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curved into a half circle

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半円の,半円形の

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出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2015/05/30 08:09:59」(JST)

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A semicircle of radius r.

In mathematics (and more specifically geometry), a semicircle is a one-dimensional locus of points that forms half of a circle. The full arc of a semicircle always measures 180° (equivalently, $π$ radians, or a half-turn). It has only one line of symmetry (reflection symmetry). In non-technical usage, the term "semicircle" is sometimes used to refer to a half-disk, which is a two-dimensional geometric shape that also includes the diameter segment from one end of the arc to the other as well as all the interior points.

By Thales' theorem, any triangle inscribed in a semicircle with a vertex at each of the endpoints of the semicircle and the third vertex elsewhere on the semicircle is a right triangle, with right angle at the third vertex.

All lines intersecting the semicircle perpendicularly are concurrent at the center of the circle containing the given semicircle.

Uses

A semicircle can be used to construct the arithmetic and geometric means of two lengths using straight-edge and compass. If we make a semicircle with a diameter of a+b, then the length of its radius is the arithmetic mean of a and b (since the radius is half of the diameter). The geometric mean can be found by dividing the diameter into two segments of lengths a and b, and then connecting their common endpoint to the semicircle with a segment perpendicular to the diameter. The length of the resulting segment is the geometric mean,^[1] which can be proved using the Pythagorean theorem. This can be used to accomplish quadrature of a rectangle (since a square whose sides are equal to the geometric mean of the sides of a rectangle has the same area as the rectangle), and thus of any figure for which we can construct a rectangle of equal area, such as any polygon (but not a circle).

Equation

The equation of a semicircle with midpoint on the diameter between its endpoints and which is entirely concave from below is

If it is entirely concave from above, the equation is

Arbelos

An arbelos is a region in the plane bounded by three semicircles connected at the corners, all on the same side of a straight line (the baseline) that contains their diameters.

References

^ Euclid's Elements, Book VI, Proposition 13

External links

Semicircle - Mathworld

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English Journal

A case of patulous Eustachian tube associated with dizziness induced by nasal respiration.

Kitajima N1, Sugita-Kitajima A2, Kitajima S3.
Auris, nasus, larynx.Auris Nasus Larynx.2016 Dec;43(6):702-5. doi: 10.1016/j.anl.2016.03.008. Epub 2016 Apr 16.
OBJECTIVE: To determine the relationship between Eustachian tube function and inner ear function in patulous Eustachian tube (pET).METHODS: We encountered a patient with pET accompanied by dizziness that was induced by nasal respiration. Eye movements were recorded using video-oculography, and Eusta
PMID 27089972

Temporal Lobe Retraction Provides Better Surgical Exposure of the Peri-Geniculate Ganglion for Facial Nerve Decompression via Transmastoid Approach.

Kim MW1, Ryu NG1, Lim BW1, Kim J2.
Yonsei medical journal.Yonsei Med J.2016 Nov;57(6):1482-7. doi: 10.3349/ymj.2016.57.6.1482.
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PMID 27593878

Safety of heat generated by endoscope light sources in simulated transcanal endoscopic ear surgery.

Ito T1, Kubota T2, Takagi A3, Watanabe T2, Futai K2, Furukawa T2, Kakehata S2.
Auris, nasus, larynx.Auris Nasus Larynx.2016 Oct;43(5):501-6. doi: 10.1016/j.anl.2015.12.014. Epub 2016 Jan 21.
OBJECTIVE: To determine whether heat generated by endoscope light sources during ear surgery is safe.METHODS: Transcanal endoscopic ear surgery (TEES) was simulated using 2.7-mm or 4-mm endoscopes coupled to xenon or LED light sources and a 3D model of human temporal bone. The endoscope tip was fixe
PMID 26806025

Japanese Journal

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NAID 120005323556

Menière論文と19世紀の反応:―第二編：優先権の主張と先行―

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NAID 130003374134

減衰型方向交代性上向性眼振例の検討

晝間清,渡部涼子
耳鼻咽喉科臨床 106(4), 299-303, 2013
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NAID 130003374041