GraphingCalculator 4; Window 84 103 712 1074; FontSizes 18; PaneDivider 459; BackgroundType 0; StackPanes 1; Slider -2 2; SliderControlValue 50; SliderOneDirection 1; 2D.BottomLeft -2.28125 -2.046875; Text "================================ Matemagi® by Ambjörn Naeve ©Dialectica ================================ The point of origin O :"; Color 17; Radius 0.1168387276785714; Expr O=vector(0,0); Color 8; Radius 0.1138741629464286; Expr O; Text "The point A :"; Color 17; Radius 0.1099330357142857; Expr A=vector(a,0); Color 3; Radius 0.08733258928571429; Expr A; Color 17; MathPaneSlider 200; Expr a=slider([0,4]); Text "The point B :"; Color 17; Radius 0.09636579241071429; Expr B=vector(0,b); Color 2; Radius 0.12890625; Expr B; Color 17; MathPaneSlider 100; Expr b=slider([0,4]); Text "The vector OA:"; Color 3; Radius 0.3044704861111111; Expr O,A; Text "The vector -OB is equal to the vector BO:"; Color 2; Radius 0.2501736111111111; Expr B,O; Color 2; Radius 0.2807291666666666; Expr O,-B; Text "Hence the two-blade -OB wedge OA is equal to the two-blade BO wedge OA :"; Color 5; Expr 0C :"; Color 17; Radius 0.0830078125; Expr C=vector(a/2+s,2*b); Radius 0.1285226004464286; Expr C; Text "The vector CO :"; Radius 0.1197048611111111; Expr C,O; Text "The vector AC :"; Color 4; Radius 0.2292100694444444; Expr A,C; Text "Sliding the purple point C parallel to the x-axis preserves the magnitude of the (yellow) triangular area, which is equal to the (light blue) rectangular area."; Color 6; Expr 0 //////////// ANALYSIS: The light-blue two-blade BO wedge OA and the yellow two-blade OA, AC, CO are two equivalent representations of the same two-blade since they have the same direction (= they lie in the same plane), the same orientation (= counterclockwise) and the same magnitude (= they enclose the same area) //////////// An auxiliary line to help determine the marking of the triangular area:"; Color 17; Expr y=1/(a/2-s)*[-(2*b*x)+2*a*b]; Text " ";