On Application of Lagrange Method of Undetermined multiplier In optimization of Triangles.

Olademo, J. O. A., Adenegan, K. E. and Famuagun, K. S.

 

Adeyemi College of Education, Ondo

Email johnsonolademo@gmail.com

Abstract: Generally, Mathematics is the study of patterns. Every day, everywhere, we are surrounded by mathematical pattern of different shapes. Common among them are tiles, ceilings, carpets, etc. This paper studied the relationship between a circle and its circumscribed triangle, formulation of model for the area of such triangle, and applied lagrange method of undetermined multiplier to obtain the shape of the triangle when the area is as least as possible. Extension of this pattern could generate chain of patterns that are beautiful to the extent of being useful in designing ceiling, tiles and other building patterns. When this pattern is extended to two or more of this figure, some mathematical shapes are found such circles, triangles, hexagons, kites, rhombus, etc.
Keywords: Calculus of Variation, Maxima, Minima, Multiplier.