Back معضلة الدائرة لغاوس Arabic Problema del círculo de Gauss Spanish Problème du cercle French בעיית המעגל של גאוס HE Gaussov problem kruga Croatian Cirkelprobleem van Gauss Dutch Problema do círculo de Gauss Portuguese Проблема круга Гаусса Russian Gaussov problem o krogu Slovenian 高斯圓問題 Chinese

Gauss circle problem

A circle of radius 5 centered at the origin has area 25π, approximately 78.54, but it contains 81 integer points, so the error in estimating its area by counting grid points is approximately 2.46. For a circle with slightly smaller radius, the area is nearly the same, but the circle contains only 69 points, producing a larger error of approximately 9.54. The Gauss circle problem concerns bounding this error more generally, as a function of the radius of the circle.

In mathematics, the Gauss circle problem is the problem of determining how many integer lattice points there are in a circle centered at the origin and with radius . This number is approximated by the area of the circle, so the real problem is to accurately bound the error term describing how the number of points differs from the area. The first progress on a solution was made by Carl Friedrich Gauss, hence its name.

Rich TVX News Network Site

Rich TVX News Network Info

© MMXXIII Rich X Search. We shall prevail. All rights reserved. Rich X Search