What is the length of the path they have traveled at the moment they reach each other?

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Consider four (dimensionless) flies, two males and two females. They are situated at the corners of one square meter. Every fly tries to reach the male/female fly in front of her/him. Their initial situation is visualized in the picture. Since the flies are flying towards another, they will meet each other at a certain time in the center of the square.

posted Jun 26, 2014

Because all flies constantly fly perpendicular to another fly, they all travel the shortest distance to each other, which is 1 meter (all flies make a kind of spiral flight to the center of the square, and during this flight, the flies constantly form a square until they meet in the center).

Conclusion: The flies all travel 1 meter.

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