Octagon is a geometric shape characterized by its eight sides and eight angles, all of which are equal in measure. The term octagon is derived from the Greek words októ, meaning eight, and gōnía, meaning angle. In Euclidean geometry, an octagon is classified as an 8-gon or octahedron, belonging to the family of polygons. Regular octagons, where all sides and angles are congruent, have been studied and utilized in various fields, including architecture, design, and art, throughout history. The octagonal shape has been employed in the construction of buildings, such as the Tower of the Winds in Athens and the Castel del Monte in Italy, as well as in the creation of decorative patterns, like those found in Islamic art and tilework. Octagons have also been used in the design of coins, medals, and seals, often chosen for their symmetry and visual appeal. In modern times, octagons continue to be utilized in various design applications, ranging from furniture and interior design elements to urban planning and transportation infrastructure, such as the iconic octagonal stop sign.
octagonal, eight-sided, polygon, symmetry, architecture, design
An octagon is a polygon with eight sides and eight angles. It is a two-dimensional shape that is commonly used in architecture, design, and mathematics. Octagons are often used in building construction as the shape provides stability and strength. The octagon is known for its symmetry and regularity, making it a popular shape in art and design. Octagons have a variety of uses in different fields. In architecture, octagonal buildings are often used for religious or ceremonial purposes. One of the most famous examples is the octagonal dome of the Florence Cathedral in Italy. In design, octagons are commonly used in tile patterns, as well as in jewelry and other decorative objects. In mathematics, octagons are used to teach geometry and trigonometry. The angles of an octagon are all equal, measuring 135 degrees each. The sum of all the angles in an octagon is 1080 degrees. Octagons have eight lines of symmetry, meaning that they can be divided into eight equal parts. This makes them ideal for creating repeating patterns. One interesting fact about octagons is that they can be used to create a regular tessellation, which is a repeating pattern of shapes that completely covers a plane without any gaps or overlaps. To create a regular tessellation with octagons, the angles of the octagon must be 135 degrees, and the angles of the surrounding shapes must add up to 360 degrees.
polygon, symmetry, regularity, tessellation, architecture
An octagon is a two-dimensional geometric figure typically composed of eight straight line segments. It is a closed figure, meaning that it has no endpoints. The sides of an octagon are all equal in length, so it is considered a regular polygon. The angles of an octagon are 135°. The sum of all the angles of an octagon is 1080°. An octagon can be inscribed in a circle, meaning that all eight vertices lie on the circumference of the circle. It has eight lines of symmetry and its area is twice the area of a triangle inscribed in the same circle.
Polygon, Regular Polygon, Lines of Symmetry, Angle Measurement, Area Calculation
CITATION : "Kenneth Harris. 'Octagon.' Design+Encyclopedia. https://design-encyclopedia.com/?E=246011 (Accessed on April 30, 2025)"
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