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Although the original problem asks for integer lattice points in a circle, there is no reason not to consider other shapes, for example conics; indeed Dirichlet's divisor problem is the equivalent problem where the circle is replaced by the rectangular hyperbola. [3]
A Mathnasium location in Franconia, Virginia. Mathnasium (also Mathnasium Learning Center) is an American education brand and supplemental math learning franchise consisting of over 1,000 learning centers in North America, South America, Europe, the Middle East, and Asia that provides instruction to students in pre-kindergarten through high school. [1]
Leonard Eugene Dickson (1920) [6] attributes to himself the following method for generating Pythagorean triples. To find integer solutions to + =, find positive integers r, s, and t such that = is a perfect square.
The area of an annulus is the difference in the areas of the larger circle of radius R and the smaller one of radius r: = = = (+) (). As a corollary of the chord formula, the area bounded by the circumcircle and incircle of every unit convex regular polygon is π /4
Ionic radius, r ion, is the radius of a monatomic ion in an ionic crystal structure. Although neither atoms nor ions have sharp boundaries, they are treated as if they were hard spheres with radii such that the sum of ionic radii of the cation and anion gives the distance between the ions in a crystal lattice.
The proton radius puzzle is an unanswered problem in physics relating to the size of the proton. [1] Historically the proton charge radius was measured by two independent methods, which converged to a value of about 0.877 femtometres (1 fm = 10 −15 m).
In mathematics, the Cauchy–Hadamard theorem is a result in complex analysis named after the French mathematicians Augustin Louis Cauchy and Jacques Hadamard, describing the radius of convergence of a power series.
In calculus, the method of normals was a technique invented by Descartes for finding normal and tangent lines to curves.It represented one of the earliest methods for constructing tangents to curves.