多面体

諸量の数式表現

Excel 多面体 諸量

久しぶりの投稿です。
近々に ダイヤモンド結晶模型の製作について載せる段取りをしています。
四角棒を素材にしたのと 丸棒での模型です。今年中にやります。

実際に 目の前で作業をし少し説明すれば分かるようなことが
文章や 画像だけで表現するのは 私には大変困難な作業です。
顔も声も出さずにできるなら YouTube に載せようかなとも 検討しています。

今回 お伝えしようとしているのは 諸量の数式表現のデータです。
今まで お伝えしていた諸量の数値をほとんど網羅しています。
Excelやその同等品に転記してください。
画面には出ていませんが かなりボリュームがあるものです。

* 後日 数式の転記作業で 不本意な事象が発生する場合もあることが判明しました。
　その回避方法を 次の回のエピソードでお伝えしています。

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　

名称 
面積 
体積 
基本数  
頂芯寸 
稜芯寸 
S面芯寸 
M面芯寸 
L面芯寸 
仰角  
S接合角 
M接合角  
L接合角  
S面角  
M面角   
 L面角 
二面角1  
二面角2 
二面角3 
 
 
 
 
 
 

 01[3,3,3] 
=SQRT(3) 
=1/(6*SQRT(2)) 
=1/SQRT(3) 
=SQRT(3/2)/2 
=1/4*SQRT(2) 
=1/12*SQRT(6) 
 
 
=180/PI()*(ASIN(SQRT(2/3))) 
=60 
 
 
=180/PI()*(ASIN(1/SQRT(3))) 
 
 
=180/PI()*(2*ASIN(1/SQRT(3))) 
 
 
SS 
 
 
 
 
 

 02[3,3,3,3] 
=2*SQRT(3) 
=SQRT(2)/3 
=1/SQRT(2) 
=SQRT(2)/2 
=1/2 
=1/SQRT(6) 
 
 
=45 
=45 
 
 
=180/PI()*(ACOS(1/SQRT(3))) 
 
 
=180/PI()*(ACOS(1/SQRT(3))*2) 
 
 
SS 
 
 
 
 
 

 03[4,4,4] 
=6 
=1 
=SQRT(2/3) 
=SQRT(3)/2 
=SQRT((1/2*SQRT(3))^2-(1/2)^2) 
=1/2 
 
 
=180/PI()*(ASIN(1/SQRT(3))) 
=60 
 
 
=45 
 
 
=90 
 
 
SS 
 
 
 
 
 

 04[3,3,3,3,3] 
=5*SQRT(3) 
=5/12*(3+SQRT(5)) 
=SQRT(1/10*(5+SQRT(5))) 
=1/4*SQRT(10 + 2*SQRT(5)) 
=1/4*(1+SQRT(5)) 
=1/12*(SQRT(15) + 3*SQRT(3)) 
 
 
=180/PI()*(ASIN(2/SQRT(10 + 2*SQRT(5)))) 
=36 
 
 
=180/PI()*(ASIN((1 + SQRT(5))/(2*SQRT(3)))) 
 
 
=180/PI()*(ASIN((1 + SQRT(5))/(2*SQRT(3)))*2) 
 
 
SS 
 
 
 
 
 

 05[3,4,3,4] 
=2*(3+SQRT(3)) 
=5*SQRT(2)/3 
=SQRT(3)/2 
=1 
=SQRT(3)/2 
=1/3*SQRT(6) 
=1/SQRT(2) 
 
=30 
=180/PI()*(ASIN(1/SQRT(3))) 
=180/PI()*(ASIN(SQRT(2/3))) 
 
=180/PI()*(ACOS(1/3)) 
=180/PI()*(ACOS(1/SQRT(3))) 
 
=180/PI()*(ACOS(1/SQRT(3))+ACOS(1/3)) 
 
 
SM 
 
 
 
 
 

 06[3,6,6] 
=7*SQRT(3) 
=23/(6*SQRT(2)) 
=3/SQRT(11) 
=SQRT(22)/4 
=1/4*(3*SQRT(2)) 
=1/12*(5*SQRT(6)) 
=1/4*SQRT(6) 
 
=180/PI()*(ASIN(SQRT(2/11))) 
=180/PI()*(ASIN(SQRT(11)/6)) 
=180/PI()*(ASIN(SQRT(11/3)/2)) 
 
=180/PI()*(ACOS(SQRT(2/3)/3)) 
=180/PI()*(ACOS(SQRT(2/3))) 
 
=180/PI()*(ACOS(SQRT(2/3)/3)+ACOS(SQRT(2/3))) 
=180/PI()*(2*ACOS(SQRT(2/3))) 
 
SM MM 
 
 
 
 
 

 07[3,3,3,3,4] 
=6+8*SQRT(3) 
=1/3*SQRT(188 + (3*(2149479 - 15037*SQRT(33)))^(1/3) + (3*(2149479 + 15037*SQRT(33)))^(1/3)) 
=1/SQRT(42/(20 + (566 - 42*SQRT(33))^(1/3) + (566 + 42*SQRT(33))^(1/3))) 
=SQRT(-(21/(2*(-22+(566-42*SQRT(33))^(1/3)+(566+42*SQRT(33))^(1/3))))) 
=1/(2*SQRT(3/(7 + (199 - 3*SQRT(33))^(1/3) + (199 + 3*SQRT(33))^(1/3)))) 
=1/(2*SQRT(3/(6 + (199 - 3*SQRT(33))^(1/3) + (199 + 3*SQRT(33))^(1/3)))) 
=1/(2*SQRT(3/(4 + (199 - 3*SQRT(33))^(1/3) + (199 + 3*SQRT(33))^(1/3)))) 
 
=180/PI()*(ASIN(1/SQRT(42/(22 - (566 - 42*SQRT(33))^(1/3) - (566 + 42*SQRT(33))^(1/3))))) 
=180/PI()*(ASIN(SQRT(21/(2*(20 + (566 - 42*SQRT(33))^(1/3) + (566 + 42*SQRT(33))^(1/3)))))) 
=180/PI()*(ASIN(SQRT(21/(20 + (566 - 42*SQRT(33))^(1/3) + (566 + 42*SQRT(33))^(1/3))))) 
 
