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The two circles in the Two points, one line problem where the line through P and Q is not parallel to the given line l, can be constructed with compass and straightedge by: Draw the line m through the given points P and Q. The point G is where the lines l and m intersect; Draw circle C that has PQ as diameter. Draw one of the tangents from G to ...
This variation of the birthday problem is interesting because there is not a unique solution for the total number of people m + n. For example, the usual 50% probability value is realized for both a 32-member group of 16 men and 16 women and a 49-member group of 43 women and 6 men.
Although solutions to Apollonius' problem generally occur in pairs related by inversion, an odd number of solutions is possible in some cases, e.g., the single solution for PPP, or when one or three of the given circles are themselves solutions. (An example of the latter is given in the section on Descartes' theorem.) However, there are no ...
Interior lines [a] (as opposed to exterior lines) is a military term, derived from the generic term line of operation or line of movement. [1] The term "interior lines" is commonly used to illustrate, describe, and analyze the various possible routes (lines) of logistics, supply, recon, approach, attack, evasion, maneuver, or retreat of armed forces.
Image credits: memeformathematicians The 'Meme for Mathematicians' page has around 250k followers and has been entertaining math enthusiasts since 2020. And it's not just a Facebook page; they're ...
Bresenham's line algorithm is a line drawing algorithm that determines the points of an n-dimensional raster that should be selected in order to form a close approximation to a straight line between two points.
This application was the motivation for Paul Erdős to find his solution for the no-three-in-line problem. [13] It remained the best area lower bound known for the Heilbronn triangle problem from 1951 until 1982, when it was improved by a logarithmic factor using a construction that was not based on the no-three-in-line problem. [14]
The pancake sorting problem and the problem to obtain the diameter of the pancake graph are equivalent. [ 16 ] The pancake graph of dimension n , P n can be constructed recursively from n copies of P n−1 , by assigning a different element from the set {1, 2, …, n} as a suffix to each copy.