# Math

Snowflakes have six identical arms. Using the centre of the snowflake as the point of rotation,what is the smallest positive angle through which you could rotate the snowflake so the arms line up?(The rotated snowflake would match the appearance of its original position.) Explain your answer. Hint: How far apart are the tips of the arms?

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1. You can use a hexagon instead of a snowflake.

Think of a straight line. If you stick a pin in the center, and turn it 180Ā°, it looks just as it did before turning it.

Take an equilateral triangle. Stick a pin in the center and turn it. After 120Ā°, the bottom corner is where the top corner started out, and the triangle looks unchanged.

Take a square. After turning it 90Ā°, it looks just as it did when you started.

So, for a regular polygon of n sides, if you turn it 360/nĀ°, it looks unchanged.

So, for a snowflake with 6-fold symmetry, if you stick a pin in the center and start turning it, after 360/6 = 60Ā°, it looks the way it started.

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posted by Steve

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