Golden Triangle: An Isosceles TriangleDate: 01/23/2001 at 17:09:22 From: Grayson Connors Subject: The Golden Triangle I have talked to my Geometry teacher about whether there is such a thing as a Golden Triangle, and he says no, but my Algebra Honors teacher tells me that there is, and it is a right triangle with the ratio 3:4:5, and any of the multiples, like if you multiply by 2, 6:8:10. I want to know if it exists. I am positive it was in my textbook from Algebra 1. Please help solve the issue. Date: 01/24/2001 at 00:37:12 From: Doctor Schwa Subject: Re: The Golden Triangle Hi Grayson, What I've heard called a golden triangle is more like a golden rectangle. A golden rectangle has the property that if you cut off a square from it, the remaining rectangle is the same shape as the original rectangle, only smaller. Its sides are in the ratio 1 : (1 + sqrt(5))/2, or about 1 : 1.618033. For a picture of these rectangles, see the Dr. Math FAQ: Golden Ratio, Fibonacci Sequence http://mathforum.org/dr.math/faq/faq.golden.ratio.html The golden triangle is an isosceles triangle. It has the property that, if you bisect one of the base angles, one of the triangles you cut off is similar to the original triangle. If its base is 1 unit long, the two equal sides are each (1 + sqrt(5))/2 units long, the same ratio as the golden rectangle. Golden triangles can be found in pentagons. In a regular pentagon ABCDE, the triangle ACD is a golden triangle: - Doctor Schwa, The Math Forum http://mathforum.org/dr.math/ |
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