Ceva's theorem - Revision history

A WASSERMANN at 07:15, 3 May 2021

2021-05-03T07:15:19Z

← Older revision		Revision as of 07:15, 3 May 2021
Line 1:		Line 1:
	TV(a,b,c) is the affine / simple ratio (Teilverhältnis), i.e the signed value of \|ac\| / \|ab\|.		<math>TV(a,b,c)</math> is the affine / simple ratio (Teilverhältnis), i.e the signed value of <math>\|ac\| / \|ab\|</math>.

	<jsxgraph width="500" height="500">		<jsxgraph width="500" height="500">

2021-05-03T07:14:58Z

← Older revision		Revision as of 07:14, 3 May 2021
Line 1:		Line 1:
	TV(a,b,c) is the affine /simple ratio, i.e the signed value of \|ac\| / \|ab\|.		TV(a,b,c) is the affine / simple ratio (Teilverhältnis), i.e the signed value of \|ac\| / \|ab\|.

	<jsxgraph width="500" height="500">		<jsxgraph width="500" height="500">

2021-05-03T07:14:35Z

← Older revision		Revision as of 07:14, 3 May 2021
Line 1:		Line 1:
	TV(a,b,c) is the affine ratio, i.e the signed value of \|ac\| / \|ab\|.		TV(a,b,c) is the affine /simple ratio, i.e the signed value of \|ac\| / \|ab\|.

	<jsxgraph width="500" height="500">		<jsxgraph width="500" height="500">
Line 22:		Line 22:
	var s5 = board.create('segment', [b, bs], {color: 'black'});		var s5 = board.create('segment', [b, bs], {color: 'black'});
	var s6 = board.create('segment', [c, cs], {color: 'black'});		var s6 = board.create('segment', [c, cs], {color: 'black'});


	var TV = function(p,q,t) {		var TV = function(p,q,t) {
Line 61:		Line 60:
	var s5 = board.create('segment', [b, bs], {color: 'black'});		var s5 = board.create('segment', [b, bs], {color: 'black'});
	var s6 = board.create('segment', [c, cs], {color: 'black'});		var s6 = board.create('segment', [c, cs], {color: 'black'});


	var TV = function(p,q,t) {		var TV = function(p,q,t) {
	~~return~~ p.Dist(t) / p.Dist(q);		var v = p.Dist(t) / p.Dist(q);
			if (JXG.Math.Geometry.isSameDir(p.coords, q.coords, p.coords, t.coords)) {
			return v;
			} else {
			return -v;
			}
	};		};

2021-05-03T07:13:57Z

← Older revision		Revision as of 07:13, 3 May 2021
Line 25:		Line 25:

	var TV = function(p,q,t) {		var TV = function(p,q,t) {
	~~return~~ p.Dist(t) / p.Dist(q);		var v = p.Dist(t) / p.Dist(q);
			if (JXG.Math.Geometry.isSameDir(p.coords, q.coords, p.coords, t.coords)) {
			return v;
			} else {
			return -v;
			}
	};		};

2021-05-02T21:00:34Z

← Older revision		Revision as of 21:00, 2 May 2021
Line 29:		Line 29:

	var txt = board.create('text', [-4.5, -4, function() {		var txt = board.create('text', [-4.5, -4, function() {
	return "TV(c,b~~,a'~~) * TV(a,c~~,b'~~) * TV(b,a~~,c'~~) = " + (TV(c,b~~,as~~)TV(a,c~~,bs~~)TV(b,a~~,cs~~)).toFixed(2); }]);		return "TV(a',c,b) * TV(b',a,c) * TV(c',b,a) = " + (TV(as,c,b)TV(bs,a,c)TV(cs,b,a)).toFixed(2); }]);

	</jsxgraph>		</jsxgraph>

2021-05-02T20:58:42Z

← Older revision		Revision as of 20:58, 2 May 2021
Line 29:		Line 29:

	var txt = board.create('text', [-4.5, -4, function() {		var txt = board.create('text', [-4.5, -4, function() {
	return "TV(~~a',~~c,b) * TV(~~b',~~a,c) * TV(~~c',~~b,a) = " + (TV(~~as,~~c,b)TV(~~bs,~~a,c)TV(~~cs,~~b,a)).toFixed(2); }]);		return "TV(c,b,a') * TV(a,c,b') * TV(b,a,c') = " + (TV(c,b,as)TV(a,c,bs)TV(b,a,cs)).toFixed(2); }]);

