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The Story of Maths is a four-part British television series outlining aspects of the history of mathematics. It was a co-production between the Open University and the BBC and aired in October 2008 on BBC Four. The material was written and presented by University of Oxford professor Marcus du Sautoy. [1]
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.
The set of all reflections in lines through the origin and rotations about the origin, together with the operation of composition of reflections and rotations, forms a group. The group has an identity: Rot(0). Every rotation Rot(φ) has an inverse Rot(−φ). Every reflection Ref(θ) is its own inverse. Composition has closure and is ...
Similar figures. In Euclidean geometry, two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other.More precisely, one can be obtained from the other by uniformly scaling (enlarging or reducing), possibly with additional translation, rotation and reflection.
When K is the field of real numbers, a pseudoreflection has matrix form diag(1, ... , 1, -1). A pseudoreflection with such matrix form is called a real reflection.If the space on which this transformation acts admits a symmetric bilinear form so that orthogonality of vectors can be defined, then the transformation is a true reflection.
A glide reflection line parallel to a true reflection line already implies this situation. This corresponds to wallpaper group cm. The translational symmetry is given by oblique translation vectors from one point on a true reflection line to two points on the next, supporting a rhombus with the true reflection line as one of the diagonals. With ...
GCSE Bitesize was launched in January 1998, covering seven subjects. For each subject, a one- or two-hour long TV programme would be broadcast overnight in the BBC Learning Zone block, and supporting material was available in books and on the BBC website. At the time, only around 9% of UK households had access to the internet at home.
In mathematics, the Schwarz reflection principle is a way to extend the domain of definition of a complex analytic function, i.e., it is a form of analytic continuation.It states that if an analytic function is defined on the upper half-plane, and has well-defined (non-singular) real values on the real axis, then it can be extended to the conjugate function on the lower half-plane.