#pretty print from autoindent and ased editor
    # ellipse properties
    # 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 {{} {semimajor length a:} {semiminor length b:} {ellipsoid length c :} {area:} {length betw. foci:}} 


    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 Ellipse Properties.
        from TCL WIKI,
        written on eTCL "
        tk_messageBox -title "About" -message $msg
    }
    proc pi {} {expr acos(-1)}
    proc ellipse5 { xx1   } {
        global side1 side2 side3
        global side4 side5 side6 side7
        set ss side1
        set tt $side2
        set cc  [ expr { $side1*$side1- $side2*$side2  } ]
        set cc  [ expr { sqrt($cc)  } ]
        set term1 [ expr { ($side1*$side1+ $side2*$side2) /2.    } ]
        set perimeterx [ expr { 2.*[pi]*sqrt($term1)} ]
        set area1 [ expr { 1.*[pi]*$side1*$side2  } ]
        set xxx [ expr { $side4*[pi]/180.  } ]
        set side4 $area1
        set side5 [expr { 2.* $cc } ]
        set side7  [ expr { 1.*$cc/$side1 } ]
        set rr  [ expr { $cc/$side1 } ]
        #set side7  [ expr { ((2.*[pi] *$side1*$side2)*(1.*$side2/$side1+($side1/$cc)*asin($rr)))} ]
        set side6 $perimeterx
        return $side7
    }
    proc calculate {     } {
        global answer2 
        global side1 side2 side3 side4 side5 side6 side7
        set answer2 5
        set answer2  [ ellipse5  $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 {} {
        global side1 side2 side3 side4 side5 side6 side7
        console show;
        puts " "
        set gg  [ expr { $side1*$side1- $side2*$side2  } ]
        set gg  [ expr { sqrt($gg)  } ]
        set cx  [ expr { $side1*$side1- $side2*$side2  } ]
        set cx  [ expr { sqrt($cx)  } ]
        set foci [ expr { 2.*$gg  } ]
        set term1 [ expr { ($side1*$side1+ $side2*$side2) /2.    } ]
        set perimeterx [ expr { 2.*[pi]*sqrt($term1)} ]
        set area1 [ expr { 1.*[pi]*$side1*$side2  } ]
        set  eccentricity  [ expr { 1.*$cx/$side1 } ]
        set pp 1.6075
        set aa  [ expr { pow($side1,$pp) } ]
        set bb  [ expr { pow($side2,$pp) } ]
        set cc  [ expr { pow($side3,$pp) } ]
        set term7  [ expr { ($aa*$bb+$aa*$cc+$bb*$cc)/3.} ]
        set term8  [ expr { 1./1.6075 } ]
        set term7  [ expr { pow($term7,$term8) } ]
        set ellipsoidarea [ expr { 1.*4.*[pi]*$term7  } ]
        set ellipsoidvolume [ expr { 1.*(4./3.)*[pi]*$side1*$side2*$side3 } ]
        puts " length between foci    $foci"
        puts " perimeter   $perimeterx"
        puts " area1   $area1"
        puts "eccentricity   $eccentricity    "
        puts "ellipsoid surface area   $ellipsoidarea   "
        puts "ellipsoid volume   $ellipsoidvolume "
    }
    frame .buttons -bg aquamarine4
    ::ttk::button .calculator -text "Solve" -command { calculate   }
    ::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 50. 10. 49. 1570.8  98. 226.5 0.97}
    ::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 200. 100. 173. 6.28E4  346. 993. 0.86}
    ::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 500. 250. 433. 3.9E5  866. 2483.  0.86 }
    ::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 . "Ellipse Properties"

1. ELLIPSE PROPERTIES – CONCEPT DIAGRAM

+====================================================================================+
| ELLIPSE PROPERTIES – BASIC GEOMETRY                                               |
+====================================================================================+
|                                                                                   |
|   An ellipse is defined by two focal points (F1 and F2).                          |
|                                                                                   |
|   Key Properties:                                                                 |
|   • Major Axis (2a)   = longest diameter                                          |
|   • Minor Axis (2b)   = shortest diameter                                         |
|   • Distance between foci = 2c                                                    |
|   • Relationship:     a² = b² + c²                                                |
|                                                                                   |
|   Eccentricity (e) = c / a   (0 = circle, closer to 1 = very elongated)          |
|                                                                                   |
|   Sum of distances from any point on ellipse to both foci is constant (2a).      |
+====================================================================================+

