{"type":"video","version":"1.0","width":1920,"height":1080,"title":"Eclipse division Lemma. - Animated Video By Shuhail Nadaf - Mango Animate","description":"Eclipse division Lemma. animation video uploaded by Shuhail Nadaf. The Eclipse division lemma is a mathematical theorem that provides a way to divide an interval into smaller subintervals while maintaining certain properties. Specifically, it states that given an interval \\( [a, b] \\) and a positive integer \\( n \\), it is possible to partition the interval into \\( n \\) subintervals such that the lengths of the subintervals form a geometric progression.In other words, if we denote the lengths of the subintervals by \\( h_1, h_2, ..., h_n \\), then the Eclipse division lemma guarantees that there exist positive real numbers \\( r \\) and \\( k \\) such that \\( h_i = k \\cdot r^{i-1} \\) for \\( i = 1, 2, ..., n \\), where \\( r \\) is the common ratio of the geometric progression and \\( k \\) is a constant.This lemma has various applications in mathematical analysis, particularly in numerical methods such as numerical integration and finite difference methods. It provides a systematic way to discretize continuous intervals into smaller intervals with controlled spacing, which is useful in approximating functions or solving differential equations numerically. Make your animation and host online for free!","url":"https:\/\/mangoanimate.com\/w\/wr0epcqt0ehcqtw\/eclipse-division-lemma\/wk5epbryzfnbsto\/","author_name":"Shuhail Nadaf","author_url":"https:\/\/mangoanimate.com\/homepage\/1ef11965-e1bd-6482-9b6a-f23c915625cf","provider_name":"Mango Animate","provider_url":"https:\/\/mangoanimate.com","thumbnail_url":"https:\/\/online.mangoanimate.com\/ai\/w\/124712370894132096\/1\/thumb.jpg","thumbnail_width":1920,"thumbnail_height":1080,"html":"