Derivation of Golden Ratio by a right trangle 

						var board = JXG.JSXGraph.initBoard('box1', {
boundingbox: [-10, 10, 10, -10],showNavigation:false, showcopyright: false, axis: false,
});

var p1 = board.create('point', [-7, -1.0],{face:'',fixed:true});
var p2 = board.create('point', [7, -1.0],{face:'',fixed:true});
var p3 = board.create('point', [-7, 6.0],{face:'',fixed:true});
var l1 = board.create('segment', [p1, p2]);
var l2 = board.create('segment', [p2, p3]);
var l3 = board.create('segment', [p3, p1]);
var bi1 = board.create('bisector', [p1, p3, p2],{visible:false});
var i1 = board.create('intersection', [l1, bi1],{face:''});
var l4 = board.create('segment', [p1, i1],{visible:false});
var l5 = board.create('segment', [i1, p3],);
var p4 = board.create('point', [p1.X()+2*l4.L(), p1.Y()],{face:''});

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  1. Gorden ratio is such a magical number that fascinated Math lovers for centuries. Not only is it an important math number, but also commonly found in nature, such as flower petals, pine cones, spiral galaxies, etc. These natural elements are perfect manifestation of the divine ratio.

    What is Golden Ratio

    In mathematics, the golden ratio is defined as the precise value of the square root expression \dfrac{\sqrt{5}+1 }{2} or decimal number 1.618033 ...

    Since \sqrt{5} is an irrational number, the golden number cannot be expressed as a ratio of integers and its decimal form is neither terminating nor recurring.

    The golden ratio is also known as golden mean, golden section, medial section, divine proportion, golden cut, and extreme and mean ratio.

    Derivation of Golden Ratio

    There are variety of geometrical shapes that could be used to derive the golden ratio. What is in common is that ultimately an equation is established, that is golden equation.

Triangle posted 1 year ago

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