Written jointly by Xuan and Venkatesh
“Every snowflake is unique, yet they are each perfect.” – Donald L. Hicks
December is the time when the weather gets colder (if you are in the Northern hemisphere) and it often reminds us to reflect on our achievements and experiences throughout the year. As Christmas and the New Year are around the corner, we hope this post inspires you to look at snowflakes through a different lens - a Mathematical and Scientific one.
You must have heard the phrase “No two snowflakes are alike”. Is there some truth to this?
Question 1: Hex is the shape of you!
“If all snowflakes are hexagonal, how are each of them unique?”
All snowflakes are hexagonal. Doesn’t that make all of them similar? The Hexagon is a 2-Dimensional shape, hence it is true to some extent that snowflakes are similar. However, if two shapes are similar doesn’t mean they are congruent. Look at the different types of hexagonal shapes! Picture 1 to 4, show snowflakes that have thin plate-like structures - just like the ones you see hanging on the Christmas tree.
Pic 1: Hexagonal shape of a snowflake (top view) — Stellar Plates
Pic 2: Hexagonal shape of a snowflake (top view) — Split Plates and Stars
Pic 3: Hexagonal shape of a snowflake (top view) — 12-sided snowflakes (2x 6-sided)
Pic 4: Hexagonal shape of a snowflake (top view) — Triangular crystals (irregular Hexagon)
The above examples of snowflakes are ‘plate-like’ i.e., more flat than tall. However, there are few rare types of snowflakes that may blow your mind. Do you believe that snowflakes do come in shapes like a prism, column, needle and even rosette?
Pic 4: Simple Prism snowflake
Pic 5: Hexagonal columns snowflake
Pic 6: Needle like snowflake
Pic 7: Bullet Rosette snowflake
Mathematicians however look at snowflakes as fractals and are interested in their formation algorithm and their calculations.
Question 2: Soft but Spiky structural features!
“If all snowflakes are made of water molecules and are hexagonal in shape, why do they have different structures?”
From the above we understand that snowflakes are hexagonal, majorly spiked hexagons (Pic1-3). If all snowflakes are made of water and are hexagonal, how can each of them have completely different structures?
The hexagonal structures develop as the water molecules settle one-by-one and freezes, thus growing the hexagons into spiked structures. This process is highly affected by the conditions around the snowflakes. In other words, as each water molecule gets added to the snowflake, the pressure, temperature, humidity and air flow around the snowflake affects the way it freezes. In addition to this, these parameters also cause some facets to grow slower or to branch out. Since no two snowflakes will experience exactly the same conditions (pressure, temperature, humidity and airflow), they will not be identical.
To give an insight of how the parameters affect, let us take the case of temperature changes. The water molecules rearrange themselves into different shapes at different temperatures as follows::
-1 degrees C : snowflakes usually look like columns
-12 to -7 degrees C: snowflakes usually look like a plate
-16 to -12 degrees C : snowflakes usually shaped like a star
(See Pics 4-6 above)
Question 3: HEY Can we eat the snow as it is made of pure water?
“If snowflakes are made of just water, would it be safe to consume?”
Nope! The snowflakes form as the water from the cloud travels down to earth. As we know, air contains pollutants and dirt. Hence, as the snowflakes form and fall down the atmosphere, the dirt also gets into it. In fact, the dirt also changes the appearance/shape of a snowflake.
Now that you are an expert on snowflakes, you will never see snow the same way again.
A question for you to ponder as you enjoy the cool weather - Do you think that the shape of snowflakes will be affected by Christmas carols? (Hint: sound waves)