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It forms a slightly brighter elliptical spot of 8–10° across directly opposite the Sun within the dimmer band of zodiacal light and zodiac constellation. [2] The intensity of the gegenschein is relatively enhanced because each dust particle is seen at full phase , [ 3 ] having a difficult to measure apparent magnitude of +5 to +6, with a ...
An early occurrence of proof by contradiction can be found in Euclid's Elements, Book 1, Proposition 6: [7] If in a triangle two angles equal one another, then the sides opposite the equal angles also equal one another. The proof proceeds by assuming that the opposite sides are not equal, and derives a contradiction.
A Morse code light is light in which appearances of light of two clearly different durations (dots and dashes) are grouped to represent a character or characters in the Morse Code. For example, "Mo(A)" is a light in which in each period light is shown for a short period (dot) followed by a long period (dash), the Morse Code for "A".
The OBJ file format is a simple data-format that represents 3D geometry alone – namely, the position of each vertex, the UV position of each texture coordinate vertex, vertex normals, and the faces that make each polygon defined as a list of vertices, and texture vertices. Vertices are stored in a counter-clockwise order by default, making ...
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The Archimedean solids have a single vertex configuration and highly symmetric properties. A vertex configuration indicates which regular polygons meet at each vertex. For instance, the configuration indicates a polyhedron in which each vertex is met by alternating two triangles and two pentagons.
As an informal thought experiment, consider cutting an infinite sheet of paper along finitely many lines. These cuts would partition the paper into convex polygons. Their edges would be one-dimensional line segments or rays, with vertices at the points where two cut lines cross. This can be formalized mathematically by classifying the points of ...
Kawasaki's theorem or Kawasaki-Justin theorem: at any vertex, the sum of all the odd angles (see image) adds up to 180 degrees, as do the even. A sheet can never penetrate a fold. Paper exhibits zero Gaussian curvature at all points on its surface, and only folds naturally along lines of zero curvature. Curved surfaces that can't be flattened ...