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.

#CoordinateGeometry #Logic #Mechanics #LogicThinking

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
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Comments

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 - 6 years, 12 months ago

@michael Thanks

Sanjeet Raria - 6 years, 12 months ago

Straight line X+y =1

Sayeeda Syed - 6 years, 12 months ago

Nope. Rethink

Sanjeet Raria - 6 years, 12 months ago

A circle.

A Brilliant Member - 6 years, 12 months ago

How? Can you prove that logically?

Sanjeet Raria - 6 years, 12 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$