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Each curve in this example is a locus defined as the conchoid of the point P and the line l.In this example, P is 8 cm from l. In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.
The CSE broadly covered GCSE grades C–G or 4–1 and the O-Level covered grades A*–C or 9–4, but the two were independent qualifications, with different grading systems. The separate qualifications were criticised for disadvantaging the bottom 42% of O-Level entrants, who failed to receive a qualification, and the highest-achieving CSE ...
where k s = 1/r s and r s are the curvature and radius of the solution circle, respectively, and similarly for the curvatures k 1, k 2 and k 3 and radii r 1, r 2 and r 3 of the three given circles. For every set of four mutually tangent circles, there is a second set of four mutually tangent circles that are tangent at the same six points.
The real part of every nontrivial zero of the Riemann zeta function is 1/2. The Riemann hypothesis is that all nontrivial zeros of the analytical continuation of the Riemann zeta function have a real part of 1 / 2 . A proof or disproof of this would have far-reaching implications in number theory, especially for the distribution of prime ...
In the same year, the puzzle also appeared in A. Cyril Pearson's puzzle book. It was there named a charming puzzle and involved nine dots. [5] [2] Both versions of the puzzle thereafter appeared in newspapers. From at least 1908, Loyd's egg-version ran as advertising for Elgin Creamery Co in Washington, DC., renamed to The Elgin Creamery Egg ...
Landau's problems [2] 4: 4: Edmund Landau: 1912 Taniyama's problems [3] 36 – Yutaka Taniyama: 1955 Thurston's 24 questions [4] [5] 24 – William Thurston: 1982 Smale's problems: 18: 14: Stephen Smale: 1998 Millennium Prize Problems: 7: 6 [6] Clay Mathematics Institute: 2000 Simon problems: 15 < 12 [7] [8] Barry Simon: 2000 Unsolved Problems ...
[1] Then, in August, 82% of 'A level' grades were computed using an algorithm devised by Ofqual. More than 4.6 million GCSEs in England – about 97% of the total – were assigned solely by the algorithm. Teacher rankings were taken into consideration, but not the teacher-assessed grades submitted by schools and colleges. [2]
Pólya mentions that there are many reasonable ways to solve problems. [3] The skill at choosing an appropriate strategy is best learned by solving many problems. You will find choosing a strategy increasingly easy. A partial list of strategies is included: Guess and check [9] Make an orderly list [10] Eliminate possibilities [11] Use symmetry [12]