Sea Island Height Slot Calculator Example

Chinese Sea Island Height Slot Calculator Example

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Introduction


goldHere are some TCL calculations for the Sea Island Height. The Sea Island Mathematics Manual was a Chinese math book by Liu Hui. (263 CE) This book is of historical interest in algebra and geometry. The Chinese mathematician Liu Hui used two sticks or poles to measure the height of a flag or standard on an elevation of a Sea Island, from the aspect lengths and the horizontal distances or baselines from the sticks. In early astronomy, sticks of one cubit length or other lengths were used to measure sun or lunar angles to the horizontal and were called gnomons by the ancient Greeks. The sticks or gnomons were used also by Hindu, Chinese, and Islamic astronomers to measure star angles above the horizon. In the commentary of Liu Hui, the poles are believed equal length. The original math problem used Chinese units of chi, but units cancel out in the calculator and any consistent units might be used like feet, cubits, or meters. The Chinese math problem on Sea Island Height. would make a good science project for middle school, I think. Question for middle school pupils, what should be the lengths of poles, baselines, and tape measures necessary to accurately measure the height of the elevation on sea island? There is no right or wrong answer to this question, but understanding the principles of geometry, one does have to swim to the Sea Island or climb the elevation of Sea Island and drop a tape measure from a cliff.


Testcase

quantitynumberunits
height of both poles 30.chi
distance between 2 poles 6000chi
back pole offset distance 762 chi
forward pole offset distance 738 chi
textbook answer was 4 li and 55 steps 7530chi
  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   

Screenshots Section

Chinese Sea Island Height Slot Calculator Example diagram.png


References:


Appendix Code

appendix TCL programs and scripts

Pretty Print Version

        # Pretty print version from autoindent and 
        # ased editor
        #  Liu Hui on Sea Island Height
        # written on Windows 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 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 answer2  
            global side1 side2 side3 side4 side5 side6 side7
            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 " "
        }
        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
        wm title . "Sea Island Height"

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