Mathematical Modeling Questions for Secondary School Curriculum | Page 16

Math and Art

Author : Mihaela Git
Consider an equilateral triangular surface ABC with unit area . Construct A 1 , B 1
, C 1 the midpoints of the sides of the triangle ABC , as in the drawing above . a ) Prove that the 4 triangles formed are congruent . b ) Repeat the construction for the triangle CA 1
B 1 , CA 2
B 2 and so on .
Calculate the sum of the areas of the blue triangular surfaces after 5 steps . Calculate the sum of the areas of the blue triangular surfaces after n steps . Approximate this value for a very large number n .
See also the construction in GeoGebra : https :// www . geogebra . org / classic / zfpvrd44
The source of inspiration for the problem : https :// geometrydaily . tumblr . com / post / 22586826330 / 128-ad-astra-a-new-minimal-geometric
Related Topics and Concepts : Congruent triangles , Areas , Geometric progression Real Life Context : Art