	</jsxgraph>		</jsxgraph>

2021-05-02T20:52:07Z

@@ Line 1: / Line 1: @@
-TV(a,b,c) is the affine ratio |ac| / |ab|.
+TV(a,b,c) is the affine ratio, i.e the signed value of |ac| / |ab|.
 <jsxgraph width="500" height="500">
@@ Line 5: / Line 5: @@
 JXG.Options.text.fontSize = 24;
-var board = JXG.JSXGraph.initBoard("jxgbox", {boundingbox: [-5,5,5,-5], axis:true, showCopyright:false, showNavigation:false});
+var board = JXG.JSXGraph.initBoard("jxgbox", {boundingbox: [-5,5,5,-5], axis:false, showCopyright:false, showNavigation:false});
 var a = board.create('point', [-4, 0], {name:'a'});
@@ Line 15: / Line 15: @@
 var s3 = board.create('segment', [c, b], {color: 'black'});
-var as = board.create('glider', [-4, 0, s3], {name:"a'"});
+var as = board.create('glider', [3, 0, s3], {name:"a'"});
 var bs = board.create('glider', [4, -3, s2], {name:"b'"});
 var cs = board.create('glider', [1, 4, s1], {name:"c'"});
@@ Line 36: / Line 36: @@
 <source lang="javascript">
 </source>
 [[Category:Examples]]
 [[Category:Geometry]]

2021-05-02T20:46:10Z

← Older revision		Revision as of 20:46, 2 May 2021
Line 18:		Line 18:
	var bs = board.create('glider', [4, -3, s2], {name:"b'"});		var bs = board.create('glider', [4, -3, s2], {name:"b'"});
	var cs = board.create('glider', [1, 4, s1], {name:"c'"});		var cs = board.create('glider', [1, 4, s1], {name:"c'"});

			var s4 = board.create('segment', [a, as], {color: 'black'});
			var s5 = board.create('segment', [b, bs], {color: 'black'});
			var s6 = board.create('segment', [c, cs], {color: 'black'});


	var TV = function(p,q,t) {		var TV = function(p,q,t) {

2021-05-02T20:44:57Z

← Older revision		Revision as of 20:44, 2 May 2021
Line 5:		Line 5:
	JXG.Options.text.fontSize = 24;		JXG.Options.text.fontSize = 24;

	var board = JXG.JSXGraph.initBoard("jxgbox", {boundingbox: [-5,5,5,-5], axis:~~false~~, showCopyright:false, showNavigation:false});		var board = JXG.JSXGraph.initBoard("jxgbox", {boundingbox: [-5,5,5,-5], axis:true, showCopyright:false, showNavigation:false});

	var a = board.create('point', [-4, 0], {name:'a'});		var a = board.create('point', [-4, 0], {name:'a'});
Line 14:		Line 14:
	var s2 = board.create('segment', [a, c], {color: 'black'});		var s2 = board.create('segment', [a, c], {color: 'black'});
	var s3 = board.create('segment', [c, b], {color: 'black'});		var s3 = board.create('segment', [c, b], {color: 'black'});

			var as = board.create('glider', [-4, 0, s3], {name:"a'"});
			var bs = board.create('glider', [4, -3, s2], {name:"b'"});
			var cs = board.create('glider', [1, 4, s1], {name:"c'"});

	var TV = function(p,q,t) {		var TV = function(p,q,t) {

2021-05-02T20:43:45Z

← Older revision		Revision as of 20:43, 2 May 2021
Line 10:		Line 10:
	var b = board.create('point', [4, -3], {name:'b'});		var b = board.create('point', [4, -3], {name:'b'});
	var c = board.create('point', [1, 4], {name:'c'});		var c = board.create('point', [1, 4], {name:'c'});

			var s1 = board.create('segment', [a, b], {color: 'black'});
			var s2 = board.create('segment', [a, c], {color: 'black'});
			var s3 = board.create('segment', [c, b], {color: 'black'});

	var TV = function(p,q,t) {		var TV = function(p,q,t) {