The Six-Cornered Snowflake
Kepler asked why snowflakes commonly have sixfold symmetry and proposed that their shape arose from the arrangement of smaller units.
THE IDEA
Kepler’s Question
In 1611, Johannes Kepler published "The Six-Cornered Snowflake" (Latin: De Nive Sexangula). He asked why snowflakes commonly show sixfold symmetry, long before the atomic structure of ice was known.
Kepler proposed that the shape arose from the packing of small, invisible units. He considered spherical units arranged closely together as a possible explanation. His question connects an observable geometric pattern with the structure of the material that produces it.
When to use it
Understanding why certain minerals form cubic or hexagonal crystals.
Explaining the geometric basis of snowflake structure in science education.
Applying the concept of symmetry to materials design (e.g., hexagonal boron nitride).
Recognizing that underlying order can explain observed patterns in nature.
FROM THEORY TO EVERYDAY LIFE
In practice
Snowflake Photography
Photographs of snow crystals show many forms with sixfold symmetry. The shared pattern can be studied alongside differences in the crystals’ detailed shapes.
Crystal Formation
Crystals such as table salt and quartz have characteristic symmetries. Comparing their shapes raises a similar question about how the arrangement of smaller units affects the visible structure.
A MOMENT TO REFLECT
Put it to work.
What might the common sixfold symmetry of snowflakes tell us about the structure of ice?
What other natural objects display regular symmetry, and what might that tell us about their structure?
How might Kepler's idea of invisible 'units' foreshadow the discovery of atoms and molecules?
Often confused with
References
- De Nive Sexangula (The Six-Cornered Snowflake) — Johannes Kepler (1611)
CONTINUE THE CONVERSATION
Source texts
- How Not to Be Wrong The Power of Mathematical Thinking (Ellenberg, Jordan)