Semicircle

Semicircle

A Semicircle is a geometric shape that forms half of a circle. The term is derived from the Latin semi- meaning "half" and circulus meaning "small ring". It is defined as the region of the plane bounded by a diameter and the part of the circumference cut off by the diameter.

Definition

In Geometry, a semicircle is a one-dimensional locus of points forming half a circle. The full arc of a semicircle always measures 180° (degrees). It has only one line of symmetry (reflectional), which is the diameter.

Properties

A semicircle has several distinct properties, including:

• Area: The area of a semicircle is half the area of the circle from which it is made. The formula for the area of a semicircle is 1/2πr², where r is the radius of the semicircle.
• Perimeter: The perimeter of a semicircle is half the circumference of the full circle plus the diameter. The formula for the perimeter of a semicircle is πr + 2r, where r is the radius of the semicircle.
• Diameter: The diameter of a semicircle is the same as the diameter of the full circle from which it is made. It is also the longest chord of the semicircle.

Applications

Semicircles have many applications in the real world. They are used in architecture, engineering, and various fields of mathematics such as Trigonometry and Calculus. In Physics, the principle of the semicircle is applied in the design of lenses and mirrors.

See also

• Circle
• Diameter
• Radius
• Circumference
• Arc
• Sector

References

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Semicircle

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  Semicircle curve
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  Quadrature of rectangle
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  Comparison Ford circles Farey diagram
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  Arbelos