Did You Know? A Polygon Can Have 11 Sides
Polygons are geometrical shapes with straight sides and angles. They are two-dimensional figures and are widely used in various fields, including mathematics, architecture, and art. Polygons can have different numbers of sides, and today we'll explore a fascinating fact - a polygon can have 11 sides!
What is an 11-sided Polygon called?
An 11-sided polygon is called an undecagon or hendecagon. The prefix "hendeca" means 11 in Greek, and the prefix "unde" means the same in Latin. Both words are commonly used to describe the 11-sided polygon.
Properties of an Undecagon
Like any other polygon, an undecagon has its unique properties. Here are a few:
- An undecagon has 11 straight sides and 11 angles.
- The sum of all the interior angles of an undecagon is 1470 degrees.
- An undecagon can be divided into 9 triangles, each having an interior angle of 180 degrees.
- The formula to calculate the area of an undecagon is A = (11/4) * s^2 * cot(π/11), where s is the length of the side.
Real-Life Examples of Undecagons
Undecagons are not commonly found in everyday life, but they do exist in various forms. Here are a few examples:
- The United Nations Building in New York City has an undecagon-shaped conference room.
- The outer ring of the Olympic Flag has 11 undecagon-shaped rings that represent each Olympiad from 1912 to 1972.
- The $1, $2, $5, $10, $20, $50, and $100 bills of the Canadian Dollar have an undecagon-shaped image of the Queen's head.
Undecagons in Mathematics
Undecagons have an interesting connection to prime numbers. A regular undecagon has 11 sides, and 11 is a prime number. In fact, the number of sides of any regular polygon that can be constructed using only a straightedge and a compass is limited to prime numbers. This is known as Gauss's Theorem.
Fun Facts about Undecagons
Here are a few fun facts about undecagons:
- An undecagon is the smallest polygon that cannot be constructed using only a straightedge and a compass.
- The word "hendecagon" was first used by Johannes Kepler in his work "Harmonices Mundi" in 1619.
- The regular undecagon is a part of the Archimedean solid called the truncated tetrahedron.
Conclusion
Undecagons are fascinating geometrical shapes with 11 straight sides and angles. They have unique properties and are not commonly found in everyday life. However, they have a significant connection to prime numbers and are an essential part of mathematics. So next time you come across an undecagon, you know what to call it!
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