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In geometry, Euler's theorem states that the distance d between the circumcenter and incenter of a triangle is given by [1] [2] = or equivalently + + =, where and denote the circumradius and inradius respectively (the radii of the circumscribed circle and inscribed circle respectively).
The history of light therapy can be traced back to ancient Egypt and India, where therapy with natural sunlight was first used to treat leucoderma. [3] In the 1850s, Florence Nightingale's advocacy of exposure to clean air and sunlight for health restoration also contributed to the initial development of light therapy for treatments. [4]
By Euler's theorem in geometry, the distance between the circumcenter O and the incenter I is ¯ = (), where r is the incircle radius and R is the circumcircle radius; hence the circumradius is at least twice the inradius (Euler's triangle inequality), with equality only in the equilateral case.
Fuss' theorem gives a relation between the inradius r, the circumradius R and the distance x between the incenter I and the circumcenter O, for any bicentric quadrilateral. The relation is [1] [11] [22] + (+) =, or equivalently
where r is the inradius and R is the circumradius of the triangle. Here the sign of the distances is taken to be negative if and only if the open line segment DX (X = F, G, H) lies completely outside the triangle. In the diagram, DF is negative and both DG and DH are positive. The theorem is named after Lazare Carnot (1753–1823).
Red light therapy for pain. Color and light therapy can also go by the name of “colorpuncture,” a complementary medical treatment that is similar to acupuncture. Instead of using a needle ...
Light from a single point of a distant object and light from a single point of a near object being brought to a focus. The accommodation reflex (or accommodation-convergence reflex) is a reflex action of the eye, in response to focusing on a near object, then looking at a distant object (and vice versa), comprising coordinated changes in vergence, lens shape (accommodation) and pupil size.
Carnot's theorem (inradius, circumradius), describing a property of the incircle and the circumcircle of a triangle; Carnot's theorem (conics), describing a relation between triangles and conic sections; Carnot's theorem (perpendiculars), describing a property of certain perpendiculars on triangle sides; In physics: