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
| quantity | number | units |
|---|---|---|
| height of both poles | 30. | chi |
| distance between 2 poles | 6000 | chi |
| back pole offset distance | 762 | chi |
| forward pole offset distance | 738 | chi |
| textbook answer was 4 li and 55 steps | 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 Screenshots Section
References:
- 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
- http://kaleidoscope.cultural-china.com/en/135Kaleidoscope5304.html
- http://math2033.uark.edu/wiki/index.php/Liu_Hui
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"Draft Figures
1. SEA ISLAND HEIGHT – CONCEPT DIAGRAM
+====================================================================================+
| SEA ISLAND HEIGHT MEASUREMENT (Liu Hui, 3rd Century CE) |
+====================================================================================+
| |
| Classic Chinese Problem: |
| Measure the height of a distant island (or mountain) without climbing it. |
| |
| Method: Use two observation points on the shore with known distance between them|
| |
| Key Principle: Similar Triangles + Double Observation |
| |
| Observer 1 sees top of island at angle α |
| Observer 2 (closer) sees top at angle β |
| |
| Height h can be calculated using the two sight lines and base distance. |
+====================================================================================+
2. eTCL CALCULATOR – BLACK BOX STYLE (Tcl/Tk 8)
+====================================================================================+
| eTCL SEA ISLAND HEIGHT SLOT CALCULATOR (Tcl/Tk 8) |
+====================================================================================+
| [ STUDENT / HISTORIAN / MATH ENTHUSIAST ] |
| ↓ |
| TCL/Tk 8 GUI (Base Distance + Eye Height + Two Angles + Calculate) |
| ↓ |
| proc sea_island_height {d1 d2 eye_height angle1 angle2} { |
| # Using similar triangles from Liu Hui's method |
| set height [expr {$eye_height + ($d1 * $d2) / ($d1 - $d2)}] |
| return $height |
| } |
| ↓ |
| Output: Island Height | Distance to Island | Verification |
| ↓ |
| Canvas: Shoreline with two observers + sight lines to island top |
+====================================================================================+
3. SLOT CALCULATOR DEMO – VARIATION EXPLORER
+====================================================================================+
| eTCL SLOT CALCULATOR DEMO – SEA ISLAND MEASUREMENT SIMULATOR |
+====================================================================================+
| |
| [ Sea Island Observation Slot Machine ] |
| |
| Observer Position → [ Far | Medium | Close ] |
| Eye Height → [ Low | Average | Tall ] |
| Measurement Quality → [ Clear Day | Hazy | Rough Estimate ] |
| |
| proc sea_island_slot {iterations} { |
| set results [monte_carlo_sea_island $iterations] |
| return [list $results average_height error_range] |
| } |
| |
| Purpose: Explore how small errors in angle or distance affect final height |
+====================================================================================+
4. MEASUREMENT METHOD FLOW
+----------------------------------------------------------------------------------+
| LIU HUI'S SEA ISLAND METHOD – STEP BY STEP |
+----------------------------------------------------------------------------------+
| |
| 1. Stand at first position (far from island) |
| 2. Measure angle to top of island (using sighting rod) |
| 3. Move forward a known distance to second position |
| 4. Measure new angle to top of island |
| 5. Use similar triangles to calculate height |
| |
| Ancient Advantage: No need to cross water or climb the island |
| Modern View: Early use of trigonometry and similar triangles |
+----------------------------------------------------------------------------------+
5. OVERVIEW DIAGRAM – HISTORICAL TO eTCL TOOL
+====================================================================================+
| FROM ANCIENT CHINA TO eTCL CALCULATOR (Sea Island Problem) |
+====================================================================================+
| |
| 3rd Century CE Liu Hui writes "Sea Island Mathematical Manual" |
| ↓ |
| Classic Problem Measure distant island height using geometry |
| ↓ |
| Mathematical Tool Similar triangles + double observation |
| ↓ |
| eTCL Calculator Interactive modern implementation in Tcl/Tk 8 |
| |
| Features: |
| • Input base distance and two observation angles |
| • Calculate island height |
| • Slot-machine style simulation of measurement errors |
| • Canvas visualization of observers and sight lines |
+====================================================================================+
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