## Objections to this Snowflake Theory

Readers are welcome to raise objections, and then submit all the rest of their arithmetic in their comments. We suggest starting with the following concerns.

- This number is too high. No snowflake could have a grain of ice surrounded by air; connections are needed; and the apparent self-symmetry reduces the possibilities.
- This number is too low. We totally ignore how thick the snowflake is, which may vary from point to point on the triangle.
- We should examine the snowflake under a microscope, so the resolution is 50 times higher, with 2500 times more bits. This makes it harder to find identical snowflakes.
- We should consider all the snowflakes that ever fell on Earth; so let’s multiply the annual snowfall by 4,000,000,000 years.
- We need to sample different types of snowflakes, and use different mathematical models for each. Duplicates might be more likely given an abundance of “plate” snowflakes.

This article suggests a mathematical framework for approaching this question, rather than claiming to have the definitive solution.

To conclude: at least two visually identical snowflakes have been found, but they had a very simple shape. It is highly improbable that there are two identical snowflakes among the complex dendrites.

## References

*Introduction to the Microscope*. Orange Coast College. (2012). PDF accessed December 24, 2012.

Choi, Charles Q. *Two snowflakes may actually be alike*. (2007). Accessed December 24, 2012.

Thangham, Chris V. *No two snowflakes are alike*. Digital Journal. (2008). Accessed December 24, 2012.

Weisstein, Eric W. *Birthday Problem*. MathWorld-A Wolfram Web Resource. Accessed December 24, 2012.

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