=180/PI()*(ACOS(1/SQRT(7 + (199 - 3*SQRT(33))^(1/3) + (199 + 3*SQRT(33))^(1/3)))) 
=180/PI()*(ACOS(SQRT(3/(7 + (199 - 3*SQRT(33))^(1/3) + (199 + 3*SQRT(33))^(1/3))))) 
 
=180/PI()*(2*(ACOS(1/SQRT(7 + (199 - 3*SQRT(33))^(1/3) + (199 + 3*SQRT(33))^(1/3))))) 
=180/PI()*(ACOS(1/SQRT(7 + (199 - 3*SQRT(33))^(1/3) + (199 + 3*SQRT(33))^(1/3)))+ACOS(SQRT(3/(7 + (199 - 3*SQRT(33))^(1/3) + (199 + 3*SQRT(33))^(1/3))))) 
 
SS SM 
 
 
 
 
 

 08[3,4,4,4] 
=2*(9+SQRT(3)) 
=4+10*SQRT(2)/3 
=1/17*SQRT(34*(6 + SQRT(2))) 
=1/2*SQRT(5+2*SQRT(2)) 
=1/2*SQRT(4 + 2*SQRT(2)) 
=SQRT(3)/2 + 1/SQRT(6) 
=1/2 + 1/SQRT(2) 
 
=180/PI()*(ASIN(1/SQRT(5 + 2*SQRT(2)))) 
=180/PI()*(ASIN(1/2*SQRT(17/(2*(6 + SQRT(2)))))) 
=180/PI()*(ASIN(1/2*SQRT(17/(6 + SQRT(2))))) 
 
=180/PI()*(ACOS(1/SQRT(3*(4 + 2*SQRT(2))))) 
=180/PI()*(3*PI()/8) 
 
=180/PI()*(ACOS(1/SQRT(3*(4 + 2*SQRT(2))))+ACOS(1/SQRT(4 + 2*SQRT(2)))) 
=135 
 
SM MM 
 
 
 
 
 

 09[5,5,5] 
=3*SQRT(25 + 10*SQRT(5)) 
=1/4*(15+7*SQRT(5)) 
=1/6*(SQRT(3)+SQRT(15)) 
=1/4*(SQRT(3)+SQRT(15)) 
=1/4*(3+SQRT(5)) 
=SQRT(5/8 + 11/(8*SQRT(5))) 
 
 
=180/PI()*(ASIN(2/(SQRT(3) + SQRT(15)))) 
=60 
 
 
=180/PI()*(ACOS(SQRT(1/10*(5 - SQRT(5))))) 
 
 
=180/PI()*(2*ACOS(SQRT(1/10*(5 - SQRT(5))))) 
 
 
SS 
 
 
 
 
 

 10[4,6,6] 
=6*(1 + 2*SQRT(3)) 
=8*SQRT(2) 
=3/SQRT(10) 
=SQRT(5/2) 
=3/2 
=SQRT(2) 
=SQRT(6)/2 
 
=180/PI()*(ASIN((1/2)/(SQRT(5/2)))) 
=180/PI()*(ASIN(SQRT(5)/3)) 
=180/PI()*(ASIN(SQRT(5/6))) 
 
=180/PI()*(ACOS(1/3)) 
=180/PI()*(ACOS(1/SQRT(3))) 
 
=180/PI()*(ACOS(1/3)+ACOS(1/SQRT(3))) 
=180/PI()*(2*ACOS(1/SQRT(3))) 
 
SM MM 
 
 
 
 
 

 11[3,5,3,5] 
=SQRT(30*(10 + 3*SQRT(5) + SQRT(15*(5 + 2*SQRT(5))))) 
=1/6*(45+17*SQRT(5)) 
=1/4*SQRT((5 + SQRT(5))*2) 
=1/2*(1+SQRT(5)) 
=1/2*SQRT(5 + 2*SQRT(5)) 
=SQRT(1/6*(7 + 3*SQRT(5))) 
=SQRT(1 + 2/SQRT(5)) 
 
=18 
=180/PI()*(ASIN(SQRT(2/(5 + SQRT(5))))) 
=180/PI()*(ASIN((1 + SQRT(5))/SQRT(2*(5 + SQRT(5))))) 
 
=180/PI()*(ACOS(1/SQRT(15 + 6*SQRT(5)))) 
=180/PI()*(ACOS(1/SQRT(5))) 
 
=180/PI()*(PI() - ATAN(3 - SQRT(5))) 
 
 
SM 
 
 
 
 
 

 12[3,8,8] 
=2*SQRT(3) + 12*(1 + SQRT(2)) 
=7/3*(3 + 2*SQRT(2)) 
=1/17*SQRT(34*(5 + 2*SQRT(2))) 
=1/2*SQRT(7+4*SQRT(2)) 
=1 + 1/SQRT(2) 
=SQRT(3)/2 + SQRT(6)/3 
=1/2*(1 + SQRT(2)) 
 
=180/PI()*(ASIN(1/SQRT(7 + 4*SQRT(2)))) 
=180/PI()*(ATAN(SQRT(23 - 16*SQRT(2)))) 
=180/PI()*(ATAN(SQRT(7 + 4*SQRT(2)))) 
 
=180/PI()*(ACOS((-1 + SQRT(2))/SQRT(6))) 
=45 
 
=180/PI()*(PI()/4 + ACOS((-1 + SQRT(2))/SQRT(6))) 
=90 
 
SM MM 
 
 
 
 
 

