tips-slideruleの変更点

• 追加された行はこのように表示されます。
• 削除された行はこのように表示されます。

!計算尺

https://ja.wikipedia.org/wiki/%E8%A8%88%E7%AE%97%E5%B0%BA

*https://www.sliderulemuseum.com/SR_Scales.htm
*https://staff.aist.go.jp/tominaga-daisuke/sliderule/rectilinear/index.html
*http://www.pi-sliderule.net/
*https://yoshi-g.com/sliderule027#27-5

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,名前,単位,
,D尺,標準(Log)
,C尺,標準(Log)
,A尺,D尺の1/2目盛
,B尺,C尺の1/2目盛
,K尺,C尺の1/3目盛
,CI尺,C尺の逆目盛
,DF尺,C尺を10ずらす
,DF尺,C尺をπずらす
,S/SI尺,SIN
,T1/T2, tan (6度から~84度まで)


! 計算式
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 R : 幅(尺の長さ)
 # : スケール(目盛の値）

 最初の列にはスケール名があります。 
 2番目の列は、そのスケールに使用される式です。 
 単純化は、読者の練習問題として残されています。 
 使用される規則では、
    Rはルールの長さを示し、
    ＃は位置が計算されているスケール上の数値を示します。 
 最後の列には、特定のスケールに関するメモが含まれています。

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,Scale 	,Formula 	,Comments
,A/B 	,(R/2)*log(#) 	,Used to calculate squares and square roots with the D scale. used to calculate the sine of an angle with the S scale on a Mannheim slide rule
,C/D 	,R*log(#) 	,Used in multiplication and division. and also used with many other scales in various operations
,CF/DF 	,(log# - logPI)*R if # less than R then add R 	,The folded scales used as a shortcut in multiplication and division
,CI 	,abs[R*log(10/#)-R] 	,The inverse of the C scale. often used as a shortcut in division
,CIF 	,abs[R*(log(1/#) - log(1/PI))] if #<(10/PI) abs[R*(log(1/#) - log(1/PI)) - 25] if #>(10/PI)	,The inverse of the CF scale
,K 	,(R/3)*log(#) 	,Used with the D scale to find the cube or cube root of a number
,L 	,#*R 	,Used with the D scale to calculate the logarithm log10(#) of a number
,LL0 	,log(ln(#))*R + 3*R 	,Contains all numbers greater than or equal to 1.001 and less than or equal to 1.01; these scales (LL0-LL3) are used for logarithms. roots. and powers
,LL1 	,log(ln(#))*R + 2*R 	,Contains all numbers greater than or equal to 1.01 and less than or equal to 1.105
,LL2 	,log(ln(#))*R + R 	,Contains all numbers greater than or equal to 1.105 and less than or equal to e
,LL3 	,log(ln(#))*R 	,This contains all numbers greater than or equal to e
,LL/0 	,log(ln(1/#))*R + 3*R 	,This contains all numbers greater than or equal to e-0.01 and less than or equal to e-0.001
,LL/1 	,log(ln(1/#))*R + 2*R 	,This contains all numbers greater than or equal to e-0.1 and less than or equal to e-0.01
,LL/2 	,log(ln(1/#))*R + R 	,This contains all numbers greater than or equal to e-1.0 and less than or equal to e-0.1
,LL/3 	,log(ln(1/#))*R 	,This contains all numbers greater than or equal to e-10.0 and less than or equal to e-1.0
,R1 	,log(#)*2*R 	,Used with the D scale to find squares and square roots; those numbers greater than about 3.13 are on the R2 scale
,R2 	,[log(#)*2*R] - 25 	,Used with the D scale to find squares and square roots; those numbers greater than about 3.13 are on the R2 scale
,Smannheim 	,(R/2)*[2 + log(sin(#))] 	,Used with the A scale to calculate the sine of a number. or the tangent of a number less than 5.7 degrees
,S/T 	,[log(100*sin(#))]*R 	,Used with the C scale to calculate the sine or the tangent of a number less than 5.7 degrees
,S 	,[log(10*sin(#))]*R 	,Used with the C scale to calculate the sine of a number greater than 5.7 degrees
,T 	,R*log[10*tan(#) 	,Used with the D scale to calculate the tangent of angles greater than 5.7 degrees 

https://www.sliderulemuseum.com/SR_Scales.htm

http://www.pi-sliderule.net/sliderule/make/program/datafile.html
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! y=log(sin(x)) (0<x<π)
 y=log(sin(x)) (0<x<π)
 y'=cos(x)/sin(x)=cot(x)=1/tan(x)
 x→+0でy→-∞
 x→π-0でy→-∞
 
 0<x<π/2でy'>0なので単調増加
 π/2<x<πでy'<0なので単調減少
 x=π/2でy'=0で極大となる。
 x=π/2で極大値（最大値）y=0
 
 増減表（等幅フォントで表示させ見てください）
 x | 0 ……π/2 …… π
 y'|+∞　＋　 0　　− -∞
 y |-∞ ↑ 極大0　↓ -∞
 
 グラフを描く補助として
 直線x=π/2に対してグラフが対称
 漸近線x=0(y軸)、直線x=π
 x=π/6および5π/6でy=log(1/2)=-log2=-0.6931…
 x=π/4および3π/4でy=log(1/√2)=-(log2)/2=-0.3465…
 x=π/3および2π/3でy=log(√3/2)=log(3)/2-log(2)=-0.1438…
 の情報を使うと良いでしょう。
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!作り方
http://osinko.hatenablog.jp/entry/2018/02/15/230704

 #!/usr/bin/env python3
 # -*- coding: utf-8 -*-
 """
 Created on Fri Mar  5 23:32:41 2021
 
 @author: green
 """
 import math
 
 def header() :
    print("\\documentclass{jsarticle} " )
    print("\\usepackage[dvipdfmx]{graphicx}")
    print("\\usepackage{tikz}")
    print("\\usetikzlibrary{intersections,calc,arrows.meta}")
    print("\\begin{document}")
    print("\\begin{tikzpicture}")
    print( "" )
 
 def footer() :
    print("\\end{tikzpicture}")
    print("\\end{document}")
    print("")
 
 D=10.0
 # C / D Rail 
 
 header()
 
 for x in range(10,101):
    x1 = (x/D)
    x2 = math.log10( x1 ) * 10.0
    # print ('\\draw (0,0) rectangle(','{:.4g}'.format(x2),',2);')
    print ('\\draw (', '{:.4g}'.format(x2), ',0 ) -- (', '{:.4g}'.format(x2),',2);')
    if ( (x % 5 ) == 0 ) :
        print ('\\draw (', '{:.4g}'.format(x2), ',0 ) node {', x1, '} ;' )
 
 footer()


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! Tips
https://www.sliderulemuseum.com/

http://49.212.24.146/~take/TakeWiki/index.php?Arduino%E5%8B%89%E5%BC%B7%E4%BC%9A%2FJ2-%E8%A8%88%E7%AE%97%E5%B0%BA%E3%81%AE%E4%BD%BF%E3%81%84%E6%96%B9#e5b24e43
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! Java_Script
http://www.pi-sliderule.net/program/sliderule/java/sliderule.html