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Answer by Joshua Wang for Geometric Pattern in Triangle Construction with...
Let the side lengths of the original triangle be $BC=a,AC=b,AB=c$, and let its area be $K$. Let the center of the square from side $BC$ be $S_{a}$, etc. and let $S_{b}S_{c}=x,...
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Geometric Pattern in Triangle Construction with Squares
I've been exploring some constructions in geometry recently and have been looking at the following algorithm:Start with an arbitrary triangle (red)Construct 3 squares from each of the sides of the...
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Answer by John Hughes for Geometric Pattern in Triangle Construction with...
Here's a slightly different approach starting from Jean-Marie's excellent proof, but avoiding the "it is well known that..." step. It's about 80% copied from that answer, so Jean-Marie deserves all the...
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Answer by Jean Marie for Geometric Pattern in Triangle Construction with Squares
Geometry with complex numbers (+ linear algebra) provides a rather interesting proof that I am going to develope.I will use the same notations for the points of the plane and for their associated...
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Answer by Cesareo for Geometric Pattern in Triangle Construction with Squares
Follows a MATHEMATICA script which generates a sequence of triangles approaching an equilateral structure.$$\Delta_k = \Phi\left(\Delta_{k-1}\right)$$Here $\Phi$ is defined as the module gTri[tri, f,...
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