 13[3,3,3,3,5] 
=20*SQRT(3)+15/SQRT(5-2*SQRT(5)) 
=1/12*(20*SQRT(2*(19+7*SQRT(5)+2^(2/3)*(5112+2285*SQRT(5)-3*SQRT(7137+3192*SQRT(5)))^(1/3)+2^(2/3)*(5112+2285*SQRT(5)+3*SQRT(7137+3192*SQRT(5)))^(1/3)))+SQRT(6*(5+2*SQRT(5))*(75+23*SQRT(5)+5*2^(2/3)*(5112+2285*SQRT(5)-3*SQRT(7137+3192*SQRT(5)))^(1/3)+5*2^(2/3)*(5112+2285*SQRT(5)+3*SQRT(7137+3192*SQRT(5)))^(1/3)))) 
= 1/SQRT(1254/(580 + 20*SQRT(5) + (2*(6192143 + 2563547*SQRT(5) - 627*SQRT(6*(5760573 + 2813807*SQRT(5)))))^(1/3) + (2*(6192143 + 2563547*SQRT(5) + 627*SQRT(6*(5760573 + 2813807*SQRT(5)))))^(1/3))) 
=1/12*SQRT(6*(27+7*SQRT(5)+(20448+9140*SQRT(5)-12*SQRT(7137+3192*SQRT(5)))^(1/3)+(20448+9140*SQRT(5)+12*SQRT(7137+3192*SQRT(5)))^(1/3))) 
=SQRT(1/24*(27 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140* SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)) - 1/4) 
=SQRT(1/24*(27 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)) - 1/3) 
=SQRT((1/12*SQRT(6*(27+7*SQRT(5)+(20448+9140*SQRT(5)-12*SQRT(7137+3192*SQRT(5)))^(1/3)+(20448+9140*SQRT(5)+12*SQRT(7137+3192*SQRT(5)))^(1/3))))^2-(1/2/SIN(PI()/5))^2) 
 
=180/PI()*(ASIN(SQRT(6/(27 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3))))) 
=180/PI()*(ASIN((1/2)/( 1/SQRT(1254/(580 + 20*SQRT(5) + (2*(6192143 + 2563547*SQRT(5) - 627*SQRT(6*(5760573 + 2813807*SQRT(5)))))^(1/3) + (2*(6192143 + 2563547*SQRT(5) + 627*SQRT(6*(5760573 + 2813807*SQRT(5)))))^(1/3)))))) 
=180/PI()*(ASIN((COS(PI()/5))/( 1/SQRT(1254/(580 + 20*SQRT(5) + (2*(6192143 + 2563547*SQRT(5) - 627*SQRT(6*(5760573 + 2813807*SQRT(5)))))^(1/3) + (2*(6192143 + 2563547*SQRT(5) + 627*SQRT(6*(5760573 + 2813807*SQRT(5)))))^(1/3)))))) 
 
=180/PI()*(ACOS((1/2/TAN(PI()/3))/(SQRT(1/24*(27 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140* SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)) - 1/4)))) 
=180/PI()*(ACOS((1/2/TAN(PI()/5))/(SQRT(1/24*(27 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140* SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)) - 1/4)))) 
 
=180/PI()*((ACOS((1/2/TAN(PI()/3))/(SQRT(1/24*(27 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140* SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)) - 1/4))))*2) 
=180/PI()*(ACOS((1/2/TAN(PI()/3))/(SQRT(1/24*(27 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140* SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)) - 1/4)))+ACOS((1/2/TAN(PI()/5))/(SQRT(1/24*(27 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140* SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)) - 1/4)))) 
 
SS SM 
 
 
 
 
 

 14[3,4,5,4] 
=30+SQRT(30*(10+3*SQRT(5)+SQRT(75+30*SQRT(5)))) 
=20+29*SQRT(5)/3 
=SQRT(2/41*(15 + 2*SQRT(5))) 
=1/2*SQRT(11+4*SQRT(5)) 
=SQRT(5/2 + SQRT(5)) 
=SQRT(5/3) + SQRT(3)/2 
=1 + SQRT(5)/2 
=3/2*SQRT(1 + 2/SQRT(5)) 
=180/PI()*(ASIN(1/SQRT(11 + 4*SQRT(5)))) 
=180/PI()*(ASIN(1/2*SQRT(3/2 - 1/SQRT(5)))) 
=180/PI()*(ATAN(SQRT(19 - 8*SQRT(5)))) 
=180/PI()*(ASIN(1/4*SQRT(7 + 9/SQRT(5)))) 
=180/PI()*(ACOS(SQRT(1/30*(5 - 2*SQRT(5))))) 
=180/PI()*(ACOS(SQRT(1/2 - 1/SQRT(5)))) 
=180/PI()*(ACOS(1/SQRT(10))) 
=180/PI()*(PI() - ASIN(SQRT(1/6*(3 - SQRT(5))))) 
=180/PI()*(ACOS(1/SQRT(10))+ACOS(SQRT(1/2 - 1/SQRT(5)))) 
 
SM ML 
 
 
 
 
 

 15[4,6,8] 
=12*(2+SQRT(2)+SQRT(3)) 
=22+14*SQRT(2) 
=SQRT(6/97*(14 + SQRT(2))) 
=(1/2*SQRT(13+6*SQRT(2))) 
=SQRT(3/2*(2 + SQRT(2))) 
=1/2*(3 + SQRT(2)) 
=1/2*(SQRT(3) + SQRT(6)) 
=1/2 + SQRT(2) 
=180/PI()*(ASIN(SQRT(1/97*(13 - 6*SQRT(2))))) 
=180/PI()*(ASIN(1/2*SQRT(1/6*(14 - SQRT(2))))) 
=180/PI()*(ATAN(SQRT(15 - 8*SQRT(2)))) 
=180/PI()*(ASIN(1/2*SQRT(13/6 + SQRT(2)))) 
=180/PI()*(ACOS(1/2*SQRT(1/3*(2 - SQRT(2))))) 
=180/PI()*(3*PI()/8) 
=180/PI()*(ACOS(1/2*SQRT(1/3*(2 + SQRT(2))))) 
=180/PI()*(ACOS(1/2*SQRT(1/3*(2 - SQRT(2))))+3*PI()/8) 
=135 
=180/PI()*(3*PI()/8+ACOS(1/2*SQRT(1/3*(2 + SQRT(2))))) 
SM SL ML 
 
 
 
 
 

 16[5,6,6] 
=3*SQRT(5*(65+2*SQRT(5)+4*SQRT(75+30*SQRT(5)))) 
=1/4*(125+43*SQRT(5)) 
=3*SQRT(1/218*(21 + SQRT(5))) 
=1/4*SQRT(2*(29+9*SQRT(5))) 
=3/4*(1 + SQRT(5)) 
=1/2*SQRT(25/2 + 41/(2*SQRT(5))) 
=1/4*(3*SQRT(3) + SQRT(15)) 
 
