Third solution -- Equilateral triangle -- Area ratio
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Uploaded by rehcaethtam on Nov 12, 2008
Without using trigonometry, I've solved a geometry problem concerning equilateral triangle. The problem is to determine the ratio of two areas, the equilateral and the quadrilateral embedded. I found this Mathematics problem very interesting and insightful, but not a so easy one. For the first 2 weeks, I have spent many hours studying the problem and at last found two solutions, as seen in part 4 and 5 of this series. However, my great interest in the problem did not fade out. It seems that there is so much hidden treasures waiting people to dig up. On the 17th day,while I was riding a bus, an idea of direct calculation suddenly came to me. Therefore, I uploaded this solution as supplementary information to the problem. Besides, I want to share the happiness and sense of achievement with every body else.
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