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gold Here is some eTCL starter code for calculating the Sumerian surveyor formula for a rectangle and 4 sided figure. Most of the testcases involve replicas or models, using assumptions and rules of thumb.
The Sumerian surveyor formula is ( (L1+L2)/2)* (W1+W2)/2) or (L1+L2 +W1+W2)/4 for a rectangle and 4 sided figure. The first testcase was all sides equal 1 meter. For the formula (L1+L2 +W1+W2)/4, substituting, area equals ( 1+1 +1+1)/4, results in 1 square meter. The perimeter is (L1+L2 +W1+W2), substituting, perimeter = ( 1+1 +1+1), 4 meters.
The second testcase was L1=2,L2=2,W1=4,and W2=4. For the formula (L1+L2 +W1+W2)/4, substituting, area equals ( 2+2 +4+4)/4, 12/4, 3 square meters. The perimeter was 2+2 +4+4, 12 meters.
The third testcase was L1=3,L2=3,W1=5,and W2=5. For the formula (L1+L2 +W1+W2)/4, substituting, area equals ( 3+3 +5+5)/4, 16/4, 4 square meters. The perimeter was 3+3 +5+5, 16 meters.
# following statements can be pasted into eTCL console set testcase_1 [ eval expr ( 1+1 +1+1)/4 ] # 1 square meters set testcase_2 [ eval expr ( 2+2 +4+4)/4 ] # 3 square meters set testcase_3 [ eval expr ( 3+3 +5+5)/4 ] # 4 square meters set testcase_1_perimeter [ eval expr ( 1+1 +1+1) ] # 4 square meters set testcase_2_perimeter [ eval expr ( 2+2 +4+4) ] # 12 square meters set testcase_3_perimeter [ eval expr ( 3+3 +5+5) ] # 16 square meters
set volume_bowl [eval expr (5./60.)*(5./60.)*(4.*60.+48.) ] # 2 sila in Babylonian calculation set conventional_vol? [eval expr 2.*((.5*.5/(3.*4.))*.09) ] # 0.00375 liters per m*m set conv_circle [eval expr 1.5*1.5*(1/12.) ] # text answer 11/60+15/3600, decimal 0.1875 set strange_formula [eval expr $area*$area*(4.*60.+48.)] # possible sila per kus*kus factor 45 carrying baskets (45*25=1125kg) per 1us (360 meters) per workday 1_15 talents dirt (1_15=1/60+15/3600=37.5 kg) for 1 dana (1 dana=beru=10.8 km) per workday 6 bricks (b=8.5 minas>>6*8.5*0.4977kg,25.3827) for beru 10.8 kilometers per day large basket (dusu) =2_13_20 volume shekel=1/27 volume shekel=13.33 kilograms=11.1 liters small basket = 1_4 volume shekel=1/48 volume shekel=7.5 kilograms=6.25 liters 1 volume shekel = 300 liters = 12 talents =12*30=360 kilograms 1 talent =12 volume shekels
# following statements can be pasted successively into eTCL console proc pi {} {expr acos(-1)} set inner_cylinder_a=b*(c*c/d*d)_ [* 0.1790[/ [* 1. 1. ] [* 4. 4. ] ]] # 0.0111 set hollow_cylinder_a=b*(c*c/d*d)_ [* 0.1790[- 1. [/ [* 1. 1. ] [* 4. 4. ]] ]] # 0.1678 set inner_cylinder_ [ eval expr [pi]*.0597*.0597*1 ] # 0.0111 set outer_cylinder_ [ eval expr [pi]*.2387*.2387*1 ] # 0.1790 set overshoot_error [eval expr (2.5424/2.40909)-1. ] # 0.05533624729669717 set error_log_coefficient [eval expr (1.-3.125/[pi])*100.] # undershoot 0.52 percent error set error_3_for_PI_coefficient [eval expr (1.-3.0/[pi])*100.] # undershoot 4.5 percent error set log_coefficient_reciprocal [ eval expr (1./4.*[pi]) ] # 0.7853981633974483 set imla_reciprocal_PI_coefficient [ eval expr (1./6.*[pi]) ] # 0.5235987755982988
In planning any software, it is advisable to gather a number of testcases to check the results of the program. The math for the testcases can be checked by pasting statements in the TCL console. Aside from the TCL calculator display, when one presses the report button on the calculator, one will have console show access to the capacity functions (subroutines).