=180/PI()*(ASIN(SQRT(2/(29 + 9*SQRT(5))))) 
=180/PI()*(ASIN(SQRT(29/72 + SQRT(5)/8))) 
=180/PI()*(ASIN(1/2*SQRT(1/6*(21 - SQRT(5))))) 
 
=180/PI()*(ACOS(1/3*SQRT(1/10*(5 + SQRT(5))))) 
=180/PI()*(ACOS(2/(SQRT(3) + SQRT(15)))) 
 
=180/PI()*(PI() - ATAN(3 - SQRT(5))) 
=180/PI()*(2*ACOS(SQRT(1/6*(3 - SQRT(5))))) 
 
SM MM 
 
 
 
 
 

 17[3,10,10] 
=5*(SQRT(3)+6*SQRT(5+2*SQRT(5))) 
=5/12*(99+47*SQRT(5)) 
=SQRT(5/122*(17 + 3*SQRT(5))) 
=1/4*SQRT(74 + 30*SQRT(5)) 
=1/4*(5 + 3*SQRT(5)) 
=(9 + 5*SQRT(5))/(4*SQRT(3)) 
=1/4*SQRT(50 + 22*SQRT(5)) 
 
=180/PI()*(ASIN(SQRT(2/(37 + 15*SQRT(5))))) 
=180/PI()*(ASIN(SQRT(61/(10*(17 + 3*SQRT(5)))))) 
=180/PI()*(ASIN(1/2*SQRT(1/10*(35 + SQRT(5))))) 
 
=180/PI()*(ACOS(SQRT(1/30*(7-3*SQRT(5))))) 
=180/PI()*(ACOS(SQRT(1/10*(5 - SQRT(5))))) 
 
=180/PI()*(PI() -ATAN(3 - SQRT(5))) 
=180/PI()*(ACOS(SQRT(1/10*(5 - SQRT(5))))*2) 
 
SM MM 
 
 
 
 
 

 18[4,6,10] 
=30*(1+SQRT(2*(4+SQRT(5)+SQRT(15+6*SQRT(5))))) 
=95+50*SQRT(5) 
=SQRT(6/241*(35 + 2*SQRT(5))) 
=(1/2*SQRT(31+12*SQRT(5))) 
=1/2*SQRT(6*(5 + 2*SQRT(5))) 
=3/2 + SQRT(5) 
=SQRT(3) + SQRT(15)/2 
=1/2*SQRT(25 + 10 *SQRT(5)) 
=180/PI()*(ASIN(1/SQRT(31 + 12*SQRT(5)))) 
=180/PI()*(ASIN(1/2*SQRT(7/3 - 2/(3*SQRT(5))))) 
=180/PI()*(ASIN(1/2*SQRT(1/10*(35 - 2*SQRT(5))))) 
=180/PI()*(ATAN(SQRT(31/5 + 12/SQRT(5)))) 
=180/PI()*(ACOS(SQRT(1/30*(5-2*SQRT(5))))) 
=180/PI()*(ACOS(SQRT(1/2 - 1/SQRT(5)))) 
=180/PI()*(ACOS(1/SQRT(6))) 
=180/PI()*(PI()- ASIN(SQRT(1/6*(3 - SQRT(5))))) 
=180/PI()*(ACOS(SQRT(1/30*(5-2*SQRT(5))))+ACOS(1/SQRT(6))) 
=180/PI()*(PI()-ATAN(3-SQRT(5))) 
SM SL ML 
 
 
 
 
 

  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 名称 
面積 
体積 
稜芯寸 
双面芯寸 
頂芯寸S 
頂芯寸M 
頂芯寸L 
双稜寸S 
双稜寸M 
双稜寸L 
稜寸結S 
稜寸結M 
稜寸結L 
二面角 
仰角S 
仰角M 
仰角L 
a稜開角/2 
b稜開角/2 
c稜開角/2 
a 稜寸 / 稜芯寸 
b 稜寸 / 稜芯寸 
c 稜寸 / 稜芯寸 
面積2 
体積2
 01双[3,3,3] 
=SQRT(3) 
=1/12*SQRT(2) 
=1/4*SQRT(2) 
=1/12*SQRT(6) 
=1/4*SQRT(6) 
 
 
=1/2 
 
 
=1 
 
 
=360/PI()*ATAN(1/SQRT(2)) 
=180/PI()* ATAN(SQRT(2)) 
 
 
=30 
 
 
=SQRT(2) 
 
 
=SQRT(3) 
=1/12*SQRT(2)
 02双[3,3,3,3] 
=3 
=1/4*SQRT(2) 
=1/2 
=1/4*SQRT(2) 
=1/4*SQRT(6) 
 
 
=1/4*SQRT(2) 
 
 
=1/2*SQRT(2) 
 
 
=90 
=180/PI()*ATAN(1/SQRT(2)) 
 
 
=45 
 
 
=1/2*SQRT(2) 
 
 
=6 
=1
 03双[4,4,4] 
=4* SQRT(3) 
=4/3 
=(1/2*SQRT(2)) 
=(1/3*SQRT(3)) 
=1 
 
 
=1/2*SQRT(2) 
 
 
=SQRT(2) 
 
 
=360/PI()*ATAN(SQRT(2)) 
=45 
 
 
=30 
 
 
=1 
 
 
=2* SQRT(3) 
=1/3*SQRT(2)
 04双[3,3,3,3,3] 
=15*SQRT(2/(5 + SQRT(5))) 
=1/4*(5 + SQRT(5)) 
=1/4*(1 + SQRT(5)) 
=1/2*SQRT(1 + 2/SQRT(5)) 
=1/2*SQRT(3) 
 
 
=SQRT((1/2*SQRT(3))^2-(1/4*(1 + SQRT(5)))^2) 
 
 
=1/2*(-1 + SQRT(5)) 
 
 
=360/PI()*ATAN(1/2*(1+SQRT(5))) 
=180/PI()*ATAN(2/(3 + SQRT(5))) 
 
 
=54 
 
 
=1/2*(3 - SQRT(5)) 
 
 
=3*SQRT(25 + 10*SQRT(5)) 
=1/4*(15 + 7*SQRT(5))
 05双[3,4,3,4] 
=27/4*SQRT(2) 
=27/16*SQRT(2) 
=SQRT(1-(1/2)^2) 
=3/4 
=3/8*SQRT(6) 
=3/4*SQRT(2) 
 
