GraphingCalculator 4;
Window 52 4 970 1310;
PaneDivider 447;
FontSizes 14;
BackgroundType 0;
BackgroundColor 255 255 255;
StackPanes 1;
2D.Scale 0.1 0.1 5 5;
2D.BottomLeft -1.65 -1.81875;
2D.Axes 0;
2D.GraphPaper 0;
Text "<size=16>Triangles

<size=14>Version 1.0 12-11-16

Specify two sides and the included angle, or draggable vertices.  Pythagorean Theorem.

To do:
(i) Illustrate proof of Pythagorean Theorem.


Length of the two sides and the included angle:";
Color 2;
MathPaneSlider 145;
Expr a=slider([0,2]);
Color 3;
MathPaneSlider 71;
Expr b=slider([0,2]);
Color 4;
MathPaneSlider 71;
Expr p=slider([0,1]);
Text "<size=16>Angle p in degrees, radians:";
Color 3;
Expr 180*p;
Color 4;
Expr pi*p;
Text "<size=16>Draws line segment joining A to B:";
Expr function(L,A,B)=A*t+B*[1-t];
Color 5;
Expr O=vector(0,0),I=vector(1,0),J=vector(0,1),X=vector(x,y);
Text "<size=16>Triangle with vertices at origin, P1, P2:";
Color 6;
Expr P_1=a*I,P_2=vector(b*cos([pi*p]),b*sin([pi*p]));
Color 17;
Grain 1;
Expr function(L,O,P_1);
Color 17;
Expr function(L,O,P_2);
Color 17;
Expr function(L,P_1,P_2);
Color 7;
Expr R=slider([0,0.25]);
Color 17;
Expr 0<theta<pi*p,r<R;
Text "<size=16>Right triangle with sides a,b:";
Color 3;
Expr function(L,O,a*I);
Color 3;
Expr function(L,O,b*J);
Color 3;
Expr function(L,a*I,b*J);
Text "<size=16>Pythagorean theorem";
Color 4;
Expr N=80;
Color 2;
Expr c=sqrt(a^2+b^2);
Text "<size=16>The squares on the sides...";
Color 4;
Expr [x-a/2]^N+[y+a/2]^N=[a/2]^N;
Color 4;
Expr [x-a/2]^N+[y+a/2]^N<[a/2]^N;
Color 5;
Expr [x+b/2]^N+[y-b/2]^N=[b/2]^N;
Color 5;
Expr [x+b/2]^N+[y-b/2]^N<[b/2]^N;
Text "<size=16>... the square on the hypotenuse:";
Color 8;
Expr T=atan([b/a]);
Color 6;
Expr function(M,s)=matrix(2,2,cos(s),-sin(s),sin(s),cos(s));
Color 2;
Expr C=vector(0,b)+function(M,-T)*vector(c/2,c/2);
Expr [dot(I,function(M,T)*[X-C])]^N+[dot(J,function(M,T)*[X-C])]^N=[c/2]^N;
Color 6;
Expr [dot(I,function(M,T)*[X-C])]^N+[dot(J,function(M,T)*[X-C])]^N<[c/2]^N;
Text "<size=16>Triangle with one vertex at the origin and draggable vertices:";
Color 7;
Expr c_3=2.275+0.03125*i;
Color 7;
Expr c_4=-0.9+2.00625*i;
Color 8;
Expr abs(c_3);
Expr abs(c_4);
Color 6;
Expr arg([c_3]);
Color 8;
Expr arg([c_4]);
Color 2;
Expr P_3=vector(Re([c_3]),Im([c_3])),P_4=vector(Re([c_4]),Im([c_4]));
Color 17;
Expr function(L,O,P_3);
Color 17;
Expr function(L,O,P_4);
Color 17;
Expr function(L,P_3,P_4);
Text "<size=16>Shade the included angle";
Expr function(A,c)=branch(if(arg([c]),arg([c])>0),if(2*pi+arg([c]),arg([c])<0));
Color 7;
Expr min([function(A,c_3),function(A,c_4)])<theta<[if(max([function(A,c_3),function(A,c_4)]),abs(function(A,c_3)-function(A,c_4))<pi)],r<R;
Color 7;
Expr max([function(A,c_3),function(A,c_4)])<[if(theta,abs(function(A,c_3)-function(A,c_4))>pi)],r<R;
Color 7;
Expr theta<[if(min([function(A,c_3),function(A,c_4)]),abs(function(A,c_3)-function(A,c_4))>pi)],r<R;
Text "<size=16>Almost, but not quite...";
Color 17;
Expr min([function(A,c_3),function(A,c_4)])<theta<max([function(A,c_3),function(A,c_4)]),r<R;
Text "<size=16>

<size=15>Author: David A. Craig <<http://web.lemoyne.edu/~craigda>";