Tangled Triangles

Math Problem
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Two students are discussing how to find the biggest value of the area: perimeter ratio for triangles. One of them suggests that this can be done with measurements of 40, 60 and 80- but forgets to say what units were used, and whether they were angles or sides.


The ancient Greeks were aware of this and often used this information in their day-to-day life. Perhaps it all started with the 'Dido's fix' in eighth century BC. However, in most of the cases, these observations were stated with any formal proof backing them. Whether it is a bubble taking a spherical shape to minimize surface energy or the hexagonal shape of honeycomb to maximize honey storage, it has only fuelled the mathematician's interest in questions of Maxima and Minima. Starting in the seventeenth century, the general theory of extreme values Proof: To find out the triangle which gives the biggest value for the area: perimeter ratio, we can either try to minimize the perimeter keeping the area consta ...
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