=1/8*SQRT(6) 
=1/4*SQRT(6) 
 
=3/8*SQRT(6) 
 
 
=360/3 
=90-(180/PI()*ACOS(1/3)) 
=180/PI()*ASIN(1/SQRT(3)) 
 
=180/PI()*ATAN(SQRT(2)) 
=180/PI()*ATAN(1/SQRT(2)) 
 
=1/4*SQRT(2) 
=1/2*SQRT(2) 
 
=8*SQRT(2) 
=1/9*16*SQRT(3)
 06双[3,6,6] 
=27/5*SQRT(11) 
=81/20*SQRT(2) 
=3/4*SQRT(2) 
=9/44*SQRT(22) 
=9/20*SQRT(6) 
=3/4*SQRT(6) 
 
=3/10 
=3/2 
 
=9/5 
=3 
 
=360/PI()*ATAN(3/SQRT(2)) 
=180/PI()* ATAN(SQRT(2)/5) 
=180/PI()*ATAN(SQRT(2)) 
 
=180/PI()*ASIN(5/6) 
=180/PI()*ASIN(1/(2*SQRT(3))) 
 
=1/5*SQRT(2) 
=SQRT(2) 
 
=5/3*SQRT(11) 
=25/36*SQRT(2)
 07双[3,3,3,3,4] 
=SQRT(6*(2501-363*SQRT(33))^(1/3)+6*(2501+363*SQRT(33))^(1/3)+228) 
=1/6*SQRT(678 + 6*(1327067 - 1419*SQRT(33))^(1/3) + 6*(1327067 + 1419*SQRT(33))^(1/3)) 
=1/(2*SQRT(3/(7 + (199 - 3*SQRT(33))^(1/3) + (199 + 3*SQRT(33))^(1/3)))) 
=1/(2*SQRT(42/(78 + (66*(6039 - 49*SQRT(33)))^(1/3) + (66*(6039 + 49*SQRT(33)))^(1/3)))) 
=1/(2*SQRT(2/(6 + (6*(9 - SQRT(33)))^(1/3) + (6 *(9 + SQRT(33)))^(1/3)))) 
=1/(2*SQRT(6/(14 + (2*(1777 - 33*SQRT(33)))^(1/3) + (2*(1777 + 33*SQRT(33)))^(1/3)))) 
 
=1/(2*(3*SQRT(33) - 13)^(1/6)*SQRT(6/(4*(3*SQRT(33) - 13)^(1/3) + 2^(1/3)*(3*SQRT(33) - 13)^(2/3) - 4*2^(2/3)))) 
=1/(2*SQRT(6/((6*(9 - SQRT(33)))^(1/3) + (6*(9 + SQRT(33)))^(1/3)))) 
 
=1/6*SQRT(24 - (24*2^(2/3))/(-13 + 3*SQRT(33))^(1/3) + 6*(-26 + 6*SQRT(33))^(1/3)) 
=1/(2*SQRT(3/(4 + (19 - 3*SQRT(33))^(1/3) + (19 + 3*SQRT(33))^(1/3)))) 
 
=360/PI()*ASIN(3/SQRT(24 - 3*(19 - 3*SQRT(33))^(1/3) - 3*(19 + 3*SQRT(33))^(1/3))) 
=180/PI()*ASIN(1/SQRT(7 + (199 - 3*SQRT(33))^(1/3) + (199 + 3*SQRT(33))^(1/3))) 
=180/PI()*ASIN(SQRT(3/(7 + (199 - 3*SQRT(33))^(1/3) + (199 + 3*SQRT(33))^(1/3)))) 
 
=180/PI()* ASIN(1/(2*SQRT(3/(4 + (19 - 3*SQRT(33))^(1/3) + (19 + 3*SQRT(33))^(1/3))))) 
=180/PI()*ASIN(SQRT(3/((54 - 6*SQRT(33))^(1/3) + (6*(9 + SQRT(33)))^(1/3)))) 
 
=1/SQRT(2/(2 - (4*2^(2/3))/(-13 + 3*SQRT(33))^(1/3) + (2*(-13 + 3*SQRT(33)))^(1/3))) 
=1/6*SQRT(-36 + 6*(54 - 6*SQRT(33))^(1/3) + 6*(54 + 6*SQRT(33))^(1/3)) 
 
=2*SQRT(3*(85 + (570862 - 19074*SQRT(33))^(1/3) + (570862 + 19074*SQRT(33))^(1/3))) 
=1/3*SQRT(3*(2047255857 - 252417*SQRT(33))^(1/3) + 3*(2047255857 + 252417*SQRT(33))^(1/3) + 3807)
 08双[3,4,4,4] 
=24/7*SQRT(62 - 16*SQRT(2)) 
=16/7*(1 + 2*SQRT(2)) 
=SQRT(1 + 1/SQRT(2)) 
=SQRT(2/17*(7 + 4*SQRT(2))) 
=1/7*(4*SQRT(3) + SQRT(6)) 
=SQRT(2) 
 
=1/7*SQRT(5 - 1/SQRT(2)) 
=SQRT(1 - 1/SQRT(2)) 
 
=2/7*SQRT(10 - SQRT(2)) 
=SQRT(4 - 2*SQRT(2)) 
 
=360/PI()*ATAN(SQRT(2*(2 + SQRT(2)))) 
=90 - 180/PI()*ACOS(1/SQRT(6*(2 + SQRT(2)))) 
=90-135/2 
 
=180/PI()*ASIN(SQRT(10 + SQRT(2))/4) 
=180/PI()*ASIN(1/2*SQRT(1 + 1/SQRT(2))) 
 
=1/7*(3 - SQRT(2)) 
=SQRT(2) - 1 
 
=6*SQRT(29 - 2*SQRT(2)) 
=SQRT(122 + 71*SQRT(2))
 09双[5,5,5] 
=5/2*(3*SQRT(3)+SQRT(15)) 
=5/12*(11 + 5*SQRT(5)) 
=1/4*(3 + SQRT(5)) 
=(2 + SQRT(5))/(2*SQRT(3)) 
=1/2*SQRT(5 + 2*SQRT(5)) 
 
