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Examples of the the word, polygon , in a Sentence Context

The word ( polygon ), is the 12937 most frequently used in English word vocabulary

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  1. To convex polygon ratio One method is to define a minimum district to convex, polygon ,ratio. To use this method, every proposed district is circumscribed by the
  2. As triangles, rectangles,and circles. Using these formulas, the area of any, polygon ,can be found by dividing the polygon into triangles. For shapes with curved
  3. Polygon is called an interior angle if it lies on the inside of that simple, polygon , A concave simple polygon has at least one interior angle that exceeds 180°. *:
  4. D.: #Mark the points E, F,G, H,where each line meets the adjacent line.: #The, polygon ,EACH is a face of the dual polyhedron. The size of the vertex figure was chosen
  5. With a carbon atom at the vertices of each polygon and a bond along each, polygon ,edge. The van der Waals diameter of a C60 molecule is about 1.1 nanometers (nm
  6. Are distinct from the Platonic solids, which are composed of only one type of, polygon ,meeting in identical vertices, and from the Johnson solids, whose regular
  7. Angle if it lies on the inside of that simple polygon . A concave simple, polygon ,has at least one interior angle that exceeds 180°. *: In Euclidean geometry
  8. The polygon ; or, if at the edge of the state, by the portion of the area of the, polygon ,within state boundaries. The advantages of this method are that it allows a
  9. A circle and a smaller polygon inside the circle. As the number of sides of the, polygon ,increases, it becomes a more accurate approximation of a circle. When the
  10. Computer. Because of this, video game animators tend to use low resolution, low, polygon , count renders, such that the graphics can be rendered in real time on a home
  11. Points (i.e., points with integer coordinates) such that all the, polygon ,'s vertices are grid points: i + \franc - 1,where i is the number of grid
  12. Identify all wells (point geometry) that are within one kilometer of a lake (, polygon ,geometry) that has a high level of pollution. Vector features can be made to
  13. At a small scale will be represented as linear features rather than as a, polygon , Line features can measure distance.: Two-dimensional polygon s are used for
  14. Of the district). Then, the area of the district is divided by the area of the, polygon ,; or, if at the edge of the state, by the portion of the area of the polygon
  15. Angle, the exterior angle should be considered negative. Even in a non-simple, polygon ,it may be possible to define the exterior angle, but one will have to pick an
  16. One full turn (360°). *Some authors use the name exterior angle of a simple, polygon ,to simply mean the elementary (not supplementary!) of the interior angle.
  17. Of pi. He did this by drawing a larger polygon outside a circle and a smaller, polygon ,inside the circle. As the number of sides of the polygon increases, it becomes
  18. Details of an image, as it is distinct from the commonly used points, lines,and, polygon ,area location symbols of scalable vector graphics as the basis of the vector
  19. Number problem for them, and showed that a regular heptadecagon (17-sided, polygon , ) can be constructed with straightedge and compass. In that same year, Italian
  20. Data contains attributes of the feature. For example, a forest inventory, polygon ,may also have an identifier value and information about tree species. In raster
  21. And distances. The editor Liu Hui listed pi as 3.141014 by using a 192 sided, polygon , and then calculated pi as 3.14159 using a 3072 sided polygon . This was more
  22. Contains the base. The volume of a bipyramid whose base is a regular n-sided, polygon ,with side length s and whose height is h is therefore:: V = \frachs^2 \cot\franc
  23. A tangential polygon , such as a tangential quadrilateral, is any convex, polygon ,within which a circle can be inscribed that is tangent to each side of the
  24. A circle can be inscribed that is tangent to each side of the polygon . A cyclic, polygon ,is any convex polygon about which a circle can be circumscribed, passing
  25. He employed it to approximate the value of pi. He did this by drawing a larger, polygon ,outside a circle and a smaller polygon inside the circle. As the number of
  26. Such that it goes through each of the triangle's three vertices. A tangential, polygon , such as a tangential quadrilateral, is any convex polygon within which a
  27. Is a polyhedron composed of two parallel copies of some particular n-sided, polygon , connected by an alternating band of triangles. Antiprisms are a subclass of
  28. That is tangent to each side of the polygon . A cyclic polygon is any convex, polygon ,about which a circle can be circumscribed, passing through each vertex. A
  29. Every proposed district is circumscribed by the smallest possible convex, polygon ,(similar to the concept of a convex hull, think of stretching a rubber band
  30. S formula ". Additional formulae Areas of 2-dimensional figures *a simple, polygon ,constructed on a grid of equal-distanced points (i.e., points with integer
  31. With a star polygon central figure, defined by triangular faces connecting each, polygon ,edge to these two points. For example, a pentagram mic bipyramid is an cathedral
  32. Within which a circle can be inscribed that is tangent to each side of the, polygon , A cyclic polygon is any convex polygon about which a circle can be
  33. Using a 192 sided polygon , and then calculated pi as 3.14159 using a 3072 sided, polygon , This was more accurate than Liu Hui's contemporary Wang Fan, a mathematician
  34. On the particular geometrical duality being considered. For example, every, polygon , is topologically self-dual (it has the same number of vertices as edges, and
  35. Newton could recognize that the user was attempting to draw a circle, a line,a, polygon , etc., and it would clean them up into perfect vector representations (with
  36. D4 as subgroups. Star bipyramids Self-intersecting bipyramids exist with a star, polygon ,central figure, defined by triangular faces connecting each polygon edge to
  37. Are grid points: i + \franc - 1,where i is the number of grid points inside the, polygon ,and b is the number of boundary points. This result is known as Pick's theorem
  38. Using these formulas, the area of any polygon can be found by dividing the, polygon ,into triangles. For shapes with curved boundary, calculus is usually required
  39. Explementary angles or conjugate angles. *An angle that is part of a simple, polygon ,is called an interior angle if it lies on the inside of that simple polygon . A
  40. Measures the amount of rotation one has to make at this vertex to trace out the, polygon , If the corresponding interior angle is a reflex angle, the exterior angle
  41. Or 360°,or 1 turn. In general, the measures of the interior angles of a simple, polygon ,with n sides add up to (n − 2) × π radians, or (n − 2) × 180°,or (2n − 4
  42. Measure. *: In Euclidean geometry, the sum of the exterior angles of a simple, polygon ,will be one full turn (360°). *Some authors use the name exterior angle of a
  43. Separate regions for inclusion in one district. Minimum district to convex, polygon ,ratio One method is to define a minimum district to convex polygon ratio. To
  44. Doubling the number of sides. The recurrence formula for the circumscribed, polygon ,is:: t_0 = \franc: t_ \franc\squad\math rm\squad t_ \franc: \pi \sim 6 \times 2^i
  45. Hexagons and twelve pentagons, with a carbon atom at the vertices of each, polygon ,and a bond along each polygon edge. The van der Waals diameter of a C60
  46. Of regular geometric figures. For example, the perimeter of a regular, polygon ,inscribed in a circle approaches the circumference with increasing numbers of
  47. Of what makes the map useful and important. Geometric generalizations A, polygon ,is a generalization of a 3-sided triangle, a 4-sided quadrilateral, and so on
  48. Data. A digitizer produces vector data as an operator traces points, lines,and, polygon ,boundaries from a map. Scanning a map results in raster data that could be
  49. A spotlight shining on it. Each wall, the floor and the ceiling is a simple, polygon , in this case, a rectangle. Each corner of the rectangles is defined by three
  50. The vertices and edges – form a graph. The high degree of symmetry of the, polygon ,is replicated in the properties of this graph, which is distance-transitive

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