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The Math Images Project is a wiki collaboration between Swarthmore College, the Math Forum at Drexel University, and the National Science Digital Library. The project aims to introduce the public to mathematics through beautiful and intriguing images found throughout the fields of math. The Math Images Project runs on MediaWiki software, as ...
Froebel star: November 2013: A line integral is an integral where the function to be integrated, be it a scalar field as here or a vector field, is evaluated along a curve.The value of the line integral is the sum of values of the field at all points on the curve, weighted by some scalar function on the curve (commonly arc length or, for a vector field, the scalar product of the vector field ...
The image of the function is the set of all output values it may produce, that is, the image of . The preimage of f {\displaystyle f} , that is, the preimage of Y {\displaystyle Y} under f {\displaystyle f} , always equals X {\displaystyle X} (the domain of f {\displaystyle f} ); therefore, the former notion is rarely used.
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Line art is a rather non-specific term sometimes used for any image that consists of distinct straight and curved lines placed against a (usually plain) background, without gradations in shade (darkness) or hue to represent two-dimensional or three-dimensional objects. Line art is usually monochromatic, although lines may be of different colors.
For calculating the image containing only the background, a series of preceding images are averaged. For calculating the background image at the instant t: (,,) = = (,,) where N is the number of preceding images taken for averaging. This averaging refers to averaging corresponding pixels in the given images.
In a general Math Circle lesson, students use pattern finding, observation, and exploration to make their own mathematical discoveries. For example, mathematical beauty arises in a Math Circle activity on symmetry designed for 2nd and 3rd graders, where students create their own snowflakes by folding a square piece of paper and cutting out ...
paste a given image at a specified offset onto the canvas; write a string of characters with a specified font, at a given position and angle; paint a simple geometric shape, such as a triangle defined by three corners, or a circle with given center and radius; draw a line segment, arc, or simple curve with a virtual pen of given width.
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