2. eTCL CALCULATOR – BLACK BOX STYLE (Tcl/Tk 8)

+====================================================================================+
| eTCL ELLIPSE PROPERTIES CALCULATOR (Tcl/Tk 8)                                    |
+====================================================================================+
| [ STUDENT / ENGINEER / MATH ENTHUSIAST ]                                          |
|         ↓                                                                         |
|   TCL/Tk 8 GUI (Semi-Major a + Semi-Minor b + Calculate)                         |
|         ↓                                                                         |
|   proc ellipse_properties {a b} {                                                 |
|       set c [expr {sqrt($a*$a - $b*$b)}]                                          |
|       set eccentricity [expr {$c / $a}]                                           |
|       set perimeter_approx [ellipse_perimeter $a $b]                              |
|       return [list $c $eccentricity $perimeter_approx]                            |
|   }                                                                               |
|         ↓                                                                         |
|   Output: Focal Distance (2c) | Eccentricity | Approx. Perimeter | Area           |
|         ↓                                                                         |
|   Canvas: Ellipse drawing with major/minor axes and foci marked                   |
+====================================================================================+

3. eTCL SLOT CALCULATOR DEMO – VARIATION SIMULATOR

+====================================================================================+
| eTCL SLOT CALCULATOR DEMO – ELLIPSE PARAMETER EXPLORER                          |
+====================================================================================+
|                                                                                   |
|   [ Ellipse Properties Slot Machine ]                                             |
|                                                                                   |
|   Semi-Major Axis (a)  →  [ Small | Medium | Large ]                              |
|   Eccentricity (e)     →  [ Near Circle | Moderate | Highly Elongated ]           |
|   Calculation Mode     →  [ Exact | Approximate ]                                 |
|                                                                                   |
|   proc ellipse_slot_sim {iterations} {                                            |
|       set results [monte_carlo_ellipse $iterations]                               |
|       return [list $results average_eccentricity variation]                       |
|   }                                                                               |
|                                                                                   |
|   Purpose: Explore how changes in a and b affect eccentricity and perimeter      |
+====================================================================================+

4. KEY FORMULAS FLOW

+----------------------------------------------------------------------------------+
| ELLIPSE KEY FORMULAS                                                           |
+----------------------------------------------------------------------------------+
|                                                                                 |
|   • Semi-major axis      a                                                      |
|   • Semi-minor axis      b                                                      |
|   • Linear eccentricity  c = √(a² - b
|   • Eccentricity         e = c / a                                              |
|   • Area                 π × a × b                                              |
|   • Approximate Perimeter  ≈ 2π √((a² + b
|                                                                                 |
|   eTCL Demo allows easy experimentation with these relationships.               |
+----------------------------------------------------------------------------------+

5. OVERVIEW DIAGRAM – EDUCATIONAL BRIDGE

+====================================================================================+
| ELLIPSE PROPERTIES – FROM GEOMETRY TO eTCL CALCULATOR                           |
+====================================================================================+
|                                                                                   |
|   Classic Geometry           →         Interactive Analysis                       |
|                                                                                   |
|   Definition by Foci         ↔         Input a and b                              |
|   Eccentricity & Axes        ↔         Real-time Calculations                     |
|   Applications (Orbits, etc) ↔         Slot-machine Parameter Explorer            |
|                                                                                   |
|   eTCL Features:                                                                  |
|   • Compute c, e, area, and perimeter                                             |
|   • Visual ellipse with marked foci                                               |
|   • Slot demo for exploring parameter space                                       |
|   • Clear numerical output for learning                                           |
|                                                                                   |
|   Goal: Make ellipse mathematics intuitive and hands-on                          |
+====================================================================================+