table 1 | printed in | tcl wiki format |
---|---|---|
quantity | value | comment, if any |
testcase number: | 1 | |
1.0 : | length L1 meters meters | |
1.0 : | length L2 meters | |
1.0 : | width W1 meters | |
1.0 : | width W2 meters | |
1.0 : | average length meters | |
1.0 : | average width meters | |
4.0 : | perimeter meters | |
1.0 : | surface area square meters |
table 2 | printed in | tcl wiki format |
---|---|---|
quantity | value | comment, if any |
testcase number: | 2 | |
2.0 : | length L1 meters meters | |
2.0 : | length L2 meters | |
4.0 : | width W1 meters | |
4.0 : | width W2 meters | |
2.0 : | average length meters | |
4.0 : | average width meters | |
12.0 : | perimeter meters | |
3.0 : | surface area square meters |
table 3 | printed in | tcl wiki format |
---|---|---|
quantity | value | comment, if any |
testcase number: | 3 | |
3.0 : | length L1 meters meters | |
3.0 : | length L2 meters | |
5.0 : | width W1 meters | |
5.0 : | width W2 meters | |
3.0 : | average length meters | |
5.0 : | average width meters | |
16.0 : | perimeter meters | |
4.0 : | surface area square meters |
# pretty print from autoindent and ased editor # Sumerian Surveyor Formula calculator # written on Windows XP on eTCL # working under TCL version 8.5.6 and eTCL 1.0.1 # gold on TCL WIKI, 15may2016 package require Tk namespace path {::tcl::mathop ::tcl::mathfunc} frame .frame -relief flat -bg aquamarine4 pack .frame -side top -fill y -anchor center set names {{} {length L1 meters :} } lappend names {length L2 meters :} lappend names {width W1 meters: } lappend names {width W2 meters :} lappend names {answers: average length meters:} lappend names {average width meters: } lappend names {surface area square meters: } lappend names {surface area square meters :} foreach i {1 2 3 4 5 6 7 8} { 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 Sumerian Surveyor from TCL WIKI, written on eTCL " tk_messageBox -title "About" -message $msg } proc pi {} {expr acos(-1)} proc calculate { } { global answer2 global side1 side2 side3 side4 side5 global side6 side7 side8 global testcase_number global average_length average_width total_surface_area incr testcase_number set side1 [* $side1 1. ] set side2 [* $side2 1. ] set side3 [* $side3 1. ] set side4 [* $side4 1. ] set side5 [* $side5 1. ] set side6 [* $side6 1. ] set side7 [* $side7 1. ] set side8 [* $side8 1. ] set length1 $side1 set length2 $side2 set width1 $side3 set width2 $side4 set average_length [/ [+ $length1 $length2 ] 2. ] set average_width [/ [+ $width1 $width2 ] 2. ] set total_surface_area [/ [+ $length1 $length2 $width1 $width2 ] 4. ] set perimeter [+ $length1 $length2 $width1 $width2 ] set side5 $average_length set side6 $average_width set side7 $perimeter set side8 $total_surface_area } proc fillup {aa bb cc dd ee ff gg hh} { .frame.entry1 insert 0 "$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" .frame.entry8 insert 0 "$hh" } proc clearx {} { foreach i {1 2 3 4 5 6 7 8 } { .frame.entry$i delete 0 end } } proc reportx {} { global side1 side2 side3 side4 side5 global side6 side7 side8 global testcase_number global average_length average_width total_surface_area console show; puts "%|table $testcase_number|printed in| tcl wiki format|% " puts "&| quantity| value| comment, if any|& " puts "&| testcase number:|$testcase_number | |&" puts "&| $side1 :|length L1 meters meters | |&" puts "&| $side2 :|length L2 meters | |& " puts "&| $side3 :|width W1 meters| |& " puts "&| $side4 :|width W2 meters| |&" puts "&| $side5 :|average length meters | |&" puts "&| $side6 :|average width meters | |&" puts "&| $side7 :|perimeter meters| |&" puts "&| $side8 :|surface area square meters| |&" } frame .buttons -bg aquamarine4 ::ttk::button .calculator -text "Solve" -command { calculate } ::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0} ::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 2. 2. 4.0 4.0 4.0 2.0 3.0 3.0 } ::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 3. 3. 5.0 5.0 4.0 2.0 4.0 4.0 } ::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} . calculator configure -background aquamarine4 -highlightcolor brown -relief raised -border 30 wm title . "Sumerian Surveyor Formula Calculator"
For the push buttons, the recommended procedure is push testcase and fill frame, change first three entries etc, push solve, and then push report. Report allows copy and paste from console.
For testcases in a computer session, the eTCL calculator increments a new testcase number internally, eg. TC(1), TC(2) , TC(3) , TC(N). The testcase number is internal to the calculator and will not be printed until the report button is pushed for the current result numbers. The current result numbers will be cleared on the next solve button. The command { calculate; reportx } or { calculate ; reportx; clearx } can be added or changed to report automatically. Another wrinkle would be to print out the current text, delimiters, and numbers in a TCL wiki style table as
puts " %| testcase $testcase_number | value| units |comment |%" puts " &| volume| $volume| cubic meters |based on length $side1 and width $side2 |&"
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