A hexagon is a six-sided polygon with all internal angles equaling 120 degrees. When constructing a hexagonal shape out of wood, it’s important to cut the wood at precise 60 degree angles so that the pieces fit together properly to form the hexagon. Cutting wood at the wrong angles will result in a misshapen hexagon that does not have equal sides and angles.
In this article, we will explore the mathematics behind hexagons and discuss the proper 60 degree angle required for cutting wood to make a hexagonal shape. We will also provide tips and techniques for accurately cutting 60 degree angles for your woodworking projects.
The Mathematics of Hexagons
A regular hexagon has six equal sides and six equal internal angles of 120 degrees each. The exterior angles of a hexagon each measure 180 degrees. Since a hexagon has six sides, the sum of the interior angles is 720 degrees (6 x 120 degrees).
How do we arrive at the 120 degree interior angles of a hexagon? All regular polygons follow a formula relating the number of sides to the measure of each internal angle:
(n – 2) x 180 degrees
Where n is the number of sides.
For a hexagon with 6 sides:
(6 – 2) x 180 degrees = 4 x 180 degrees = 720 degrees
720 degrees / 6 sides = 120 degrees
So the interior angles of a regular hexagon always measure 120 degrees, no matter the size of the hexagon. This consistent internal angle is what allows hexagonal shapes to tile perfectly and gives them unique structural properties.
Cutting 60 Degree Angles for Hexagons
Now that we know the interior angle of a hexagon is 120 degrees, how does this help us determine the angle to cut wood to construct a hexagonal shape?
The key is that a hexagon is made up of equilateral triangles – triangles with all three sides equal. To form an equilateral triangle, you need to cut 60 degree angles. Why 60 degrees? Because:
– There are 180 degrees in a triangle
– An equilateral triangle has three equal angles
– 180 degrees divided by 3 angles = 60 degrees
So if we cut our wood at precise 60 degree angles, these angles will fit together to form the 120 degree angles needed to create a hexagonal shape.
For example, if we cut six pieces of wood all with 60 degree angle ends, we can fit them together in a hexagonal formation where each joint forms a 120 degree angle inside the hexagon:
| Piece 1: 60 degrees | Piece 2: 60 degrees |
| Piece 3: 60 degrees | Piece 4: 60 degrees |
| Piece 5: 60 degrees | Piece 6: 60 degrees |
So in summary, to create 120 degree interior angles for a hexagon, you need to cut the wood at 60 degree angles.
Cutting Precise 60 Degree Angles
Accuracy is key when cutting 60 degree angles for hexagonal projects. Even being a few degrees off can prevent the pieces from fitting together properly. Here are some tips for precisely cutting 60 degree miter angles:
– Use a miter saw calibrated to 60 degrees. Carefully line up the 60 degree notch on the miter scale with the blade. Always double check this alignment before cutting.
– For hand-held circular saws, use a speed square to mark a 60 degree cutting line on your wood. Clamp the speed square securely as a guide. Cut slowly and carefully along the edge of the square.
– Cut test pieces to dial in your saw setup before cutting your final wood pieces. Check the angles with a triangle or protractor to confirm they are 60 degrees.
– Make sure your wood is held tightly and unable to move during the cut. Any shift will throw off the accuracy of your 60 degree angle. Use vises, clamps, and other workholding tools.
– Cut slightly outside your line, leaving extra material. Then use a file, sandpaper block, or belt sander to finesse the angle to exactly 60 degrees.
– Mark all your cuts on the same face/side of the wood to improve consistency. Flipping wood can introduce slight variations.
– When possible, use a miter gauge, sled, or other jigs to ensure the wood travels through the saw blade at the proper 60 degree path every time.
Taking the time to carefully cut accurate 60 degree angles will result in hexagonal wood projects that fit together perfectly at crisp 120 degree vertices. The precision and symmetry of your hexagons relies wholly on those key 60 degree cuts.
Example Projects Using 60 Degree Angles
Here are some example hexagonal projects that require cutting wood at 60 degree angles:
– Hexagonal picnic table – The tabletop and benches are assembled from wood boards mitered at 60 degrees. When fit together, they create the hexagonal shape.
– Hexagonal shelf – Shelves made from individual wood boards with 60 degree angled ends arranged in a hexagon pattern.
– Hexagon planter box – Similar to the shelf, but larger in scale. 60 degree angle cuts allow the wood boards to form a hexagonal-shaped planter.
– Hexagonal gazebo – The roof structure of a gazebo is often a hexagonal shape. Each roof section meets at a joint made up of 60 degree angle cuts.
– Hexagon raised garden beds – Creating hexagonal gardening boxes, cold frames, or compost bins using wood cut to 60 degree angles.
– Hexagonal picture frames or mirrors – Framing hexagon-shaped art, photos, or mirrors using mitered trim pieces cut to 60 degrees.
– Honeycomb shelving – Honeycomb-patterned shelves made from half hexagons. The 60 degree tips fit together in offset rows mimicking a beehive.
– Hexagon wedding backdrop – Creating a statement focal wall as a wedding backdrop using many small hexagonal wood pieces all cut at 60 degree angles.
As you can see, cutting wood at 60 degrees allows for endless creative applications for constructing hexagonal objects both small and large. The key is achieving those precise 60 degree cuts on your miter or circular saw.
Conclusion
In summary, constructing a hexagonal shape from wood requires cutting the wood at 60 degree angles. This is because the interior angle of a hexagon is 120 degrees, and joining 60 degree angles together forms the 120 degree angles needed. Cutting accurate 60 degree miters for your woodworking project takes precise setup and measurement of your saws, attention to detail, and testing your cuts on scrap material. But the effort pays off when you bring together the final pieces and have a perfect hexagonal shape with all angles and sides equal. So be diligent in cutting those 60 degree wood pieces, and your hexagonal creation will come together seamlessly.
References
[1] Weisstein, Eric W. “Hexagon.” From MathWorld–A Wolfram Web Resource. https://mathworld.wolfram.com/Hexagon.html
[2] “Hexagon.” Wikipedia. https://en.wikipedia.org/wiki/Hexagon
[3] “How to Cut a 60 Degree Angle.” Family Handyman. https://www.familyhandyman.com/project/how-to-cut-a-60-degree-angle/
[4] “Cutting Hexagons.” Sawdust Girl. https://sawdustgirl.com/cutting-hexagons/
[5] “How to Cut a 60° Angle Using a Miter Saw.” Home Guides | SF Gate. https://homeguides.sfgate.com/cut-60-angle-using-miter-saw-98546.html