![]() Hexagons aren’t limited to earth!!! Scientists discovered that Saturn’s north pole has a warming, high altitude vortex in the shape of a hexagon! They’re also quite pretty to look at! SaturnĬredit: and The snowflake is such an intricate design in nature, thanks in part, to its hexagonal structure. It’s a bit more complicated than that but that’s the gist of it. When temperatures drop below freezing, water molecules arrange themselves in a way that has hexagonal symmetry. The process of forming a snowflake is called crystallization. Keeping in mind that the chemical compound for water is H 2O, the water molecules in the ice structures allow the one oxygen and two hydrogen atoms to bond together in a hexagonal form. Each snowflake is a crystal that is subject to specific weather conditions which account for the variations among different snowflakes. That’s fascinating! At some point in your life, to verify this, you may have even observed snowflakes up close to compare them. If we align three pentagons together on a floor, we’ll get a gap:Īnother example from nature is the snowflake! Perhaps you created paper snowflakes at some point in school if so, you probably remember that each snowflake contains six points and is made up of a hexagonal structure – notice the hexagon at the center of the snowflake above.Įvery snowflake is unique – no two are the same. The measure of each interior angle of a regular pentagon is: Let’s try the same thing, this time with n = 5. Can we tile a floor by using regular pentagons? Since each interior angle of a regular hexagon is 120°, if we align three hexagons, the interior angles add to 360 which won’t leave gaps between the tiles. The measure of each interior angle of a regular polygon is:įor a regular hexagon, n = 6 ,so we have: What is the measure of each of the interior angles of a regular hexagon? Let’s look at the tiling problem a bit closer. If the polygon is regular, then each interior ![]() The sum of the interior angles of a polygon It’s helpful to remember how to calculate the measure of each angle in a regular polygon. In order to tile a floor with a regular polygon, the interior angles must add to 360°. In fact, regular hexagons can be used to tile a floor. Have you ever looked at different shapes and patterns of floor tiles? While many floors are tiled with squares, you likely have come across floors that are tiled with hexagons. You can tile a plane (or a floor!) with regular hexagons. While Varro never proved his theory, in 1999 a mathematician from the University of Michigan named Thomas Hale proved Varro’s conjecture! (Source: ) Tiling floors Total perimeter of any subdivision of the plane into The Honeycomb ConjectureĪ regular hexagonal grid or honeycomb has the least ![]() His theory is known as The Honeycomb Conjecture. ![]() The hexagons fit tightly together, with no gaps between them and can store the most amount of honey. The hexagon allows the bees to make the most efficient use of space. Why not use squares or triangles to create the honeycomb? Good question! This is a question people have pondered for a long time.Īs far back as 36 BC, a Roman scholar named Tarrentius Varro questioned this and theorized that the hexagonal shape of the honeycomb allowed the honeybees to maximize the amount of honey they can store in each hexagon while minimizing the amount of wax they need to create the honeycomb. If you imagine that they used circles, there would be gaps between the circles, wasting the wax they produce. Why do honeybees make their honeycombs in this shape? Well, the answer is relatively simple. Honeycomb cells have the shape of hexagons.
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