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Alhazen's problem, also known as Alhazen's billiard problem, is a mathematical problem in geometrical optics first formulated by Ptolemy in 150 AD. [1] It is named for the 11th-century Arab mathematician Alhazen ( Ibn al-Haytham ) who presented a geometric solution in his Book of Optics .
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
Point Q is the reflection of point P through the line AB. In a plane (or, respectively, 3-dimensional) geometry, to find the reflection of a point drop a perpendicular from the point to the line (plane) used for reflection, and extend it the same distance on the other side. To find the reflection of a figure, reflect each point in the figure.
Roger Penrose's solution of the illumination problem using elliptical arcs (blue) and straight line segments (green), with 3 positions of the single light source (red spot). The purple crosses are the foci of the larger arcs. Lit and unlit regions are shown in yellow and grey respectively.
Calculator Applications is one of several academic events sanctioned by the University Interscholastic League (UIL) in Texas, US. It is also a competition held by the Texas Math and Science Coaches Association, using the same rules as the UIL. Calculator Applications is designed to test students' abilities to use general calculator functions.
Any combination of reflections, translations, and rotations is called an isometry. Any combination of reflections, dilations, translations, and rotations is a similarity. All of these are conformal maps, and in fact, where the space has three or more dimensions, the mappings generated by inversion are the only conformal mappings.
The morphism is called the A-reflection arrow. (Although often, for the sake of brevity, we speak about A B {\displaystyle A_{B}} only as being the A -reflection of B ). This is equivalent to saying that the embedding functor E : A ↪ B {\displaystyle E\colon \mathbf {A} \hookrightarrow \mathbf {B} } is a right adjoint.
In mathematics, a reflection formula or reflection relation for a function f is a relationship between f(a − x) and f(x). It is a special case of a functional equation . It is common in mathematical literature to use the term "functional equation" for what are specifically reflection formulae.
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