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May 23, 2024 · The reflection point groups, defined by 1 to 3 mirror planes, can also be given by their Coxeter group and related polyhedra. The [3,3] group can be doubled, written as [[3,3]], mapping the first and last mirrors onto each other, doubling the symmetry to 48, and isomorphic to the [4,3] group.
3 days ago · The point E is an arbitrary point on the parabola. The focus is F, the vertex is A (the origin), and the line FA is the axis of symmetry. The line EC is parallel to the axis of symmetry, intersects the x axis at D and intersects the directrix at C. The point B is the midpoint of the line segment FC. Deductions
May 23, 2024 · Fig. 1: Underwater plants in a fish tank, and their inverted images (top) formed by total internal reflection in the water–air surface. In physics, total internal reflection (TIR) is the phenomenon in which waves arriving at the interface (boundary) from one medium to another (e.g., from water to air) are not refracted into the second ("external") medium, but completely reflected back into ...
2 days ago · Symmetry describes when several parts of an object are identical, such that it's possible to flip, spin, and/or move the object without ultimately changing what it looks like. Symmetry is extremely powerful and beautiful problem-solving tool and it appears all over the place: in art, architecture, nature, and all fields of mathematics! The three basic kinds of 2-dimensional symmetry are ...
6 days ago · Light can behave in many ways like a wave or a packet of photons which travel in a straight line exhibiting the property of rectilinear propagation. Geometrical optics deals with the propagation of light in a straight line and phenomena such as reflection, refraction, polarization, etc. A ray of light gives the direction of propagation of light. In the absence of an obstacle, the rays advance ...
2 days ago · Burnside's lemma is a result in group theory that can help when counting objects with symmetry taken into account. It gives a formula to count objects, where two objects that are related by a symmetry (rotation or reflection, for example) are not to be counted as distinct. Burnside's lemma gives a way to count the number of orbits of a finite set acted on by a finite group. In other ...
May 9, 2024 · Aki Sasamoto (b. 1980, Kanagawa, Japan) is a New York-based artist working in performance, installation, and video to explore the questions and conditions underlying the systems and structures of everyday life. She has had solo exhibitions and performances at venues including: Arts and Letters, New York (2023); Danspace Project, New York (2020 ...