 
=1/4*(1 + SQRT(5)) 
 
 
=1/2*(1 + SQRT(5)) 
 
 
=360/PI()*ATAN(1/2*(3 + SQRT(5))) 
=90-180/PI()*ACOS(SQRT(1/10*(5 - SQRT(5)))) 
 
 
=30 
 
 
=1/2*(SQRT(5) - 1) 
 
 
=5*SQRT(3) 
=5/12*(3 + SQRT(5))
 10双[4,6,6] 
=27/2*SQRT(5) 
=81/8*SQRT(2) 
=3/2 
=9/20*SQRT(10) 
=9/8*(SQRT(2)) 
=3/4*(SQRT(6)) 
 
=3/8*SQRT(2) 
=3/4*SQRT(2) 
 
=9/8*SQRT(2) 
=3/2*SQRT(2) 
 
=360/PI()*ATAN(3) 
=180/PI()*ASIN(1/3) 
=180/PI()*ASIN(1/SQRT(3)) 
 
=180/PI()*ASIN(2/3) 
=180/PI()*ASIN(1/SQRT(6)) 
 
=1/4*SQRT(2) 
=1/2*SQRT(2) 
 
=16/3*SQRT(5) 
=32/9
 11双[3,5,3,5] 
=75/8*(1 + SQRT(5)) 
=25/16*(5 + 2*SQRT(5)) 
=1/2*SQRT(5 + 2*SQRT(5)) 
=1/8*(5 + 3*SQRT(5)) 
=1/8*SQRT(3)*(5 + SQRT(5)) 
=1/4*SQRT(25 + 10*SQRT(5)) 
 
=1/4*SQRT(1/2*(5 - SQRT(5))) 
=1/4*SQRT(5 + 2*SQRT(5)) 
 
=1/8*SQRT(10*(5 + SQRT(5))) 
 
 
=360*2/5 
=180/PI()*ASIN(1/SQRT(15 + 6*SQRT(5))) 
=180/PI()*ATAN(1/2) 
 
=180/PI()*ATAN(1/2*(1+SQRT(5))) 
=180/PI()*ASIN(SQRT(1/10*(5 - SQRT(5)))) 
 
=1/4*(3 - SQRT(5)) 
=1/2 
 
=12*SQRT(5) 
=4*SQRT(5 + 2*SQRT(5))
 12双[3,8,8] 
=12*SQRT(7 + 4*SQRT(2)) 
=12 + 8*SQRT(2) 
=1/2*(2 + SQRT(2)) 
=SQRT(1/17*(23 + 16*SQRT(2))) 
=SQRT(3) 
=1 + SQRT(2) 
 
=1/2*(2 - SQRT(2)) 
=1/2*(2 + SQRT(2)) 
 
=2 
=2+SQRT(2) 
 
=360/PI()*ATAN(2+SQRT(2)) 
=180/PI()*ATAN(3 - 2*SQRT(2)) 
=45 
 
=180/PI()*ASIN(1/(2*(2 - SQRT(2)))) 
=180/PI()*ASIN(1/2*SQRT(1 - 1/SQRT(2))) 
 
=3 - 2*SQRT(2) 
=1 
 
=3*SQRT(7+4*SQRT(2)) 
=3/2 + SQRT(2)
 13双[3,3,3,3,5] 
=(((1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2/(1/(2*SQRT(6/(19 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3))))))*COS(ACOS(2*SQRT(2/(27 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3))))))*(1/4)*240+(((1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2/(1/(2*SQRT(30/(75 + 23*SQRT(5) + 5*2^(2/3)*(5112 + 2285*SQRT(5) - 3*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 5*2^(2/3)*(5112 + 2285*SQRT(5) + 3*SQRT(7137 + 3192*SQRT(5)))^(1/3))))))*COS(ACOS(2*SQRT((3*(5 + SQRT(5)))/(5*(27 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))))))*(1/8*(1 + SQRT(5)))*60 
=((((1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2/(1/(2*SQRT(6/(19 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3))))))*COS(ACOS(2*SQRT(2/(27 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3))))))*(1/4)*240)*(((1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2/(1/(2*SQRT(6/(19 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3))))))*SIN(ACOS(2*SQRT(2/(27 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3))))))/3+((((1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2/(1/(2*SQRT(30/(75 + 23*SQRT(5) + 5*2^(2/3)*(5112 + 2285*SQRT(5) - 3*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 5*2^(2/3)*(5112 + 2285*SQRT(5) + 3*SQRT(7137 + 3192*SQRT(5)))^(1/3))))))*COS(ACOS(2*SQRT((3*(5 + SQRT(5)))/(5*(27 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))))))*(1/8*(1 + SQRT(5)))*60)*(((1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2/(1/(2*SQRT(6/(19 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3))))))*SIN(ACOS(2*SQRT(2/(27 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3))))))/3 
=1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)) 
=((1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2/(1/(2*SQRT(6/(19 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3))))))*SIN(ACOS(2*SQRT(2/(27 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3))))) 
=(1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2/(1/(2*SQRT(6/(19 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3))))) 
=(1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2/(1/(2*SQRT(30/(75 + 23*SQRT(5) + 5*2^(2/3)*(5112 + 2285*SQRT(5) - 3*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 5*2^(2/3)*(5112 + 2285*SQRT(5) + 3*SQRT(7137 + 3192*SQRT(5)))^(1/3))))) 
 
=SQRT(((1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2/(1/(2*SQRT(6/(19 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3))))))^2-(1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2) 
=SQRT(((1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2/(1/(2*SQRT(30/(75 + 23*SQRT(5) + 5*2^(2/3)*(5112 + 2285*SQRT(5) - 3*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 5*2^(2/3)*(5112 + 2285*SQRT(5) + 3*SQRT(7137 + 3192*SQRT(5)))^(1/3))))))^2-(1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2) 
 
=SQRT(((1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2/(1/(2*SQRT(6/(19 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3))))))^2-(1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2)*2 
=SQRT(((1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2/(1/(2*SQRT(6/(19 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3))))))^2-(1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2)+SQRT(((1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2/(1/(2*SQRT(30/(75 + 23*SQRT(5) + 5*2^(2/3)*(5112 + 2285*SQRT(5) - 3*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 5*2^(2/3)*(5112 + 2285*SQRT(5) + 3*SQRT(7137 + 3192*SQRT(5)))^(1/3))))))^2-(1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2) 
 
