How to Inscribe a Hexagon in any Circle

Creating a hexagon inside a circle is a fascinating geometric task. Imagine drawing a six-sided shape with all sides equal, where all six angles are the same, and it fits perfectly inside a given circle. This challenge has intrigued mathematics enthusiasts for thousands of years and is a testament to the wonder of mathematics. In this construction,Chris Tisdell shows us how to do it using a circle arc template, making this seemingly complex task more accessible.

The primary aim of this construction is to make a hexagon, a shape with six equal sides and angles. It's like fitting puzzle pieces together, but in this case, the pieces are a circle and a hexagon. It’s also about creating something visually stunning and recognising how different geometric shapes can work together beautifully.

Tisdell's method begins with the circle itself, together with its centre. Chris introduces a tool called the circle arc template and draws an arc with the centre at the same point as the original circle’s centre. Chris then moves along the circle's edge to create six equally spaced points where the arcs intersect. These points are like markers, guiding the creation of the hexagon.

Now that you have these six markers, it's time to connect them to their antipodal (or opposite) points that also contain the circle's centre. As you connect the endpoints of these lines, you'll notice the hexagon taking shape. The sides come together, forming a symmetrical figure within the circle.

To confirm that this construction indeed results in a regular hexagon, you need to check its properties. A regular hexagon has equal sides and angles. You can use a protractor to measure the angles at each corner, ensuring they're all the same. You can also compare the lengths of the sides to verify their equality.

This video demonstrates that creating a hexagon inside a circle is a classic and fun geometric challenge that showcases the inherent beauty and symmetry in mathematical concepts. Chris Tisdell's method, involving the use of a circle arc template, simplifies this classic construction, enabling anyone to appreciate the elegance of geometry and the precise relationships between different shapes. It's a testament to the enduring fascination with geometry, demonstrating how mathematics can be both a science and an art form, where precision and aesthetics come together.