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Striving for the equation of path

There are four flies on the vertices of a square of side a. Two males and two females. Male flies are diagonally opposite to each other. At a point of time they all started flying towards their next opposite sex with a common speed. They meet at the center. What's the equation of a particular fly's path.

Note by Sanjeet Raria
3 years, 3 months ago

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Logarithmic spirals have the property of being self-similar, which would apply in this case, because at any time, the 4 flies are at the vertices of a square chasing each other as before. In other words, scaling up the spirals will leave it looking the same as before, except maybe for rotation. Michael Mendrin · 3 years, 3 months ago

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@Michael Mendrin @michael Thanks Sanjeet Raria · 3 years, 3 months ago

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A circle. Paramjit Singh · 3 years, 3 months ago

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@Paramjit Singh How? Can you prove that logically? Sanjeet Raria · 3 years, 3 months ago

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Straight line X+y =1 Sayeeda Syed · 3 years, 3 months ago

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@Sayeeda Syed Nope. Rethink Sanjeet Raria · 3 years, 3 months ago

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