=180/PI()*(ASIN((1/4)/((1/4)*2*COS(ASIN((1/4)/((1/6*SQRT(3))*(1/12*SQRT(((-12*SQRT(3*(2379 + 1064*SQRT(5))) + 9140*SQRT(5) + 20448)^(1/3) + 7*SQRT(5) + (12*SQRT(3*(2379 + 1064*SQRT(5))) + 9140* SQRT(5) + 20448)^(1/3) + 21)*6))/(1/12*SQRT(114 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3))))))))*2) 
=90-(180/PI()*ACOS(2*SQRT(3/(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3))))) 
=90-(180/PI()*(ACOS(((1/2*SQRT(1 + 2/SQRT(5))))/(1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))))) 
 
=180/PI()*(ASIN((1/4)/(SQRT(((1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2/(1/(2*SQRT(6/(19 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3))))))^2-(1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2)))) 
=180/PI()*(ASIN(1/8*(1 + SQRT(5))/(SQRT(((1/12*SQRT(126+42*SQRT(5)+6*(20448+9140*SQRT(5)-12*SQRT(7137+3192*SQRT(5)))^(1/3)+6*(20448+9140*SQRT(5)+12*SQRT(7137+3192*SQRT(5)))^(1/3)))^2/(1/(2*SQRT(30/(75+23*SQRT(5)+5*2^(2/3)*(5112+2285*SQRT(5)-3*SQRT(7137+3192*SQRT(5)))^(1/3)+5*2^(2/3)*(5112+2285*SQRT(5)+3*SQRT(7137+3192*SQRT(5)))^(1/3))))))^2-(1/12*SQRT(126+42*SQRT(5)+6*(20448+9140*SQRT(5)-12*SQRT(7137+3192*SQRT(5)))^(1/3)+6*(20448+9140*SQRT(5)+12*SQRT(7137+3192*SQRT(5)))^(1/3)))^2)))) 
 
=SQRT(((1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2/(1/(2*SQRT(6/(19 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3))))))^2-(1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2)/(1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3))) 
=(SQRT(((1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2/(1/(2*SQRT(30/(75 + 23*SQRT(5) + 5*2^(2/3)*(5112 + 2285*SQRT(5) - 3*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 5*2^(2/3)*(5112 + 2285*SQRT(5) + 3*SQRT(7137 + 3192*SQRT(5)))^(1/3))))))^2-(1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2))/(1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3))) 
 
=((((1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2/(1/(2*SQRT(6/(19 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3))))))*COS(ACOS(2*SQRT(2/(27 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3))))))*(1/4)*240+(((1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2/(1/(2*SQRT(30/(75 + 23*SQRT(5) + 5*2^(2/3)*(5112 + 2285*SQRT(5) - 3*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 5*2^(2/3)*(5112 + 2285*SQRT(5) + 3*SQRT(7137 + 3192*SQRT(5)))^(1/3))))))*COS(ACOS(2*SQRT((3*(5 + SQRT(5)))/(5*(27 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))))))*(1/8*(1 + SQRT(5)))*60)/(SQRT(((1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2/(1/(2*SQRT(6/(19 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3))))))^2-(1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2)*2)^2 
=(((((1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2/(1/(2*SQRT(6/(19 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3))))))*COS(ACOS(2*SQRT(2/(27 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3))))))*(1/4)*240)*(((1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2/(1/(2*SQRT(6/(19 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3))))))*SIN(ACOS(2*SQRT(2/(27 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3))))))/3+((((1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2/(1/(2*SQRT(30/(75 + 23*SQRT(5) + 5*2^(2/3)*(5112 + 2285*SQRT(5) - 3*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 5*2^(2/3)*(5112 + 2285*SQRT(5) + 3*SQRT(7137 + 3192*SQRT(5)))^(1/3))))))*COS(ACOS(2*SQRT((3*(5 + SQRT(5)))/(5*(27 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))))))*(1/8*(1 + SQRT(5)))*60)*(((1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2/(1/(2*SQRT(6/(19 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3))))))*SIN(ACOS(2*SQRT(2/(27 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3))))))/3)/(SQRT(((1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2/(1/(2*SQRT(6/(19 + 7*SQRT(5) + (20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + (20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3))))))^2-(1/12*SQRT(126 + 42*SQRT(5) + 6*(20448 + 9140*SQRT(5) - 12*SQRT(7137 + 3192*SQRT(5)))^(1/3) + 6*(20448 + 9140*SQRT(5) + 12*SQRT(7137 + 3192*SQRT(5)))^(1/3)))^2)*2)^3
 14双[3,4,5,4] 
=100/11*SQRT(79 - 16*SQRT(5)) 
=100/33*(5 + 4*SQRT(5)) 
=SQRT(5/2 + SQRT(5)) 
=SQRT(5/41*(19 + 8*SQRT(5))) 
=1/11*(5 + 4*SQRT(5))*SQRT(3) 
=SQRT(5) 
=1/3*SQRT(5*(5+2*SQRT(5))) 
=1/22*SQRT(50 - 4*SQRT(5)) 
=SQRT(5/2 - SQRT(5)) 
=1/3*SQRT(5/2 + SQRT(5)) 
=1/11*SQRT(425 - 155*SQRT(5)) 
=1/3*SQRT(25 - 5*SQRT(5)) 
 
