97)(y-95).............(y-3)(y-1)}{(y-99)(y-97)(y-95).............(y-3)(y-1)}$ ¨Ö§äÁè¹ÔÂÒÁ¤ÃѺ
µÍº¾ÃéÍÁÍéÒ§ÍÔ§¢éͤÇÒÁ¹Õé
  #36  
Old 12 àÁÉÒ¹ 2010, 10:14
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2.Çѹ˹Ö觢³Ð·Õè´.ª.¡ ä¡è à´Ô¹ä»ÃéÒ¹¢¹Á»Ñ§à¢ÒÊǹ·Ò§¡Ñºà´ç¡ 4¤¹ààµèÅФ¹¾Ò¹éͧÁÒÍÕ¡ 4¤¹ ¹éͧ¢Í§à´ç¡ààµèÅФ¹ÍØéÁààÁǤ¹ÅÐ 4µÑÇ

¶ÒÁÇèÒÁÕ¤¹ààÅÐààÁǨӹǹà·èÒä÷Õèä»ÃéÒ¹¢¹Á»Ñ§
¶éÒà»ç¹»Ñ­ËÒàªÒÇì µéͧµÍºÇèÒÁÕà¾Õ§´.ª.¡ ä¡è ¤¹à´ÕÂÇ ·Õèà´Ô¹ä»ÃéÒ¹¢¹Á»Ñ§¤ÃѺ

à¾ÃÒФÓÇèÒ "Êǹ·Ò§¡Ñº" äÁèä´é¡Ó˹´ÇèҨеéͧÍÍ¡ÁÒ¨Ò¡ÃéÒ¹¢¹Á»Ñ§àÊÁÍ令ÃѺ
µÍº¾ÃéÍÁÍéÒ§ÍÔ§¢éͤÇÒÁ¹Õé
  #37  
Old 12 àÁÉÒ¹ 2010, 16:28
¹Ñ¡Ê׺ÍѨ©ÃÔÂÐ's Avatar
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µÍº¾ÃéÍÁÍéÒ§ÍÔ§¢éͤÇÒÁ¹Õé
  #38  
Old 15 àÁÉÒ¹ 2010, 22:44
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  #39  
Old 17 àÁÉÒ¹ 2010, 16:30
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Post ¡Ñ¹Ë¹èͤÃѺ
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  #40  
Old 19 àÁÉÒ¹ 2010, 14:05
¡ÃкÕèäÃé¤Á's Avatar
¡ÃкÕèäÃé¤Á ¡ÃкÕèäÃé¤Á äÁèÍÂÙèã¹Ãкº
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sin1 à·èҡѺà·èÒääÃѺ (ÍÂÒ¡ÃÙéÁÒ¡¡¡¡¤ÃѺ)
0.017452¤ÃѺ¼Á
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µÍº¾ÃéÍÁÍéÒ§ÍÔ§¢éͤÇÒÁ¹Õé
  #41  
Old 19 ¡Ã¡®Ò¤Á 2010, 19:34
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Êâµ¹àΨ¹ì ÍÂÙè·Õèä˹ (¹Õèä§â¨·ÂìËÔ¹)
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Fight
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Fight to .........
µÍº¾ÃéÍÁÍéÒ§ÍÔ§¢éͤÇÒÁ¹Õé
  #42  
Old 19 ¡Ã¡®Ò¤Á 2010, 19:42
kimchiman kimchiman äÁèÍÂÙèã¹Ãкº
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$Cosec 10^o - \sqrt{3}Sec 10^o=?$
µÍº¾ÃéÍÁÍéÒ§ÍÔ§¢éͤÇÒÁ¹Õé
  #43  
Old 19 ¡Ã¡®Ò¤Á 2010, 19:53
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ÍéÒ§ÍÔ§:
¢éͤÇÒÁà´ÔÁà¢Õ¹â´Â¤Ø³ kimchiman View Post
$\csc 10^\circ - \sqrt{3}\sec 10^\circ=?$
á¡ÐÃÐËÇèÒ§à¤Ã×èͧËÁÒÂà·èҡѺàͧà¹éÍ
$\displaystyle \csc 10^\circ - \sqrt{3}\sec 10^\circ = \frac{4}{\sin 20^\circ}(\frac12\cos 10^\circ-\frac{\sqrt3}{2}\sin 10^\circ)=4\frac{\sin 20^\circ}{\sin 20^\circ}=4$
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¤¹ä·ÂÃèÇÁã¨ÍÂèÒãªéÀÒÉÒÇԺѵÔ
½Ö¡¾ÔÁ¾ìÊÑ­ÅѡɳìÊÑ¡¹Ô´ ªÕÇÔµ(¤¹µÍºáÅФ¹¶ÒÁ)¨Ð§èÒ¢Öé¹àÂÍÐ (¨ÃÔ§æ¹Ð)

Stay Hungry. Stay Foolish.

19 ¡Ã¡®Ò¤Á 2010 19:56 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ nongtum
µÍº¾ÃéÍÁÍéÒ§ÍÔ§¢éͤÇÒÁ¹Õé
  #44  
Old 19 ¡Ã¡®Ò¤Á 2010, 19:54
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