Anzeige
Erschienen in:
2014 | OriginalPaper | Buchkapitel
Finding the Symbolic Solution of a Geometric Problem Through Numerical Computations
verfasst von : Liangyu Chen, Tuo Leng, Liyong Shen, Min Wu, Zhengfeng Yang, Zhenbing Zeng
Erschienen in: Computer Mathematics
Verlag: Springer Berlin Heidelberg
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
Abstract
In this paper we prove that if \(L\) is the maximal perimeter of triangles inscribed in an ellipse with \(a,b\) as semi-axes, then by accomplishing the following tasks through numeric computations: (1) compute the determinants of matrices of order from \(25\) to \(34\) whose entries are polynomials of degree up to \(44\), (2) construct a series of rectangles \(R_1,R_2,\ldots ,R_N\) so that if \(L,a,b\) satisfies the relation \(f(L,a,b)=0\) then and, (3) present a mechanical procedure to decide the validity of where \(R\) is a closed rectangle region and \(C(F)\) is an algebraic curve defined by \(F(x,y)=0\).
$$ (a^2-b^2)^2\cdot L^4-8(2a^2-b^2)(2b^2-a^2)(a^2+b^2)\cdot L^2-432a^4b^4=0 $$
$$ C_1:=\{(b,L)|f(L,1,b)=0, 0\le b\le 1\}\subset R_1\cup R_2\cup \cdots \cup R_N, $$
$$ R\cap C(F)=\emptyset , $$