=360/PI()*ATAN(SQRT(10 + 4*SQRT(5))) 
=180/PI()*ASIN(SQRT(1/30*(5 - 2*SQRT(5)))) 
=180/PI()*ASIN(1/SQRT(10 + 4*SQRT(5))) 
=180/PI()*ASIN(1/SQRT(10)) 
=180/PI()*ASIN(SQRT(5/8+1/(4*SQRT(5)))) 
=180/PI()*ASIN(SQRT(1/4 + 1/(2*SQRT(5)))) 
=180/PI()*ASIN(3/4*SQRT(1 - 1/SQRT(5))) 
=1/11*(-3 + 2*SQRT(5)) 
=SQRT(5) - 2 
=1/3 
=(100/11*SQRT(79 - 16*SQRT(5)))/(1/11*SQRT(425 - 155*SQRT(5)))^2 
=1/3*SQRT(29530 + 13204*SQRT(5))
 15双[4,6,8] 
=72/7*SQRT(26 + 12*SQRT(2)) 
=144/7*(1 + SQRT(2)) 
=1/2*SQRT(6*(2 + SQRT(2))) 
=3*SQRT(2/97*(15 + 8*SQRT(2))) 
=3/7*(4 + SQRT(2)) 
=SQRT(6) 
=3/7*(2 + 3*SQRT(2)) 
=1/14*SQRT(6*(10 - SQRT(2))) 
=SQRT(3 - 3/SQRT(2)) 
=1/7*SQRT(51 + 69/SQRT(2)) 
=2/7*SQRT(30 - 3*SQRT(2)) 
=3/7*SQRT(12 + 6*SQRT(2)) 
=2/7*SQRT(60 + 6*SQRT(2)) 
=360/PI()*ASIN(2*SQRT(3/(14 - SQRT(2)))) 
=180/PI()*ASIN(1/SQRT(6*(2 + SQRT(2)))) 
=45/2 
=90 - 180/PI()*ACOS(1/2*SQRT(1/3 *(2 + SQRT(2)))) 
=180/PI()*ASIN(1/2*SQRT(1/6*(10 + SQRT(2)))) 
=180/PI()*ASIN(SQRT(2 + SQRT(2))/4) 
=180/PI()*ASIN(1/2*SQRT(1/6*(11 - 6*SQRT(2)))) 
=1/7*(3 - SQRT(2)) 
=SQRT(2) - 1 
=1/7*(3 + SQRT(2)) 
=6/7*SQRT(783+436*SQRT(2)) 
=SQRT(6582/49 + (4539*SQRT(2))/49)
 16双[5,6,6] 
=135/38*SQRT(922 - 210*SQRT(5)) 
=405/76*(9 + SQRT(5)) 
=3/4*(1 + SQRT(5)) 
=9/2*SQRT(1/109*(17 + 6*SQRT(5))) 
=9/38*SQRT(65 + 22*SQRT(5)) 
=1/2*(3*SQRT(3)) 
 
=3/76*(7 + 5*SQRT(5)) 
=3/4*(SQRT(5) - 1) 
 
=9/19*(2*SQRT(5) - 1) 
=3/2*(SQRT(5) - 1) 
 
=360/PI()* ATAN(3/2*(1 + SQRT(5))) 
=180/PI()*ASIN(1/3*SQRT(1/10*(5 + SQRT(5)))) 
=180/PI()*ASIN((-1 + SQRT(5))/(2*SQRT(3))) 
 
=180/PI()*ASIN(1/12*(9 - SQRT(5))) 
=180/PI()*ASIN(1/(SQRT(3)*(-1 + SQRT(5)))) 
 
=1/38*(9 + SQRT(5)) 
=1/2*(3 - SQRT(5)) 
 
=5/6*SQRT((421 + 63*SQRT(5))*2) 
=5/36*(41 + 25*SQRT(5))
 17双[3,10,10] 
=75/22*SQRT(2*(313 + 117*SQRT(5))) 
=125/44*(19 + 9*SQRT(5)) 
=1/4*(5 + 3*SQRT(5)) 
=5/122*SQRT(2501 + 1098*SQRT(5)) 
=5/22*SQRT(3)*(3 + 2*SQRT(5)) 
=1/2*SQRT(25 + 10*SQRT(5)) 
 
=1/44*(15-SQRT(5)) 
=1/4*(5 + SQRT(5)) 
 
=5/22*(7 + SQRT(5)) 
=1/2*(5 + SQRT(5)) 
 
=360/PI()* ATAN(1/2*(5 + 3*SQRT(5))) 
=180/PI()*ASIN(SQRT(1/30*(7 - 3*SQRT(5)))) 
=90-(180/PI()*ACOS(SQRT(1/10*(5-SQRT(5))))) 
 
=180/PI()*ASIN(11/(15 - SQRT(5))) 
=180/PI()*ASIN(1/2*SQRT(1/10*(5 - SQRT(5)))) 
 
=1/22*(5*SQRT(5) - 9) 
=1/2*(SQRT(5) - 1) 
 
=3/2*SQRT((173 - 9*SQRT(5))*2) 
=1/4*(19 + 13*SQRT(5))
 18双[4,6,10] 
=180/11*SQRT(179 - 24*SQRT(5)) 
=180/11*(5 + 4*SQRT(5)) 
=1/2*SQRT(30 + 12*SQRT(5)) 
=3/241*SQRT(46995 + 19280*SQRT(5)) 
=3/11*(5 + 4*SQRT(5)) 
=SQRT(15) 
=3*SQRT(1 + 2/SQRT(5)) 
=1/22*SQRT(6*(25 - 2*SQRT(5))) 
=1/2*SQRT(6*(5 - 2*SQRT(5))) 
=SQRT(3/2 + 3/SQRT(5)) 
=1/11*SQRT(1275 - 465*SQRT(5)) 
=3/11*SQRT(39 + 57/SQRT(5)) 
=2*SQRT(3 - 3/SQRT(5)) 
=360/PI()*ATAN(SQRT(6*(5 + 2*SQRT(5)))) 
=180/PI()*ASIN(SQRT(1/30*(5 - 2*SQRT(5)))) 
=-(180/PI()*ATAN(2 - SQRT(5))) 
=180/PI()*ATAN(1/SQRT(5)) 
=180/PI()*ASIN(SQRT(5/12 + 1/(6*SQRT(5)))) 
=180/PI()*ASIN(SQRT(1/8 + 1/(4*SQRT(5)))) 
=180/PI()*ASIN(1/4*SQRT(5 - (5*SQRT(5))/3)) 
=1/11*(-3+2*SQRT(5)) 
=SQRT(5) - 2 
=1/5*SQRT(5) 
=3/5*SQRT(10*(1257 + 541*SQRT(5))) 
=1/5*SQRT(88590 + 39612*SQRT(5))
     
 

2021年12月13日