This page is under development. Comments are
welcome, but please load any comments
in the comments section
at the middle of the page. Thanks,[gold] [gold] Here is an eTCL script on
to estimate Sea Island Height.
Sea Island was a Chinese math book by
Hui. In planning any software,
need a good testcase.
height of both poles was 30 chi
distance between 2 poles was 6000 chi
back pole offset distance was 762 chi
forward pole offset distance was 738 chi.
textbook answer was 4 li and 55 steps
or 7530 chi.
checking the math by hand calculator:
((pole height * distance between 2 poles)/
(back pole offset distance - forward pole offset distance)) +pole height
((30 chi * 6000 chi)/(762 chi - 738 chi)) +30 chi
equals 7530 chi
reverse
on
***Screenshots Section***
'''Comments Section'''
Please place any comments here, Thanks. http://wwmat.mat.fc.ul.pt/~jnsilva/Sherlock/china2.pdf
Liu Hui
http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Liu_Hui.html
http://www.hardsumsclub.co.uk/quiz/liu.pdf
http://en.wikipedia.org/wiki/The_Sea_Island_Mathematical_Manual
http://math.ucsd.edu/programs/undergraduate/history_of_math_resource/history_papers/math_history_01.pdf
kaleidoscope.cultural-china.com/en/135Kaleidoscope5304.html
http://math2033.uark.edu/wiki/index.php/Liu_Hui
****Appendix Code****
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# Liu Hui on Sea Island Height
# written on Windowws XP on eTCL
# working under TCL version 8.5.6 and eTCL 1.0.1
# gold on TCL WIKI , 18aug2010
frame .frame -relief flat -bg aquamarine4
pack .frame -side top -fill y -anchor center
set names {{} {both poles height:} {distance tween 2 poles:} {back poll offset :} {front pole offset:} {height:} {answer height :} {height/1000:}}
foreach i {1 2 3 4 5 6 7} {
label .frame.label$i -text [lindex $names $i] -anchor e
entry .frame.entry$i -width 35 -textvariable side$i
grid .frame.label$i .frame.entry$i -sticky ew -pady 2 -padx 1
}
proc about {} {
set msg "Calculator for Sea Island Height.
from TCL WIKI,
written on eTCL "
tk_messageBox -title "About" -message $msg
}
proc pi {} {expr acos(-1)}
proc interlinear { xx1 yy1 xx3 yy3 xx2 } {
return [expr { ((($xx2-$xx1)*($yy3-$yy1))/($xx3-$xx1))+ $yy1 } ] ;}
proc pol { xx1 yy1 xx3 yy3 xx2 } {
return [expr { ((($xx2-$xx1)*($yy3-$yy1))/($xx3-$xx1))+ $yy1 } ] ;}
proc errorx {aa bb} {expr { $aa > $bb ? (($aa*1.)/$bb -1.)*100. : (($bb*1.)/$aa -1.)*100.}}
proc height5 { aa bb cc } {
set bb [ expr { $cc*[pi]/180. } ]
set cc [ expr { $cc*[pi]/180. } ]
set dd [ expr { 1.*$aa*tan($bb)*tan($cc)/( tan($cc)-tan($bb))} ]
return $dd
}
proc seaisland5 { xx1 } {
global side1 side2 side3
global side4 side5 side6 side7
set ss side1
set tt $side2
set xxx [ expr { $side4*[pi]/180. } ]
set side5 [ expr { ((1.*$side1*$side2)/(1.*$side3-1.*$side4))+$side1} ]
set side6 [ expr { ((1.*$side1*$side2)/(1.*$side3-1.*$side4))+$side1} ]
set side7 [ expr { ((1.*$side1*$side2)/(1.*$side3-1.*$side4))+$side1} ]
set side7 [ expr { $side7*.001} ]
return $side7
}
proc calculate { } {
global colorwarning
global colorback
global answer2 answer3
global side1 side2 side3 side4 side5 side6 side7
set answer2 5
set answer2 [ seaisland5 $side1 ]
set side7 $answer2
}
proc fillup {aa bb cc dd ee ff gg} {
.frame.entry1 insert 0 "$aa"
.frame.entry2 insert 0 "$bb"
.frame.entry3 insert 0 "$cc"
.frame.entry4 insert 0 "$dd"
.frame.entry5 insert 0 "$ee"
.frame.entry6 insert 0 "$ff "
.frame.entry7 insert 0 "$gg "
}
proc clearx {} {
foreach i {1 2 3 4 5 6 7} {
.frame.entry$i delete 0 end
}
}
proc reportx {} {
console show;
puts "
The interpolation function takes
two know points on a line and
solves for an intermediate point.
The points are xx1,yy1 xx2,yy2 and xx3,?yy3?
The input order of the five items
is xx1 yy1 xx2 yy2 xx3
and solving for ?yy3?.
The interpolation function loaded as
proc pol. User should be able to write
pol 50. 1000. 200. 1200. 150.
and save answer (1133.3) on console."
}
frame .buttons -bg aquamarine4
::ttk::button .calculator -text "Solve" -command { calculate }
::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 30. 6000. 762. 738. 7530. 7530. 7530.}
::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 30. 6000. 762. 738. 7530. 7530. 7530.}
::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 30. 6000. 762. 738. 7530. 7530. 7530. }
::ttk::button .clearallx -text clear -command {clearx }
::ttk::button .about -text about -command about
::ttk::button .cons -text report -command { reportx }
::ttk::button .exit -text exit -command {exit}
pack .calculator -in .buttons -side top -padx 10 -pady 5
pack .clearallx .cons .about .exit .test4 .test3 .test2 -side bottom -in .buttons
grid .frame .buttons -sticky ns -pady {0 10}
. configure -background aquamarine4 -highlightcolor brown -relief raised -border 30
bind . <Motion> {wm title . "Sea Island Height"}
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